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Friday, July 28, 2023

File system

From Wikipedia, the free encyclopedia

In computing, a file system or filesystem (often abbreviated to fs) is a method and data structure that the operating system uses to control how data are stored and retrieved. Without a file system, data placed in a storage medium would be one large body of data with no way to tell where one piece of data stopped and the next began, or where any piece of data was located when it was time to retrieve it. By separating the data into pieces and giving each piece a name, the data are easily isolated and identified. Taking its name from the way a paper-based data management system is named, each group of data is called a "file". The structure and logic rules used to manage the groups of data and their names is called a "file system."

There are many kinds of file systems, each with unique structure and logic, properties of speed, flexibility, security, size and more. Some file systems have been designed to be used for specific applications. For example, the ISO 9660 and UDF file systems are designed specifically for optical discs.

File systems can be used on many types of storage devices using various media. As of 2019, hard disk drives have been key storage devices and are projected to remain so for the foreseeable future. Other kinds of media that are used include SSDs, magnetic tapes, and optical discs. In some cases, such as with tmpfs, the computer's main memory (random-access memory, RAM) is used to create a temporary file system for short-term use.

Some file systems are used on local data storage devices; others provide file access via a network protocol (for example, NFS, SMB, or 9P clients). Some file systems are "virtual", meaning that the supplied "files" (called virtual files) are computed on request (such as procfs and sysfs) or are merely a mapping into a different file system used as a backing store. The file system manages access to both the content of files and the metadata about those files. It is responsible for arranging storage space; reliability, efficiency, and tuning with regard to the physical storage medium are important design considerations.

Origin of the term

From c.1900 and before the advent of computers the terms file system and system for filing were used to describe a method of storing and retrieving paper documents. By 1961, the term file system was being applied to computerized filing alongside the original meaning. By 1964, it was in general use.

Architecture

A file system consists of two or three layers. Sometimes the layers are explicitly separated, and sometimes the functions are combined.

The logical file system is responsible for interaction with the user application. It provides the application program interface (API) for file operations — OPEN, CLOSE, READ, etc., and passes the requested operation to the layer below it for processing. The logical file system "manage[s] open file table entries and per-process file descriptors". This layer provides "file access, directory operations, [and] security and protection".

The second optional layer is the virtual file system. "This interface allows support for multiple concurrent instances of physical file systems, each of which is called a file system implementation".

The third layer is the physical file system. This layer is concerned with the physical operation of the storage device (e.g. disk). It processes physical blocks being read or written. It handles buffering and memory management and is responsible for the physical placement of blocks in specific locations on the storage medium. The physical file system interacts with the device drivers or with the channel to drive the storage device.

Aspects of file systems

Space management

Note: this only applies to file systems used in storage devices.

An example of slack space, demonstrated with 4,096-byte NTFS clusters: 100,000 files, each five bytes per file, which equal to 500,000 bytes of actual data but require 409,600,000 bytes of disk space to store

File systems allocate space in a granular manner, usually multiple physical units on the device. The file system is responsible for organizing files and directories, and keeping track of which areas of the media belong to which file and which are not being used. For example, in Apple DOS of the early 1980s, 256-byte sectors on 140 kilobyte floppy disk used a track/sector map.

This results in unused space when a file is not an exact multiple of the allocation unit, sometimes referred to as slack space. For a 512-byte allocation, the average unused space is 256 bytes. For 64 KB clusters, the average unused space is 32 KB. The size of the allocation unit is chosen when the file system is created. Choosing the allocation size based on the average size of the files expected to be in the file system can minimize the amount of unusable space. Frequently the default allocation may provide reasonable usage. Choosing an allocation size that is too small results in excessive overhead if the file system will contain mostly very large files.

File systems may become fragmented

File system fragmentation occurs when unused space or single files are not contiguous. As a file system is used, files are created, modified and deleted. When a file is created, the file system allocates space for the data. Some file systems permit or require specifying an initial space allocation and subsequent incremental allocations as the file grows. As files are deleted, the space they were allocated eventually is considered available for use by other files. This creates alternating used and unused areas of various sizes. This is free space fragmentation. When a file is created and there is not an area of contiguous space available for its initial allocation, the space must be assigned in fragments. When a file is modified such that it becomes larger, it may exceed the space initially allocated to it, another allocation must be assigned elsewhere and the file becomes fragmented.

In some operating systems, a system administrator may use disk quotas to limit the allocation of disk space.

Filenames

A filename (or file name) is used to identify a storage location in the file system. Most file systems have restrictions on the length of filenames. In some file systems, filenames are not case sensitive (i.e., the names MYFILE and myfile refer to the same file in a directory); in others, filenames are case sensitive (i.e., the names MYFILE, MyFile, and myfile refer to three separate files that are in the same directory).

Most modern file systems allow filenames to contain a wide range of characters from the Unicode character set. However, they may have restrictions on the use of certain special characters, disallowing them within filenames; those characters might be used to indicate a device, device type, directory prefix, file path separator, or file type.

Directories

File systems typically have directories (also called folders) which allow the user to group files into separate collections. This may be implemented by associating the file name with an index in a table of contents or an inode in a Unix-like file system. Directory structures may be flat (i.e. linear), or allow hierarchies where directories may contain subdirectories. The first file system to support arbitrary hierarchies of directories was used in the Multics operating system. The native file systems of Unix-like systems also support arbitrary directory hierarchies, as do, for example, Apple's Hierarchical File System and its successor HFS+ in classic Mac OS, the FAT file system in MS-DOS 2.0 and later versions of MS-DOS and in Microsoft Windows, the NTFS file system in the Windows NT family of operating systems, and the ODS-2 (On-Disk Structure-2) and higher levels of the Files-11 file system in OpenVMS.

Metadata

Other bookkeeping information is typically associated with each file within a file system. The length of the data contained in a file may be stored as the number of blocks allocated for the file or as a byte count. The time that the file was last modified may be stored as the file's timestamp. File systems might store the file creation time, the time it was last accessed, the time the file's metadata was changed, or the time the file was last backed up. Other information can include the file's device type (e.g. block, character, socket, subdirectory, etc.), its owner user ID and group ID, its access permissions and other file attributes (e.g. whether the file is read-only, executable, etc.).

A file system stores all the metadata associated with the file—including the file name, the length of the contents of a file, and the location of the file in the folder hierarchy—separate from the contents of the file.

Most file systems store the names of all the files in one directory in one place—the directory table for that directory—which is often stored like any other file. Many file systems put only some of the metadata for a file in the directory table, and the rest of the metadata for that file in a completely separate structure, such as the inode.

Most file systems also store metadata not associated with any one particular file. Such metadata includes information about unused regions—free space bitmap, block availability map—and information about bad sectors. Often such information about an allocation group is stored inside the allocation group itself.

Additional attributes can be associated on file systems, such as NTFS, XFS, ext2, ext3, some versions of UFS, and HFS+, using extended file attributes. Some file systems provide for user defined attributes such as the author of the document, the character encoding of a document or the size of an image.

Some file systems allow for different data collections to be associated with one file name. These separate collections may be referred to as streams or forks. Apple has long used a forked file system on the Macintosh, and Microsoft supports streams in NTFS. Some file systems maintain multiple past revisions of a file under a single file name; the filename by itself retrieves the most recent version, while prior saved version can be accessed using a special naming convention such as "filename;4" or "filename(-4)" to access the version four saves ago.

See comparison of file systems#Metadata for details on which file systems support which kinds of metadata.

File system as an abstract user interface

In some cases, a file system may not make use of a storage device but can be used to organize and represent access to any data, whether it is stored or dynamically generated (e.g. procfs).

Utilities

File systems include utilities to initialize, alter parameters of and remove an instance of the file system. Some include the ability to extend or truncate the space allocated to the file system.

Directory utilities may be used to create, rename and delete directory entries, which are also known as dentries (singular: dentry), and to alter metadata associated with a directory. Directory utilities may also include capabilities to create additional links to a directory (hard links in Unix), to rename parent links (".." in Unix-like operating systems), and to create bidirectional links to files.

File utilities create, list, copy, move and delete files, and alter metadata. They may be able to truncate data, truncate or extend space allocation, append to, move, and modify files in-place. Depending on the underlying structure of the file system, they may provide a mechanism to prepend to or truncate from the beginning of a file, insert entries into the middle of a file, or delete entries from a file. Utilities to free space for deleted files, if the file system provides an undelete function, also belong to this category.

Some file systems defer operations such as reorganization of free space, secure erasing of free space, and rebuilding of hierarchical structures by providing utilities to perform these functions at times of minimal activity. An example is the file system defragmentation utilities.

Some of the most important features of file system utilities are supervisory activities which may involve bypassing ownership or direct access to the underlying device. These include high-performance backup and recovery, data replication, and reorganization of various data structures and allocation tables within the file system.

Restricting and permitting access

There are several mechanisms used by file systems to control access to data. Usually the intent is to prevent reading or modifying files by a user or group of users. Another reason is to ensure data is modified in a controlled way so access may be restricted to a specific program. Examples include passwords stored in the metadata of the file or elsewhere and file permissions in the form of permission bits, access control lists, or capabilities. The need for file system utilities to be able to access the data at the media level to reorganize the structures and provide efficient backup usually means that these are only effective for polite users but are not effective against intruders.

