Teachers are responsible for managing and monitoring student learning.
Teachers think systematically about their practice and learn from experience.
Teachers are members of learning communities.
To promote understanding, explicit instruction in metacognition should be integrated into the curriculum. Thus, instruction should create tasks and conditions under which student thinking can be revealed so that students, with their teachers, can review, assess, and reflect upon what they have learned and how. Additionally, teachers should make their reasoning and problem-solving strategies visible to students whenever possible (Collins and Smith, 1982; Lester et al., 1994; Schoenfeld, 1983, 1985).
Effective instruction in advanced courses should involve building and nurturing a community of learners. A community of learners encourages students to take academic risks by providing opportunities for them to make mistakes, obtain feedback, and revise their thinking while learning from others with whom they are engaged in inquiry and cooperative problem-solving activities.
To nurture the capacity of students to generalize and transfer their learning to new problems, teachers must help students explore old understandings in new ways. To this end, teachers must draw out misconceptions in order to challenge and displace them (Blumenfeld, Marx, Patrick, Krajcik, and Soloway, 1997; Caravita and Hallden, 1994; Jones, Rua, and Carter, 1998; NRC, 2000b; Pearsall, Skipper, and Mintzes, 1997;).
Since intrinsic motivation is self-sustaining, instruction should be planned so as to maximize the opportunity for developing a strong intrinsic motivation to learn. Students benefit when they can experience success and develop the confidence of a successful learner—one who has the tools to ask relevant questions, formulate problems and reframe issues, and assess his or her own knowledge and understanding (Alaiyemola, Jegede, and Okebukola, 1990; Stipek, 1998). Table 7-2 illustrates the emphases of instructional practices to support learning with understanding.
Educational assessments can be designed for any number of purposes, from conducting large-scale evaluations of multiple components of educational programs to measuring individual students’ mastery of a specified skill. Understanding assessment results requires that the user draw inferences from available data and observations that are supported by the assessment. Three key concepts related to assessments—reliability, validity, and fairness—underlie a user’s ability to draw appropriate inferences from the
"Subnet" redirects here. For subnets in the mathematics of topology, see subnet (mathematics).
A subnetwork or subnet is a logical subdivision of an IP network. The practice of dividing a network into two or more networks is called subnetting.
Computers that belong to a subnet are addressed with a common, identical, most-significant bit-group in their IP address. This results in the logical division of an IP address into two fields, a network number or routing prefix and the rest field or host identifier. The rest field is an identifier for a specific host or network interface.
The routing prefix may be expressed in Classless Inter-Domain Routing (CIDR) notation written as the first address of a network, followed by a slash character (/), and ending with the bit-length of the prefix. For example, 192.168.1.0/24 is the prefix of the Internet Protocol version 4 network starting at the given address, having 24 bits allocated for the network prefix, and the remaining 8 bits reserved for host addressing. The IPv6 address specification 2001:db8::/32 is a large address block with 296 addresses, having a 32-bit routing prefix.
For IPv4, a network may also be characterized by its subnet mask or netmask, which is the bitmask that when applied by a bitwise AND operation to any IP address in the network, yields the routing prefix. Subnet masks are also expressed in dot-decimal notation like an address. For example, 255.255.255.0 is the subnet mask for the 192.168.1.0/24 prefix.
Traffic is exchanged between subnetworks through routers when the routing prefixes of the source address and the destination address differ. A router serves as a logical or physical boundary between the subnets.
The benefits of subnetting an existing network vary with each deployment scenario. In the address allocation architecture of the Internet using CIDR and in large organizations, it is necessary to allocate address space efficiently. Subnetting may also enhance routing efficiency, or have advantages in network management when subnetworks are administratively controlled by different entities in a larger organization. Subnets may be arranged logically in a hierarchical architecture, partitioning an organization's network address space into a tree-like routing structure.
Network addressing and routing
Computers participating in a network such as the Internet each have at least one network address. Usually this address is unique to each device and can either be configured automatically with the Dynamic Host Configuration Protocol (DHCP) by a network server, manually by an administrator, or automatically by stateless address autoconfiguration.
An address fulfills the functions of identifying the host and locating it on the network. The most common network addressing architecture is Internet Protocol version 4 (IPv4), but its successor, IPv6, has been increasingly deployed since approximately 2006. An IPv4 address consists of 32 bits, for readability written in a form consisting of four decimal octets separated by dots, called dot-decimal notation. An IPv6 address consists of 128 bits written in a hexadecimal notation and groupings of 16 bits, called hextets, separated by colons. An IP address is divided into two logical parts, the network prefix and the host identifier. All hosts on a subnetwork have the same network prefix. This prefix occupies the most-significant bits of the address. The number of bits allocated within a network to the prefix may vary between subnets, depending on the network architecture. The host identifier is a unique local identification and is either a host number on the local network or an interface identifier.