Methods for encrypting file data are sometimes included in the file system. This is very effective since there is no need for file system utilities to know the encryption seed to effectively manage the data. The risks of relying on encryption include the fact that an attacker can copy the data and use brute force to decrypt the data. Additionally, losing the seed means losing the data.

Maintaining integrity

One significant responsibility of a file system is to ensure that the file system structures in secondary storage remain consistent, regardless of the actions by programs accessing the file system. This includes actions taken if a program modifying the file system terminates abnormally or neglects to inform the file system that it has completed its activities. This may include updating the metadata, the directory entry and handling any data that was buffered but not yet updated on the physical storage media.

Other failures which the file system must deal with include media failures or loss of connection to remote systems.

In the event of an operating system failure or "soft" power failure, special routines in the file system must be invoked similar to when an individual program fails.

The file system must also be able to correct damaged structures. These may occur as a result of an operating system failure for which the OS was unable to notify the file system, a power failure, or a reset.

The file system must also record events to allow analysis of systemic issues as well as problems with specific files or directories.

User data

The most important purpose of a file system is to manage user data. This includes storing, retrieving and updating data.

Some file systems accept data for storage as a stream of bytes which are collected and stored in a manner efficient for the media. When a program retrieves the data, it specifies the size of a memory buffer and the file system transfers data from the media to the buffer. A runtime library routine may sometimes allow the user program to define a record based on a library call specifying a length. When the user program reads the data, the library retrieves data via the file system and returns a record.

Some file systems allow the specification of a fixed record length which is used for all writes and reads. This facilitates locating the nth record as well as updating records.

An identification for each record, also known as a key, makes for a more sophisticated file system. The user program can read, write and update records without regard to their location. This requires complicated management of blocks of media usually separating key blocks and data blocks. Very efficient algorithms can be developed with pyramid structures for locating records.

Using a file system

Utilities, language specific run-time libraries and user programs use file system APIs to make requests of the file system. These include data transfer, positioning, updating metadata, managing directories, managing access specifications, and removal.

Multiple file systems within a single system

Frequently, retail systems are configured with a single file system occupying the entire storage device.

Another approach is to partition the disk so that several file systems with different attributes can be used. One file system, for use as browser cache or email storage, might be configured with a small allocation size. This keeps the activity of creating and deleting files typical of browser activity in a narrow area of the disk where it will not interfere with other file allocations. Another partition might be created for the storage of audio or video files with a relatively large block size. Yet another may normally be set read-only and only periodically be set writable.

A third approach, which is mostly used in cloud systems, is to use "disk images" to house additional file systems, with the same attributes or not, within another (host) file system as a file. A common example is virtualization: one user can run an experimental Linux distribution (using the ext4 file system) in a virtual machine under his/her production Windows environment (using NTFS). The ext4 file system resides in a disk image, which is treated as a file (or multiple files, depending on the hypervisor and settings) in the NTFS host file system.

Having multiple file systems on a single system has the additional benefit that in the event of a corruption of a single partition, the remaining file systems will frequently still be intact. This includes virus destruction of the system partition or even a system that will not boot. File system utilities which require dedicated access can be effectively completed piecemeal. In addition, defragmentation may be more effective. Several system maintenance utilities, such as virus scans and backups, can also be processed in segments. For example, it is not necessary to backup the file system containing videos along with all the other files if none have been added since the last backup. As for the image files, one can easily "spin off" differential images which contain only "new" data written to the master (original) image. Differential images can be used for both safety concerns (as a "disposable" system - can be quickly restored if destroyed or contaminated by a virus, as the old image can be removed and a new image can be created in matter of seconds, even without automated procedures) and quick virtual machine deployment (since the differential images can be quickly spawned using a script in batches).

Design limitations

All file systems have some functional limit that defines the maximum storable data capacity within that system. These functional limits are a best-guess effort by the designer based on how large the storage systems are right now and how large storage systems are likely to become in the future. Disk storage has continued to increase at near exponential rates (see Moore's law), so after a few years, file systems have kept reaching design limitations that require computer users to repeatedly move to a newer system with ever-greater capacity.

File system complexity typically varies proportionally with the available storage capacity. The file systems of early 1980s home computers with 50 KB to 512 KB of storage would not be a reasonable choice for modern storage systems with hundreds of gigabytes of capacity. Likewise, modern file systems would not be a reasonable choice for these early systems, since the complexity of modern file system structures would quickly consume or even exceed the very limited capacity of the early storage systems.

Types of file systems

File system types can be classified into disk/tape file systems, network file systems and special-purpose file systems.

Disk file systems

A disk file system takes advantages of the ability of disk storage media to randomly address data in a short amount of time. Additional considerations include the speed of accessing data following that initially requested and the anticipation that the following data may also be requested. This permits multiple users (or processes) access to various data on the disk without regard to the sequential location of the data. Examples include FAT (FAT12, FAT16, FAT32), exFAT, NTFS, ReFS, HFS and HFS+, HPFS, APFS, UFS, ext2, ext3, ext4, XFS, btrfs, Files-11, Veritas File System, VMFS, ZFS, ReiserFS, NSS and ScoutFS. Some disk file systems are journaling file systems or versioning file systems.

Optical discs

ISO 9660 and Universal Disk Format (UDF) are two common formats that target Compact Discs, DVDs and Blu-ray discs. Mount Rainier is an extension to UDF supported since 2.6 series of the Linux kernel and since Windows Vista that facilitates rewriting to DVDs.

Flash file systems

A flash file system considers the special abilities, performance and restrictions of flash memory devices. Frequently a disk file system can use a flash memory device as the underlying storage media, but it is much better to use a file system specifically designed for a flash device.

Tape file systems

A tape file system is a file system and tape format designed to store files on tape. Magnetic tapes are sequential storage media with significantly longer random data access times than disks, posing challenges to the creation and efficient management of a general-purpose file system.

In a disk file system there is typically a master file directory, and a map of used and free data regions. Any file additions, changes, or removals require updating the directory and the used/free maps. Random access to data regions is measured in milliseconds so this system works well for disks.

Tape requires linear motion to wind and unwind potentially very long reels of media. This tape motion may take several seconds to several minutes to move the read/write head from one end of the tape to the other.

Consequently, a master file directory and usage map can be extremely slow and inefficient with tape. Writing typically involves reading the block usage map to find free blocks for writing, updating the usage map and directory to add the data, and then advancing the tape to write the data in the correct spot. Each additional file write requires updating the map and directory and writing the data, which may take several seconds to occur for each file.

Tape file systems instead typically allow for the file directory to be spread across the tape intermixed with the data, referred to as streaming, so that time-consuming and repeated tape motions are not required to write new data.

However, a side effect of this design is that reading the file directory of a tape usually requires scanning the entire tape to read all the scattered directory entries. Most data archiving software that works with tape storage will store a local copy of the tape catalog on a disk file system, so that adding files to a tape can be done quickly without having to rescan the tape media. The local tape catalog copy is usually discarded if not used for a specified period of time, at which point the tape must be re-scanned if it is to be used in the future.

IBM has developed a file system for tape called the Linear Tape File System. The IBM implementation of this file system has been released as the open-source IBM Linear Tape File System — Single Drive Edition (LTFS-SDE) product. The Linear Tape File System uses a separate partition on the tape to record the index meta-data, thereby avoiding the problems associated with scattering directory entries across the entire tape.

Tape formatting

Writing data to a tape, erasing, or formatting a tape is often a significantly time-consuming process and can take several hours on large tapes. With many data tape technologies it is not necessary to format the tape before over-writing new data to the tape. This is due to the inherently destructive nature of overwriting data on sequential media.

Because of the time it can take to format a tape, typically tapes are pre-formatted so that the tape user does not need to spend time preparing each new tape for use. All that is usually necessary is to write an identifying media label to the tape before use, and even this can be automatically written by software when a new tape is used for the first time.

Database file systems

Another concept for file management is the idea of a database-based file system. Instead of, or in addition to, hierarchical structured management, files are identified by their characteristics, like type of file, topic, author, or similar rich metadata.

IBM DB2 for i  (formerly known as DB2/400 and DB2 for i5/OS) is a database file system as part of the object based IBM i operating system (formerly known as OS/400 and i5/OS), incorporating a single level store and running on IBM Power Systems (formerly known as AS/400 and iSeries), designed by Frank G. Soltis IBM's former chief scientist for IBM i. Around 1978 to 1988 Frank G. Soltis and his team at IBM Rochester have successfully designed and applied technologies like the database file system where others like Microsoft later failed to accomplish. These technologies are informally known as 'Fortress Rochester' and were in few basic aspects extended from early Mainframe technologies but in many ways more advanced from a technological perspective.

Some other projects that aren't "pure" database file systems but that use some aspects of a database file system:

  • Many Web content management systems use a relational DBMS to store and retrieve files. For example, XHTML files are stored as XML or text fields, while image files are stored as blob fields; SQL SELECT (with optional XPath) statements retrieve the files, and allow the use of a sophisticated logic and more rich information associations than "usual file systems." Many CMSs also have the option of storing only metadata within the database, with the standard filesystem used to store the content of files.
  • Very large file systems, embodied by applications like Apache Hadoop and Google File System, use some database file system concepts.

Transactional file systems

Some programs need to either make multiple file system changes, or, if one or more of the changes fail for any reason, make none of the changes. For example, a program which is installing or updating software may write executables, libraries, and/or configuration files. If some of the writing fails and the software is left partially installed or updated, the software may be broken or unusable. An incomplete update of a key system utility, such as the command shell, may leave the entire system in an unusable state.

Transaction processing introduces the atomicity guarantee, ensuring that operations inside of a transaction are either all committed or the transaction can be aborted and the system discards all of its partial results. This means that if there is a crash or power failure, after recovery, the stored state will be consistent. Either the software will be completely installed or the failed installation will be completely rolled back, but an unusable partial install will not be left on the system. Transactions also provide the isolation guarantee, meaning that operations within a transaction are hidden from other threads on the system until the transaction commits, and that interfering operations on the system will be properly serialized with the transaction.

Windows, beginning with Vista, added transaction support to NTFS, in a feature called Transactional NTFS, but its use is now discouraged. There are a number of research prototypes of transactional file systems for UNIX systems, including the Valor file system, Amino, LFS, and a transactional ext3 file system on the TxOS kernel, as well as transactional file systems targeting embedded systems, such as TFFS.

Ensuring consistency across multiple file system operations is difficult, if not impossible, without file system transactions. File locking can be used as a concurrency control mechanism for individual files, but it typically does not protect the directory structure or file metadata. For instance, file locking cannot prevent TOCTTOU race conditions on symbolic links. File locking also cannot automatically roll back a failed operation, such as a software upgrade; this requires atomicity.

Journaling file systems is one technique used to introduce transaction-level consistency to file system structures. Journal transactions are not exposed to programs as part of the OS API; they are only used internally to ensure consistency at the granularity of a single system call.

Data backup systems typically do not provide support for direct backup of data stored in a transactional manner, which makes the recovery of reliable and consistent data sets difficult. Most backup software simply notes what files have changed since a certain time, regardless of the transactional state shared across multiple files in the overall dataset. As a workaround, some database systems simply produce an archived state file containing all data up to that point, and the backup software only backs that up and does not interact directly with the active transactional databases at all. Recovery requires separate recreation of the database from the state file after the file has been restored by the backup software.

Network file systems

A network file system is a file system that acts as a client for a remote file access protocol, providing access to files on a server. Programs using local interfaces can transparently create, manage and access hierarchical directories and files in remote network-connected computers. Examples of network file systems include clients for the NFS, AFS, SMB protocols, and file-system-like clients for FTP and WebDAV.

Shared disk file systems

A shared disk file system is one in which a number of machines (usually servers) all have access to the same external disk subsystem (usually a storage area network). The file system arbitrates access to that subsystem, preventing write collisions. Examples include GFS2 from Red Hat, GPFS, now known as Spectrum Scale, from IBM, SFS from DataPlow, CXFS from SGI, StorNext from Quantum Corporation and ScoutFS from Versity.

Special file systems

A special file system presents non-file elements of an operating system as files so they can be acted on using file system APIs. This is most commonly done in Unix-like operating systems, but devices are given file names in some non-Unix-like operating systems as well.

Device file systems

A device file system represents I/O devices and pseudo-devices as files, called device files. Examples in Unix-like systems include devfs and, in Linux 2.6 systems, udev. In non-Unix-like systems, such as TOPS-10 and other operating systems influenced by it, where the full filename or pathname of a file can include a device prefix, devices other than those containing file systems are referred to by a device prefix specifying the device, without anything following it.

Other special file systems

  • In the Linux kernel, configfs and sysfs provide files that can be used to query the kernel for information and configure entities in the kernel.
  • procfs maps processes and, on Linux, other operating system structures into a filespace.

Minimal file system / audio-cassette storage

In the 1970s disk and digital tape devices were too expensive for some early microcomputer users. An inexpensive basic data storage system was devised that used common audio cassette tape.

When the system needed to write data, the user was notified to press "RECORD" on the cassette recorder, then press "RETURN" on the keyboard to notify the system that the cassette recorder was recording. The system wrote a sound to provide time synchronization, then modulated sounds that encoded a prefix, the data, a checksum and a suffix. When the system needed to read data, the user was instructed to press "PLAY" on the cassette recorder. The system would listen to the sounds on the tape waiting until a burst of sound could be recognized as the synchronization. The system would then interpret subsequent sounds as data. When the data read was complete, the system would notify the user to press "STOP" on the cassette recorder. It was primitive, but it (mostly) worked. Data was stored sequentially, usually in an unnamed format, although some systems (such as the Commodore PET series of computers) did allow the files to be named. Multiple sets of data could be written and located by fast-forwarding the tape and observing at the tape counter to find the approximate start of the next data region on the tape. The user might have to listen to the sounds to find the right spot to begin playing the next data region. Some implementations even included audible sounds interspersed with the data.

Flat file systems

In a flat file system, there are no subdirectories; directory entries for all files are stored in a single directory.

When floppy disk media was first available this type of file system was adequate due to the relatively small amount of data space available. CP/M machines featured a flat file system, where files could be assigned to one of 16 user areas and generic file operations narrowed to work on one instead of defaulting to work on all of them. These user areas were no more than special attributes associated with the files; that is, it was not necessary to define specific quota for each of these areas and files could be added to groups for as long as there was still free storage space on the disk. The early Apple Macintosh also featured a flat file system, the Macintosh File System. It was unusual in that the file management program (Macintosh Finder) created the illusion of a partially hierarchical filing system on top of EMFS. This structure required every file to have a unique name, even if it appeared to be in a separate folder. IBM DOS/360 and OS/360 store entries for all files on a disk pack (volume) in a directory on the pack called a Volume Table of Contents (VTOC).

While simple, flat file systems become awkward as the number of files grows and makes it difficult to organize data into related groups of files.

A recent addition to the flat file system family is Amazon's S3, a remote storage service, which is intentionally simplistic to allow users the ability to customize how their data is stored. The only constructs are buckets (imagine a disk drive of unlimited size) and objects (similar, but not identical to the standard concept of a file). Advanced file management is allowed by being able to use nearly any character (including '/') in the object's name, and the ability to select subsets of the bucket's content based on identical prefixes.

File systems and operating systems

Many operating systems include support for more than one file system. Sometimes the OS and the file system are so tightly interwoven that it is difficult to separate out file system functions.

There needs to be an interface provided by the operating system software between the user and the file system. This interface can be textual (such as provided by a command line interface, such as the Unix shell, or OpenVMS DCL) or graphical (such as provided by a graphical user interface, such as file browsers). If graphical, the metaphor of the folder, containing documents, other files, and nested folders is often used (see also: directory and folder).

Unix and Unix-like operating systems

Unix-like operating systems create a virtual file system, which makes all the files on all the devices appear to exist in a single hierarchy. This means, in those systems, there is one root directory, and every file existing on the system is located under it somewhere. Unix-like systems can use a RAM disk or network shared resource as its root directory.

Unix-like systems assign a device name to each device, but this is not how the files on that device are accessed. Instead, to gain access to files on another device, the operating system must first be informed where in the directory tree those files should appear. This process is called mounting a file system. For example, to access the files on a CD-ROM, one must tell the operating system "Take the file system from this CD-ROM and make it appear under such-and-such directory." The directory given to the operating system is called the mount point – it might, for example, be /media. The /media directory exists on many Unix systems (as specified in the Filesystem Hierarchy Standard) and is intended specifically for use as a mount point for removable media such as CDs, DVDs, USB drives or floppy disks. It may be empty, or it may contain subdirectories for mounting individual devices. Generally, only the administrator (i.e. root user) may authorize the mounting of file systems.

Unix-like operating systems often include software and tools that assist in the mounting process and provide it new functionality. Some of these strategies have been coined "auto-mounting" as a reflection of their purpose.

  • In many situations, file systems other than the root need to be available as soon as the operating system has booted. All Unix-like systems therefore provide a facility for mounting file systems at boot time. System administrators define these file systems in the configuration file fstab (vfstab in Solaris), which also indicates options and mount points.
  • In some situations, there is no need to mount certain file systems at boot time, although their use may be desired thereafter. There are some utilities for Unix-like systems that allow the mounting of predefined file systems upon demand.
  • Removable media allow programs and data to be transferred between machines without a physical connection. Common examples include USB flash drives, CD-ROMs, and DVDs. Utilities have therefore been developed to detect the presence and availability of a medium and then mount that medium without any user intervention.
  • Progressive Unix-like systems have also introduced a concept called supermounting; see, for example, the Linux supermount-ng project. For example, a floppy disk that has been supermounted can be physically removed from the system. Under normal circumstances, the disk should have been synchronized and then unmounted before its removal. Provided synchronization has occurred, a different disk can be inserted into the drive. The system automatically notices that the disk has changed and updates the mount point contents to reflect the new medium.
  • An automounter will automatically mount a file system when a reference is made to the directory atop which it should be mounted. This is usually used for file systems on network servers, rather than relying on events such as the insertion of media, as would be appropriate for removable media.

Linux

Linux supports numerous file systems, but common choices for the system disk on a block device include the ext* family (ext2, ext3 and ext4), XFS, JFS, and btrfs. For raw flash without a flash translation layer (FTL) or Memory Technology Device (MTD), there are UBIFS, JFFS2 and YAFFS, among others. SquashFS is a common compressed read-only file system.

Solaris

Solaris in earlier releases defaulted to (non-journaled or non-logging) UFS for bootable and supplementary file systems. Solaris defaulted to, supported, and extended UFS.

Support for other file systems and significant enhancements were added over time, including Veritas Software Corp. (journaling) VxFS, Sun Microsystems (clustering) QFS, Sun Microsystems (journaling) UFS, and Sun Microsystems (open source, poolable, 128 bit compressible, and error-correcting) ZFS.

Kernel extensions were added to Solaris to allow for bootable Veritas VxFS operation. Logging or journaling was added to UFS in Sun's Solaris 7. Releases of Solaris 10, Solaris Express, OpenSolaris, and other open source variants of the Solaris operating system later supported bootable ZFS.

Logical Volume Management allows for spanning a file system across multiple devices for the purpose of adding redundancy, capacity, and/or throughput. Legacy environments in Solaris may use Solaris Volume Manager (formerly known as Solstice DiskSuite). Multiple operating systems (including Solaris) may use Veritas Volume Manager. Modern Solaris based operating systems eclipse the need for volume management through leveraging virtual storage pools in ZFS.

macOS

macOS (formerly Mac OS X) uses the Apple File System (APFS), which in 2017 replaced a file system inherited from classic Mac OS called HFS Plus (HFS+). Apple also uses the term "Mac OS Extended" for HFS+. HFS Plus is a metadata-rich and case-preserving but (usually) case-insensitive file system. Due to the Unix roots of macOS, Unix permissions were added to HFS Plus. Later versions of HFS Plus added journaling to prevent corruption of the file system structure and introduced a number of optimizations to the allocation algorithms in an attempt to defragment files automatically without requiring an external defragmenter.

Filenames can be up to 255 characters. HFS Plus uses Unicode to store filenames. On macOS, the filetype can come from the type code, stored in file's metadata, or the filename extension.

HFS Plus has three kinds of links: Unix-style hard links, Unix-style symbolic links, and aliases. Aliases are designed to maintain a link to their original file even if they are moved or renamed; they are not interpreted by the file system itself, but by the File Manager code in userland.

macOS 10.13 High Sierra, which was announced on June 5, 2017 at Apple's WWDC event, uses the Apple File System on solid-state drives.

macOS also supported the UFS file system, derived from the BSD Unix Fast File System via NeXTSTEP. However, as of Mac OS X Leopard, macOS could no longer be installed on a UFS volume, nor can a pre-Leopard system installed on a UFS volume be upgraded to Leopard. As of Mac OS X Lion UFS support was completely dropped.

Newer versions of macOS are capable of reading and writing to the legacy FAT file systems (16 and 32) common on Windows. They are also capable of reading the newer NTFS file systems for Windows. In order to write to NTFS file systems on macOS versions prior to Mac OS X Snow Leopard third party software is necessary. Mac OS X 10.6 (Snow Leopard) and later allow writing to NTFS file systems, but only after a non-trivial system setting change (third party software exists that automates this).

Finally, macOS supports reading and writing of the exFAT file system since Mac OS X Snow Leopard, starting from version 10.6.5.

OS/2

OS/2 1.2 introduced the High Performance File System (HPFS). HPFS supports mixed case file names in different code pages, long file names (255 characters), more efficient use of disk space, an architecture that keeps related items close to each other on the disk volume, less fragmentation of data, extent-based space allocation, a B+ tree structure for directories, and the root directory located at the midpoint of the disk, for faster average access. A journaled filesystem (JFS) was shipped in 1999.

PC-BSD

PC-BSD is a desktop version of FreeBSD, which inherits FreeBSD's ZFS support, similarly to FreeNAS. The new graphical installer of PC-BSD can handle / (root) on ZFS and RAID-Z pool installs and disk encryption using Geli right from the start in an easy convenient (GUI) way. The current PC-BSD 9.0+ 'Isotope Edition' has ZFS filesystem version 5 and ZFS storage pool version 28.

Plan 9

Plan 9 from Bell Labs treats everything as a file and accesses all objects as a file would be accessed (i.e., there is no ioctl or mmap): networking, graphics, debugging, authentication, capabilities, encryption, and other services are accessed via I/O operations on file descriptors. The 9P protocol removes the difference between local and remote files. File systems in Plan 9 are organized with the help of private, per-process namespaces, allowing each process to have a different view of the many file systems that provide resources in a distributed system.

The Inferno operating system shares these concepts with Plan 9.

Microsoft Windows

Directory listing in a Windows command shell

Windows makes use of the FAT, NTFS, exFAT, Live File System and ReFS file systems (the last of these is only supported and usable in Windows Server 2012, Windows Server 2016, Windows 8, Windows 8.1, and Windows 10; Windows cannot boot from it).

Windows uses a drive letter abstraction at the user level to distinguish one disk or partition from another. For example, the path C:\WINDOWS represents a directory WINDOWS on the partition represented by the letter C. Drive C: is most commonly used for the primary hard disk drive partition, on which Windows is usually installed and from which it boots. This "tradition" has become so firmly ingrained that bugs exist in many applications which make assumptions that the drive that the operating system is installed on is C. The use of drive letters, and the tradition of using "C" as the drive letter for the primary hard disk drive partition, can be traced to MS-DOS, where the letters A and B were reserved for up to two floppy disk drives. This in turn derived from CP/M in the 1970s, and ultimately from IBM's CP/CMS of 1967.

FAT

The family of FAT file systems is supported by almost all operating systems for personal computers, including all versions of Windows and MS-DOS/PC DOS, OS/2, and DR-DOS. (PC DOS is an OEM version of MS-DOS, MS-DOS was originally based on SCP's 86-DOS. DR-DOS was based on Digital Research's Concurrent DOS, a successor of CP/M-86.) The FAT file systems are therefore well-suited as a universal exchange format between computers and devices of most any type and age.

The FAT file system traces its roots back to an (incompatible) 8-bit FAT precursor in Standalone Disk BASIC and the short-lived MDOS/MIDAS project.

Over the years, the file system has been expanded from FAT12 to FAT16 and FAT32. Various features have been added to the file system including subdirectories, codepage support, extended attributes, and long filenames. Third parties such as Digital Research have incorporated optional support for deletion tracking, and volume/directory/file-based multi-user security schemes to support file and directory passwords and permissions such as read/write/execute/delete access rights. Most of these extensions are not supported by Windows.

The FAT12 and FAT16 file systems had a limit on the number of entries in the root directory of the file system and had restrictions on the maximum size of FAT-formatted disks or partitions.

FAT32 addresses the limitations in FAT12 and FAT16, except for the file size limit of close to 4 GB, but it remains limited compared to NTFS.

FAT12, FAT16 and FAT32 also have a limit of eight characters for the file name, and three characters for the extension (such as .exe). This is commonly referred to as the 8.3 filename limit. VFAT, an optional extension to FAT12, FAT16 and FAT32, introduced in Windows 95 and Windows NT 3.5, allowed long file names (LFN) to be stored in the FAT file system in a backwards compatible fashion.

NTFS

NTFS, introduced with the Windows NT operating system in 1993, allowed ACL-based permission control. Other features also supported by NTFS include hard links, multiple file streams, attribute indexing, quota tracking, sparse files, encryption, compression, and reparse points (directories working as mount-points for other file systems, symlinks, junctions, remote storage links).

exFAT

exFAT has certain advantages over NTFS with regard to file system overhead.

exFAT is not backward compatible with FAT file systems such as FAT12, FAT16 or FAT32. The file system is supported with newer Windows systems, such as Windows XP, Windows Server 2003, Windows Vista, Windows 2008, Windows 7, Windows 8, Windows 8.1, Windows 10 and Windows 11.

exFAT is supported in macOS starting with version 10.6.5 (Snow Leopard). Support in other operating systems is sparse since implementing support for exFAT requires a license. exFAT is the only file system that is fully supported on both macOS and Windows that can hold files larger than 4 GB.

OpenVMS

MVS

Prior to the introduction of VSAM, OS/360 systems implemented a hybrid file system. The system was designed to easily support removable disk packs, so the information relating to all files on one disk (volume in IBM terminology) is stored on that disk in a flat system file called the Volume Table of Contents (VTOC). The VTOC stores all metadata for the file. Later a hierarchical directory structure was imposed with the introduction of the System Catalog, which can optionally catalog files (datasets) on resident and removable volumes. The catalog only contains information to relate a dataset to a specific volume. If the user requests access to a dataset on an offline volume, and they have suitable privileges, the system will attempt to mount the required volume. Cataloged and non-cataloged datasets can still be accessed using information in the VTOC, bypassing the catalog, if the required volume id is provided to the OPEN request. Still later the VTOC was indexed to speed up access.

Conversational Monitor System

The IBM Conversational Monitor System (CMS) component of VM/370 uses a separate flat file system for each virtual disk (minidisk). File data and control information are scattered and intermixed. The anchor is a record called the Master File Directory (MFD), always located in the fourth block on the disk. Originally CMS used fixed-length 800-byte blocks, but later versions used larger size blocks up to 4K. Access to a data record requires two levels of indirection, where the file's directory entry (called a File Status Table (FST) entry) points to blocks containing a list of addresses of the individual records.

AS/400 file system

Data on the AS/400 and its successors consists of system objects mapped into the system virtual address space in a single-level store. Many types of objects are defined including the directories and files found in other file systems. File objects, along with other types of objects, form the basis of the AS/400's support for an integrated relational database.

Other file systems

  • The Prospero File System is a file system based on the Virtual System Model. The system was created by Dr. B. Clifford Neuman of the Information Sciences Institute at the University of Southern California.
  • RSRE FLEX file system - written in ALGOL 68
  • The file system of the Michigan Terminal System (MTS) is interesting because: (i) it provides "line files" where record lengths and line numbers are associated as metadata with each record in the file, lines can be added, replaced, updated with the same or different length records, and deleted anywhere in the file without the need to read and rewrite the entire file; (ii) using program keys files may be shared or permitted to commands and programs in addition to users and groups; and (iii) there is a comprehensive file locking mechanism that protects both the file's data and its metadata.

Limitations

Converting the type of a file system

It may be advantageous or necessary to have files in a different file system than they currently exist. Reasons include the need for an increase in the space requirements beyond the limits of the current file system. The depth of path may need to be increased beyond the restrictions of the file system. There may be performance or reliability considerations. Providing access to another operating system which does not support the existing file system is another reason.

In-place conversion

In some cases conversion can be done in-place, although migrating the file system is more conservative, as it involves a creating a copy of the data and is recommended. On Windows, FAT and FAT32 file systems can be converted to NTFS via the convert.exe utility, but not the reverse. On Linux, ext2 can be converted to ext3 (and converted back), and ext3 can be converted to ext4 (but not back), and both ext3 and ext4 can be converted to btrfs, and converted back until the undo information is deleted. These conversions are possible due to using the same format for the file data itself, and relocating the metadata into empty space, in some cases using sparse file support.

Migrating to a different file system

Migration has the disadvantage of requiring additional space although it may be faster. The best case is if there is unused space on media which will contain the final file system.

For example, to migrate a FAT32 file system to an ext2 file system, a new ext2 file system is created. Then the data from the FAT32 file system is copied to the ext2 one, and the old file system is deleted.

An alternative, when there is not sufficient space to retain the original file system until the new one is created, is to use a work area (such as a removable media). This takes longer but has the benefit of producing a backup.

Long file paths and long file names

In hierarchical file systems, files are accessed by means of a path that is a branching list of directories containing the file. Different file systems have different limits on the depth of the path. File systems also have a limit on the length of an individual filename.

Copying files with long names or located in paths of significant depth from one file system to another may cause undesirable results. This depends on how the utility doing the copying handles the discrepancy.

Thursday, July 27, 2023

Active learning

From Wikipedia, the free encyclopedia
Classroom teaching

Active learning is "a method of learning in which students are actively or experientially involved in the learning process and where there are different levels of active learning, depending on student involvement." Bonwell & Eison (1991) states that "students participate [in active learning] when they are doing something besides passively listening." According to Hanson and Moser (2003) using active teaching techniques in the classroom can create better academic outcomes for students. Scheyvens, Griffin, Jocoy, Liu, & Bradford (2008) further noted that “by utilizing learning strategies that can include small-group work, role-play and simulations, data collection and analysis, active learning is purported to increase student interest and motivation and to build students ‘critical thinking, problem-solving and social skills”. In a report from the Association for the Study of Higher Education, authors discuss a variety of methodologies for promoting active learning. They cite literature that indicates students must do more than just listen in order to learn. They must read, write, discuss, and be engaged in solving problems. This process relates to the three learning domains referred to as knowledge, skills and attitudes (KSA). This taxonomy of learning behaviors can be thought of as "the goals of the learning process." In particular, students must engage in such higher-order thinking tasks as analysis, synthesis, and evaluation.

Nature of active learning

There are a wide range of alternatives for the term active learning and specific strategies, such as: learning through play, technology-based learning, activity-based learning, group work, project method, etc. The common factors in these are some significant qualities and characteristics of active learning. Active learning is the opposite of passive learning; it is learner-centered, not teacher-centered, and requires more than just listening; the active participation of each and every student is a necessary aspect in active learning. Students must be doing things and simultaneously think about the work done and the purpose behind it so that they can enhance their higher order thinking capabilities.

Many research studies have proven that active learning as a strategy has promoted achievement levels and some others say that content mastery is possible through active learning strategies. However, some students as well as teachers find it difficult to adapt to the new learning technique.

There are intensive uses of scientific and quantitative literacy across the curriculum, and technology-based learning is also in high demand in concern with active learning.

Barnes (1989) suggested principles of active learning:

  1. Purposive: the relevance of the task to the students' concerns.
  2. Reflective: students' reflection on the meaning of what is learned.
  3. Negotiated: negotiation of goals and methods of learning between students and teachers.
  4. Critical: students appreciate different ways and means of learning the content.
  5. Complex: students compare learning tasks with complexities existing in real life and making reflective analysis.
  6. Situation-driven: the need of the situation is considered in order to establish learning tasks.
  7. Engaged: real life tasks are reflected in the activities conducted for learning.

Active learning requires appropriate learning environments through the implementation of correct strategy. Characteristics of learning environment are:

  1. Aligned with constructivist strategies and evolved from traditional philosophies.
  2. Promoting research based learning through investigation and contains authentic scholarly content.
  3. Encouraging leadership skills of the students through self-development activities.
  4. Creating atmosphere suitable for collaborative learning for building knowledgeable learning communities.
  5. Cultivating a dynamic environment through interdisciplinary learning and generating high-profile activities for a better learning experience.
  6. Integration of prior with new knowledge to incur a rich structure of knowledge among the students.
  7. Task-based performance enhancement by giving the students a realistic practical sense of the subject matter learnt in the classroom.

Constructivist framework

Active learning coordinates with the principles of constructivism which are, cognitive, meta-cognitive, evolving and effective in nature. Studies have shown that immediate results in construction of knowledge is not possible through active learning as the child first goes through the process of knowledge construction, knowledge recording and then knowledge absorption. This process of knowledge construction is dependent on previous knowledge of the learner where the learner is self-aware of the process of cognition and can control and regulate it by themselves. There are several aspects of learning and some of them are:

  1. Learning through meaningful reception, influenced by David Ausubel, who emphasizes the previous knowledge the learner possesses and considers it a key factor in learning.
  2. Learning through discovery, influenced by Jerome Bruner, where students learn through discovery of ideas with the help of situations provided by the teacher.
  3. Conceptual change: misconceptions takes place as students discover knowledge without any guidance; teachers provide knowledge keeping in mind the common misconceptions about the content and keep an evaluatory check on the knowledge constructed by the students.
  4. Constructivism, influenced by researchers such as Lev Vygotsky, suggests collaborative group work within the framework of cognitive strategies like questioning, clarifying, predicting and summarizing.

Science of active learning

Active learning can be used effectively for teaching comprehension and memory. The reason it is efficient is that it draws on underlying characteristics of how the brain operates during learning. These characteristics have been documented by thousands of empirical studies (e.g., Smith & Kosslyn, 2011) and have been organized into a set of principles. Each of these principles can be drawn on by various active learning exercises. They also offer a framework for designing activities that will promote learning; when used systematically, Stephen Kosslyn (2017) notes these principles enable students to "learn effectively—sometimes without even trying to learn".

The principles of learning

One way to organize the empirical literature on learning and memory specifies 16 distinct principles, which fall under two umbrella "maxims". The first maxim, "Think it Through", includes principles related to paying close attention and thinking deeply about new information. The second, "Make and Use Associations", focuses on techniques for organizing, storing, and retrieving information.

The principles can be summarized as follows.

Maxim I: Think it through

  • Evoking deep processing: extending thinking beyond "face value" of information (Craig et al., 2006; Craik & Lockhart, 1972)
  • Using desirable difficulty: ensuring that the activity is neither too easy nor too hard (Bjork, 1988, 1999; VanLehn et al., 2007)
  • Eliciting the generation effect: requiring recall of relevant information (Butler & Roediger, 2007; Roediger & Karpicke, 2006)
  • Engaging in deliberate practice: promoting practice focused on learning from errors (Brown, Roediger, & McDaniel, 2014; Ericsson, Krampe, & Tesch-Romer, 1993)
  • Using interleaving: intermixing different problem types
  • Inducing dual coding: presenting information both verbally and visually (Kosslyn, 1994; Mayer, 2001; Moreno & Valdez, 2005)
  • Evoking emotion: generating feelings to enhance recall (Erk et al., 2003; Levine & Pizarro, 2004; McGaugh, 2003, 2004)

Maxim II: Make and use associations

  • Promoting chunking: collecting information into organized units (Brown, Roediger, & McDaniel, 2014; Mayer & Moreno, 2003)
  • Building on prior associations: connecting new information to previously stored information (Bransford, Brown, & Cocking, 2000; Glenberg & Robertson, 1999; Mayer, 2001)
  • Presenting foundational material first: providing basic information as a structural "spine" onto which new information can be attached (Bransford, Brown, & Cocking, 2000; Wandersee, Mintzes, & Novak, 1994)
  • Exploiting appropriate examples: offering examples of the same idea in multiple contexts (Hakel & Halpern, 2005)
  • Relying on principles, not rote: explicitly characterizing the dimensions, factors or mechanisms that underlie a phenomenon (Kozma & Russell, 1997; Bransford, Brown, & Cocking, 2000)
  • Creating associative chaining: sequencing chunks of information into stories (Bower & Clark, 1969; Graeser, Olde, & Klettke, 2002)
  • Using spaced practice: spreading learning out over time (Brown, Roediger, & McDaniel, 2014; Cepeda et al., 2006, 2008; Cull, 2000)
  • Establishing different contexts: associating material with a variety of settings (Hakel & Halpern, 2005; Van Merrienboer et al., 2006)
  • Avoiding interference: incorporating distinctive retrieval cues to avoid confusion (Adams, 1967; Anderson & Neely, 1996)

Active learning typically draws on combinations of these principles. For example, a well-run debate will draw on virtually all, with the exceptions of dual coding, interleaving, and spaced practice. In contrast, passively listening to a lecture rarely draws on any.

Active learning exercises

Bonwell and Eison (1991) suggested learners work collaboratively, discuss materials while role-playing, debate, engage in case study, take part in cooperative learning, or produce short written exercises, etc. The argument is "when should active learning exercises be used during instruction?". Numerous studies have shown that introducing active learning activities (such as simulations, games, contrasting cases, labs,..) before, rather than after lectures or readings, results in deeper learning, understanding, and transfer. The degree of instructor guidance students need while being "active" may vary according to the task and its place in a teaching unit.

In an active learning environment learners are immersed in experiences within which they engage in meaning-making inquiry, action, imagination, invention, interaction, hypothesizing and personal reflection (Cranton 2012).

Examples of "active learning" activities include

  • A class discussion may be held in person or in an online environment. Discussions can be conducted with any class size, although it is typically more effective in smaller group settings. This environment allows for instructor guidance of the learning experience. Discussion requires the learners to think critically on the subject matter and use logic to evaluate their and others' positions. As learners are expected to discuss material constructively and intelligently, a discussion is a good follow-up activity given the unit has been sufficiently covered already. Some of the benefits of using discussion as a method of learning are that it helps students explore a diversity of perspectives, it increases intellectual agility, it shows respect for students' voices and experiences, it develops habits of collaborative learning, it helps students develop skills of synthesis and integration (Brookfield 2005). In addition, by having the teacher actively engage with the students, it allows for them to come to class better prepared and aware of what is taking place in the classroom.
  • A think-pair-share activity is when learners take a minute to ponder the previous lesson, later to discuss it with one or more of their peers, finally to share it with the class as part of a formal discussion. It is during this formal discussion that the instructor should clarify misconceptions. However students need a background in the subject matter to converse in a meaningful way. Therefore, a "think-pair-share" exercise is useful in situations where learners can identify and relate what they already know to others. It can also help teachers or instructors to observe students and see if they understand the material being discussed. This is not a good strategy to use in large classes because of time and logistical constraints (Bonwell and Eison, 1991). Think-pair-share is helpful for the instructor as it enables organizing content and tracking students on where they are relative to the topic being discussed in class, saves time so that he/she can move to other topics, helps to make the class more interactive, provides opportunities for students to interact with each other (Radhakrishna, Ewing, and Chikthimmah, 2012).
  • A learning cell is an effective way for a pair of students to study and learn together. The learning cell was developed by Marcel Goldschmid of the Swiss Federal Institute of Technology in Lausanne (Goldschmid, 1971). A learning cell is a process of learning where two students alternate asking and answering questions on commonly read materials. To prepare for the assignment, the students read the assignment and write down questions that they have about the reading. At the next class meeting, the teacher randomly puts students in pairs. The process begins by designating one student from each group to begin by asking one of their questions to the other. Once the two students discuss the question, the other student ask a question and they alternate accordingly. During this time, the teacher goes from group to group giving feedback and answering questions. This system is also called a student dyad.
  • A short written exercise that is often used is the "one-minute paper". This is a good way to review materials and provide feedback. However a "one-minute paper" does not take one minute and for students to concisely summarize it is suggested that they have at least 10 minutes to work on this exercise. (See also: Quiz § In education.)
  • A collaborative learning group is a successful way to learn different material for different classes. It is where you assign students in groups of 3-6 people and they are given an assignment or task to work on together. To create participation and draw on the wisdom of all the learners the classroom arrangement needs to be flexible seating to allow for the creation of small groups. (Bens, 2005)
  • A student debate is an active way for students to learn because they allow students the chance to take a position and gather information to support their view and explain it to others.
  • A reaction to a video is also an example of active learning.
  • A small group discussion is also an example of active learning because it allows students to express themselves in the classroom. It is more likely for students to participate in small group discussions than in a normal classroom lecture because they are in a more comfortable setting amongst their peers, and from a sheer numbers perspective, by dividing the students up more students get opportunities to speak out. There are so many different ways a teacher can implement small group discussion in to the class, such as making a game out of it, a competition, or an assignment. Statistics show that small group discussions is more beneficial to students than large group discussions when it comes to participation, expressing thoughts, understanding issues, applying issues, and overall status of knowledge.
  • Just-in-time teaching promotes active learning by using pre-class questions to create common ground among students and teachers before the class period begins. These warmup exercises are generally open ended questions designed to encourage students to prepare for class and to elicit student's thoughts on learning goals.
  • A class game is also considered an energetic way to learn because it not only helps the students to review the course material before a big exam but it helps them to enjoy learning about a topic. Different games such as Jeopardy! and crossword puzzles always seem to get the students' minds going.
  • Learning by teaching is also an example of active learning because students actively research a topic and prepare the information so that they can teach it to the class. This helps students learn their own topic even better and sometimes students learn and communicate better with their peers than their teachers.
  • Gallery walk is where students in groups move around the classroom or workshop actively engaging in discussions and contributing to other groups and finally constructing knowledge on a topic and sharing it.
  • In a learning factory production-related subjects can be learned interactively in a realistic learning environment.
  • Problem based learning or "PBL" is an active learning strategy that provides students with the problem first and has been found as an effective strategy with topics as advanced as medicine. 

Use of technology

The use of multimedia and technology tools helps enhance the atmosphere of the classroom, thus enhancing the active learning experience. In this way, each student actively engages in the learning process. Teachers can use movies, videos, games, and other fun activities to enhance the effectiveness of the active learning process. The use of technology also stimulates the "real-world" idea of active learning as it mimics the use of technology outside of the classroom. Incorporating technology combined with active learning have been researched and found a relationship between the use and increased positive behavior, an increase in effective learning, "motivation" as well as a connecting between students and the outside world. The theoretical foundations of this learning process are:

  1. Flow: Flow is a concept to enhance the focus level of the student as each and every individual becomes aware and completely involved in the learning atmosphere. In accordance with one's own capability and potential, through self-awareness, students perform the task at hand. The first methodology to measure flow was Csikszentmihalyi's Experience Sampling.
  2. Learning styles: Acquiring knowledge through one's own technique is called learning style. Learning occurs in accordance with potential as every child is different and has particular potential in various areas. It caters to all kinds of learners: visual, kinesthetic, cognitive and affective.
  3. Locus of control: Ones with high internal locus of control believe that every situation or event is attributable to their resources and behavior. Ones with high external locus of control believe that nothing is under their control.
  4. Intrinsic motivation: Intrinsic motivation is a factor that deals with self-perception concerning the task at hand. Interest, attitude, and results depend on the self-perception of the given activity.

Research evidence

Shimer College Home Economics cooking 1942

Numerous studies have shown evidence to support active learning, given adequate prior instruction.

A meta-analysis of 225 studies comparing traditional lecture to active learning in university math, science, and engineering courses found that active learning reduces failure rates from 32% to 21%, and increases student performance on course assessments and concept inventories by 0.47 standard deviations. Because the findings were so robust with regard to study methodology, extent of controls, and subject matter, the National Academy of Sciences publication suggests that it might be unethical to continue to use traditional lecture approach as a control group in such studies. The largest positive effects were seen in class sizes under 50 students and among students under-represented in STEM fields.

Richard Hake (1998) reviewed data from over 6000 physics students in 62 introductory physics courses and found that students in classes that utilized active learning and interactive engagement techniques improved 25 percent points, achieving an average gain of 48% on a standard test of physics conceptual knowledge, the Force Concept Inventory, compared to a gain of 23% for students in traditional, lecture-based courses.

Similarly, Hoellwarth & Moelter (2011) showed that when instructors switched their physics classes from traditional instruction to active learning, student learning improved 38 percent points, from around 12% to over 50%, as measured by the Force Concept Inventory, which has become the standard measure of student learning in physics courses.

In "Does Active Learning Work? A Review of the Research", Prince (2004) found that "there is broad but uneven support for the core elements of active, collaborative, cooperative and problem-based learning" in engineering education.

Michael (2006), in reviewing the applicability of active learning to physiology education, found a "growing body of research within specific scientific teaching communities that supports and validates the new approaches to teaching that have been adopted".

In a 2012 report titled "Engage to Excel", the United States President's Council of Advisors on Science and Technology described how improved teaching methods, including engaging students in active learning, will increase student retention and improve performance in STEM courses. One study described in the report found that students in traditional lecture courses were twice as likely to leave engineering and three times as likely to drop out of college entirely compared with students taught using active learning techniques. In another cited study, students in a physics class that used active learning methods learned twice as much as those taught in a traditional class, as measured by test results.

Active learning has been implemented in large lectures and it has been shown that both domestic and International students perceive a wide array of benefits. In a recent study, broad improvements were shown in student engagement and understanding of unit material among international students.

Active learning approaches have also been shown to reduce the contact between students and faculty by two thirds, while maintaining learning outcomes that were at least as good, and in one case, significantly better, compared to those achieved in traditional classrooms. Additionally, students' perceptions of their learning were improved and active learning classrooms were demonstrated to lead to a more efficient use of physical space.

A 2019 study by Deslauriers et al. claimed that students have a biased perception of active learning and they feel they learn better with traditional teaching methods than active learning activities. It can be corrected by early preparation and continuous persuasion that the students are benefiting from active instruction.

In a different study conducted by Wallace et al. (2021), they came to the conclusion that in a comparison between students being taught by an active-learning instructor vs. a traditional learning instructor, students who engaged in active-learning outperformed their counterparts in exam environments. In this setting, the instructor focused on active-learning was a first-time instructor, and the individual who was teaching the traditional style of learning was a long-time instructor. The researchers acknowledged the limitations of this study in that individuals may have done better because of depth in specific sections of the class, so the researchers removed questions that could be favoring one section more than the other out of this analysis.

Mathematical anxiety

From Wikipedia, the free encyclopedia
 

Mathematical anxiety, also known as math phobia, is a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in daily life and academic situations. This is, arguably, distinct from statistics anxiety where the negative state is the result of encountering statistics at any level but related to but distinct from mathematical anxiety.

Math Anxiety

Mark H. Ashcraft defines math anxiety as "a feeling of tension, apprehension, or fear that interferes with math performance" (2002, p. 1). It is a phenomenon that is often considered when examining students' problems in mathematics. According to the American Psychological Association, mathematical anxiety is often linked to testing anxiety. This anxiety can cause distress and likely causes a dislike and avoidance of all math-related tasks. The academic study of math anxiety originates as early as the 1950s, when Mary Fides Gough introduced the term mathemaphobia to describe the phobia-like feelings of many towards mathematics. The first math anxiety measurement scale was developed by Richardson and Suinn in 1972. Since this development, several researchers have examined math anxiety in empirical studies. Hembree (1990) conducted a meta-analysis of 151 studies concerning math anxiety. The study determined that math anxiety is related to poor math performance on math achievement tests and to negative attitudes concerning math. Hembree also suggests that math anxiety is directly connected with math avoidance.

Ashcraft (2002) suggests that highly anxious math students will avoid situations in which they have to perform mathematical tasks. Unfortunately, math avoidance results in less competency, exposure and math practice, leaving students more anxious and mathematically unprepared to achieve. In college and university, anxious math students take fewer math courses and tend to feel negative towards the subject. In fact, Ashcraft found that the correlation between math anxiety and variables such as self-confidence and motivation in math is strongly negative.

According to Schar, because math anxiety can cause math avoidance, an empirical dilemma arises. For instance, when a highly math-anxious student performs disappointingly on a math question, it could be due to math anxiety or the lack of competency in math because of math avoidance. Ashcraft determined that by administering a test that becomes increasingly more mathematically challenging, he noticed that even highly math-anxious individuals do well on the first portion of the test measuring performance. However, on the latter and more difficult portion of the test, there was a stronger negative relationship between accuracy and math anxiety.

According to the research found at the University of Chicago by Sian Beilock and her group, math anxiety is not simply about being bad at math. After using brain scans, scholars confirmed that the anticipation or the thought of solving math actually causes math anxiety. The brain scans showed that the area of the brain that is triggered when someone has math anxiety overlaps the same area of the brain where bodily harm is registered. And Trezise and Reeve show that students' math anxiety can fluctuate throughout the duration of a math class.

Performance

The impact of mathematics anxiety on mathematics performance has been studied in more recent literature. An individual with math anxiety does not necessarily lack ability in mathematics, rather, they cannot perform to their full potential due to the interfering symptoms of their anxiety. Math anxiety manifests itself in a variety of ways, including physical, psychological, and behavioral symptoms, that can all disrupt a student's mathematical performance. The strong negative correlation between high math anxiety and low achievement is often thought to be due to the impact of math anxiety on working memory. Working memory has a limited capacity. A large portion of this capacity is dedicated to problem-solving when solving mathematical tasks. However, in individuals with math anxiety, much of this space is taken up by anxious thoughts, thus compromising the individual's ability to perform. In addition, a frequent reliance in schools on high-stakes and timed testing, where students tend to feel the most anxiety, can lead to lower achievement for math-anxious individuals. Programme for International Student Assessment (PISA) results demonstrate that students experiencing high math anxiety demonstrate mathematics scores that are 34 points lower than students who do not have math anxiety, equivalent to one full year of school. Besides, researchers Elisa Cargnelutti et al show that the influence of mathematical anxiety on math-related performance increases over time due to the accumulation of passive experience in the subject or other factors like more requirements on mathematics as children grow up. These findings demonstrate the clear link between math anxiety and reduced levels of achievement, suggesting that alleviating math anxiety may lead to a marked improvement in student achievement.

Anxiety rating scale

A rating scale for mathematics anxiety was developed in 1972 by Richardson and Suinn. Richardson and Suinn defined mathematical anxiety as "feelings of apprehension and tension concerning manipulation of numbers and completion of mathematical problems in various contexts". Richardson and Suinn introduced the MARS (Mathematics Anxiety Rating Scale) in 1972. Elevated scores on the MARS test translate to high math anxiety. The authors presented the normative data, including a mean score of 215.38 with a standard deviation of 65.29, collected from 397 students that replied to an advertisement for behavior therapy treatment for math anxiety. For test-retest reliability, the Pearson product-moment coefficient was used and a score of 0.85 was calculated, which was favorable and comparable to scores found on other anxiety tests. Richardson and Suinn validated the construct of this test by sharing previous results from three other studies that were very similar to the results achieved in this study. They also administered the Differential Aptitude Test, a 10-minute math test including simple to complex problems.

Calculation of the Pearson product-moment correlation coefficient between the MARS test and Differential Aptitude Test scores was −0.64 (p < .01), indicating that higher MARS scores relate to lower math test scores and "since high anxiety interferes with performance, and poor performance produces anxiety, this result provides evidence that the MARS does measure mathematics anxiety". This test was intended for use in diagnosing math anxiety, testing the efficacy of different math anxiety treatment approaches and possibly designing an anxiety hierarchy to be used in desensitization treatments. The MARS test is of interest to those in counseling psychology and the test is used profusely in math anxiety research. It is available in several versions of varying lengths and is considered psychometrically sound. Other tests are often given to measure different dimensionalities of math anxiety, such as Elizabeth Fennema and Julia Sherman's Fennema-Sherman Mathematics Attitudes Scales (FSMAS). The FSMAS evaluates nine specific domains using Likert-type scales: attitude toward success, mathematics as a male domain, mother's attitude, father's attitude, teacher's attitude, confidence in learning mathematics, mathematics anxiety, affectance motivation and mathematics usefulness. Despite the introduction of newer instrumentation, the use of the MARS test appears to be the educational standard for measuring math anxiety due to its specificity and prolific use.

Math and culture

While there are overarching similarities concerning the acquisition of math skills, researchers have shown that children's mathematical abilities differ across countries. In Canada, students score substantially lower in math problem-solving and operations than students in Korea, India and Singapore. Researchers have conducted thorough comparisons between countries and determined that in some areas, such as Taiwan and Japan, parents place more emphasis on effort rather than one's innate intellectual ability in school success. By placing a higher emphasis on effort rather than one's innate intellectual ability, they are helping their child develop a growth mindset. People who develop a growth mindset believe that everyone has the ability to grow their intellectual ability, learn from their mistakes, and become more resilient learners. Rather than getting stuck on a problem and giving up, students with a growth mindset try other strategies to solve the problem. A growth mindset can benefit everyone, not just people trying to solve math computations. Moreover, parents in these countries tend to set higher expectations and standards for their children. In turn, students spend more time on homework and value homework more than American children.

In addition, researchers Jennifer L. Brown et al. shows that difference in level of mathematical anxiety among different countries may result from varying degrees of the courses. In the same culture, there is little difference in anxiety scale that is associated with gender, while the anxiety is more related with its type. Samples show greater degree of anxiety at subscale.

MEA (Mathematical Evaluation Anxiety) compared with LMA (Learning Mathematical Anxiety).

Math and gender

Another difference in mathematic abilities often explored in research concerns gender disparities. There has been research examining gender differences in performance on standardized tests across various countries. Beller and Gafni's have shown that children at approximately nine years of age do not show consistent gender differences in relation to math skills. However, in 17 out of the 20 countries examined in this study, 13-year-old boys tended to score higher than girls. Moreover, mathematics is often labeled as a masculine ability; as a result, girls often have low confidence in their math capabilities. These gender stereotypes can reinforce low confidence in girls and can cause math anxiety as research has shown that performance on standardized math tests is affected by one's confidence. As a result, educators have been trying to abolish this stereotype by fostering confidence in math in all students in order to avoid math anxiety.

While on the other hand, results obtained by Monika Szczygiel show that girls have a higher level of anxiety on testing and in total, although there is no gender difference in general learning math anxiety. Therefore, the gender gap in math anxiety may result from the type of anxiety. Tests triggers greater anxiety in girls compared with boys, but they feel same level of anxiety learning math.

Math pedagogy

The principles of mathematics are generally understood at an early age; preschoolers can comprehend the majority of principles underlying counting. By kindergarten, it is common for children to use counting in a more sophisticated manner by adding and subtracting numbers. While kindergarteners tend to use their fingers to count, this habit is soon abandoned and replaced with a more refined and efficient strategy; children begin to perform addition and subtraction mentally at approximately six years of age. When children reach approximately eight years of age, they can retrieve answers to mathematical equations from memory. With proper instruction, most children acquire these basic mathematical skills and are able to solve more complex mathematical problems with sophisticated training. (Kail & Zolner, 2005).

High-risk teaching styles are often explored to gain a better understanding of math anxiety. Goulding, Rowland, and Barber (2002) suggest that there are linkages between a teacher's lack of subject knowledge and the ability to plan teaching material effectively. These findings suggest that teachers who do not have a sufficient background in mathematics may struggle with the development of comprehensive lesson plans for their students. Similarly, Laturner's research (2002) shows that teachers with certification in math are more likely to be passionate and committed to teaching math than those without certification. However, those without certification vary in their commitment to the profession depending on coursework preparation.

A study conducted by Kawakami, Steele, Cifa, Phills, and Dovidio (2008) examined attitudes towards math and behavior during math examinations. The study examined the effect of extensive training in teaching women how to approach math. The results showed that women who were trained to approach rather than avoid math showed a positive implicit attitude towards math. These findings were only consistent with women low in initial identification with math. This study was replicated with women who were either encouraged to approach math or who received neutral training. Results were consistent and demonstrated that women taught to approach math had an implicit positive attitude and completed more math problems than women taught to approach math in a neutral manner.

Johns, Schmader, and Martens (2005) conducted a study in which they examined the effect of teaching stereotype threat as a means of improving women's math performance. The researchers concluded that women tended to perform worse than men when problems were described as math equations. However, women did not differ from men when the test sequence was described as problem-solving or in a condition in which they learned about stereotype threats. This research has practical implications. The results suggested that teaching students about stereotype threat could offer a practical means of reducing its detrimental effects and lead to an improvement in a girl's performance and mathematical ability, leading the researchers to conclude that educating female teachers about stereotype threat can reduce its negative effects in the classroom.

Common beliefs

According to Margaret Murray, female mathematicians in the United States have almost always been a minority. Although the exact difference fluctuates with the times, as she has explored in her book Women Becoming Mathematicians: Creating a Professional Identity in Post-World War II America, "Since 1980, women have earned over 17 percent of the mathematics doctorates.... [In The United States]". The trends in gender are by no means clear, but perhaps parity is still a way to go. Since 1995, studies have shown that the gender gap favored males in most mathematical standardized testing as boys outperformed girls in 15 out of 28 countries. However, as of 2015 the gender gap has almost been reversed, showing an increase in female presence. This is being caused by women's steadily increasing performance on math and science testing and enrollment, but also by males' losing ground at the same time. This role reversal can largely be associated with the gender normative stereotypes that are found in the Science, technology, engineering, and mathematics (STEM) field, deeming "who math is for" and "who STEM careers are for". These stereotypes can fuel mathematical anxiety that is already present among young female populations. Thus parity will take more work to overcome mathematical anxiety and this is one reason why women in mathematics are role models for younger women.

In schools

According to John Taylor Gatto, as expounded in several lengthy books, modern Western schools were deliberately designed during the late 19th century to create an environment which is ideal for fostering fear and anxiety, and for preventing or delaying learning. Many who are sympathetic to Gatto's thesis regard his position as unnecessarily extreme. Diane Ravitch, former assistant secretary of education during the George H. W. Bush administration, agrees with Gatto up to a point, conceding that there is an element of social engineering (i.e. the manufacture of the compliant citizenry) in the construction of the American education system, which prioritizes conformance over learning.

The role of attachment has been suggested as having an impact in the development of the anxiety. Children with an insecure attachment style were more likely to demonstrate the anxiety.

Math used to be taught as a right and wrong subject and as if getting the right answer were paramount. In contrast to most subjects, mathematics problems almost always have a right answer but there are many ways to obtain the answer. Previously, the subject was often taught as if there were a right way to solve the problem and any other approaches would be wrong, even if students got the right answer. Thankfully, mathematics has evolved and so has teaching it. Students used to have higher anxiety because of the way math was taught. "Teachers benefit children most when they encourage them to share their thinking process and justify their answers out loud or in writing as they perform math operations. ... With less of an emphasis on right or wrong and more of an emphasis on process, teachers can help alleviate students' anxiety about math".

Theoretical "solutions"

There have been many studies that show parent involvement in developing a child's educational processes is essential. A student's success in school is increased if their parents are involved in their education both at home and school (Henderson & Map, 2002). As a result, one of the easiest ways to reduce math anxiety is for the parent to be more involved in their child's education. In addition, research has shown that a parent's perception on mathematics influences their child's perception and achievement in mathematics (Yee & Eccles, 1988).

Furthermore, studies by Herbert P. Ginsburg, Columbia University, show the influence of parents' and teachers' attitudes on "'the child's expectations in that area of learning.'... It is less the actual teaching and more the attitude and expectations of the teacher or parents that count". This is further supported by a survey of Montgomery County, Maryland students who "pointed to their parents as the primary force behind the interest in mathematics".

Claudia Zaslavsky contends that math has two components. The first component is to calculate the answer. This component also has two subcomponents, namely the answer and the process or method used to determine the answer. Focusing more on the process or method enables students to make mistakes, but not 'fail at math'. The second component is to understand the mathematical concepts that underlay the problem being studied. "... and in this respect studying mathematics is much more like studying, say, music or painting than it is like studying history or biology."

Amongst others supporting this viewpoint is the work of Eugene Geist. Geist's recommendations include focusing on the concepts rather than the right answer and letting students work on their own and discuss their solutions before the answer is given.

National Council of Teachers of Mathematics (NCTM) (1989, 1995b) suggestions for teachers seeking to prevent math anxiety include:

  • Accommodating for different learning styles
  • Creating a variety of testing environments
  • Designing positive experiences in math classes
  • Refraining from tying self-esteem to success with math
  • Emphasizing that everyone makes mistakes in mathematics
  • Making math relevant
  • Letting students have some input into their own evaluations
  • Allowing for different social approaches to learning mathematics
  • Emphasizing the importance of original, quality thinking rather than rote manipulation of formulas

Hackworth (1992) suggests that the following activities can help students in reducing and mitigating mathematical anxiety:

  • Discuss and write about math feelings;
  • Become acquainted with good math instruction, as well as study techniques;
  • Recognize what type of information needs to be learned;
  • Be an active learner, and create problem-solving techniques;
  • Evaluate your own learning;
  • Develop calming/positive ways to deal with fear of math, including visualization, positive messages, relaxation techniques, frustration breaks;
  • Use gradual, repeated success to build math confidence in students

B R Alimin and D B Widjajanti (2019) recommend teachers:

  • Never make students embarrassed in front of the class
  • Build harmony and friendship between teachers and students
  • Give hints to students so that they can learn from mistakes
  • Encourage students not to give up when they encounter with challenges
  • Teach students to help each other working on math problem

Several studies have shown that relaxation techniques can be used to help alleviate anxiety related to mathematics. In her workbook Conquering Math Anxiety, Cynthia Arem offers specific strategies to reduce math avoidance and anxiety. One strategy she advocates for is relaxation exercises and indicates that by practicing relaxation techniques on a regular basis for 10–20 minutes students can significantly reduce their anxiety.

Dr. Edmundo Jacobson's Progressive Muscle Relaxation taken from the book Mental Toughness Training for Sports, Loehr (1986) can be used in a modified form to reduce anxiety as posted on the website HypnoGenesis.

According to Mina Bazargan and Mehdi Amiri, Modular Cognitive Behavior Therapy (MCBT) can reduce the level of mathematical anxiety and increase students' self-esteem.

Visualization has also been used effectively to help reduce math anxiety. Arem has a chapter that deals with reducing test anxiety and advocates the use of visualization. In her chapter titled Conquer Test Anxiety (Chapter 9) she has specific exercises devoted to visualization techniques to help the student feel calm and confident during testing.

Studies have shown students learn best when they are active rather than passive learners.

The theory of multiple intelligences suggests that there is a need for addressing different learning styles. Math lessons can be tailored for visual/spatial, logical/mathematics, musical, auditory, body/kinesthetic, interpersonal and intrapersonal and verbal/linguistic learning styles. This theory of learning styles has never been demonstrated to be true in controlled trials. Studies show no evidence to support tailoring lessons to an individual students learning style to be beneficial.

New concepts can be taught through play acting, cooperative groups, visual aids, hands on activities or information technology. To help with learning statistics, there are many applets found on the Internet that help students learn about many things from probability distributions to linear regression. These applets are commonly used in introductory statistics classes, as many students benefit from using them.

Active learners ask critical questions, such as: Why do we do it this way, and not that way? Some teachers may find these questions annoying or difficult to answer, and indeed may have been trained to respond to such questions with hostility and contempt, designed to instill fear. Better teachers respond eagerly to these questions, and use them to help the students deepen their understanding by examining alternative methods so the students can choose for themselves which method they prefer. This process can result in meaningful class discussions. Talking is the way in which students increase their understanding and command of math. Teachers can give students insight as to why they learn certain content by asking students questions such as "what purpose is served by solving this problem?" and "why are we being asked to learn this?"

Reflective journals help students develop metacognitive skills by having them think about their understanding. According to Pugalee, writing helps students organize their thinking which helps them better understand mathematics. Moreover, writing in mathematics classes helps students problem solve and improve mathematical reasoning. When students know how to use mathematical reasoning, they are less anxious about solving problems.

Children learn best when math is taught in a way that is relevant to their everyday lives. Children enjoy experimenting. To learn mathematics in any depth, students should be engaged in exploring, conjecturing, and thinking, as well as in rote learning of rules and procedures.


Inequality (mathematics)

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