This addressing structure permits the selective routing of IP packets across multiple networks via special gateway computers, called routers, to a destination host if the network prefixes of origination and destination hosts differ, or sent directly to a target host on the local network if they are the same. Routers constitute logical or physical borders between the subnets, and manage traffic between them. Each subnet is served by a designated default router, but may consist internally of multiple physical Ethernet segments interconnected by network switches.
The routing prefix of an address is identified by the subnet mask, written in the same form used for IP addresses. For example, the subnet mask for a routing prefix that is composed of the most-significant 24 bits of an IPv4 address is written as 255.255.255.0.
The modern standard form of specification of the network prefix is CIDR notation, used for both IPv4 and IPv6. It counts the number of bits in the prefix and appends that number to the address after a slash (/) character separator. This notation was introduced with Classless Inter-Domain Routing (CIDR) in RFC 4632. In IPv6 this is the only acceptable form to denote network or routing prefixes.
- 192.168.0.0, subnet mask 255.255.255.0 is written as 192.168.0.0/24
- In IPv6, 2001:db8::/32 designates the address 2001:db8:: and its network prefix consisting of the most significant 32 bits.
In classful networking in IPv4, prior to the introduction of CIDR, the network prefix could be directly obtained from the IP address, based on its highest order bit sequence. This determined the class (A, B, C) of the address and therefore the subnet mask. Since the introduction of CIDR, however, assignment of an IP address to a network interface requires two parameters, the address and its subnet mask.
In IPv4, on-link determination for an IP address is given simply by the address and subnet mask configuration, as the address cannot be disassociated from the on-link prefix. For IPv6, however, on-link determination is different in detail and requires the Neighbor Discovery Protocol (NDP). IPv6 address assignment to an interface carries no requirement of a matching on-link prefix and vice versa, with the exception of link-local addresses.
While subnetting may improve network performance in an organizational network, it increases routing complexity, since each locally connected subnet must be represented by a separate entry in the routing tables of each connected router. However, by careful design of the network, routes to collections of more distant subnets within the branches of a tree-hierarchy can be aggregated by single routes. Variable-length subnet masking (VLSM) functionality in commercial routers made the introduction of CIDR seamless across the Internet and in enterprise networks.
Internet Protocol version 4
See also: IPv4 subnetting reference
Determining the network prefix
An IPv4 subnet mask consists of 32 bits, a sequence of ones (1) followed by a block of zeros (0). The trailing block of zeros designates that part as being the host identifier.
The following example shows the separation of the network prefix and the host identifier from an address (192.168.5.130) and its associated /24 subnet mask (255.255.255.0). The operation is visualized in a table using binary address formats.
|Binary form||Dot-decimal notation|
The result of the bitwise AND operation of IP address and the subnet mask is the network prefix 192.168.5.0. The host part, which is 130, is derived by the bitwise AND operation of the address and the one's complement of the subnet mask.
Subnetting is the process of designating some high-order bits from the host part as part of the network prefix and adjusting the subnet mask appropriately. This divides a network into smaller subnets. The following diagram modifies the example by moving 2 bits from the host part to the network prefix to form four smaller subnets one quarter the previous size:
|Binary form||Dot-decimal notation|
Special addresses and subnets
Internet Protocol version 4 uses specially designated address formats to facilitate recognition of special address functionality. The first and the last subnets obtained by subnetting have traditionally had a special designation and, early on, special usage implications. In addition, IPv4 uses the all ones host address, i.e. the last address within a network, for broadcast transmission to all hosts on the link.
Subnet zero and the all-ones subnet
The first subnet obtained from subnetting has all bits in the subnet bit group set to zero (0). It is therefore called subnet zero. The last subnet obtained from subnetting has all bits in the subnet bit group set to one (1). It is therefore called the all-ones subnet.
The IETF originally discouraged the production use of these two subnets due to possible confusion of having a network and subnet with the same address. The practice of avoiding subnet zero and the all-ones subnet was declared obsolete in 1995 by RFC 1878, an informational, but now historical document.
Subnet and host counts
The number of subnetworks available, and the number of possible hosts in a network may be readily calculated. In the example (above) two bits were borrowed to create subnetworks, thus creating 4 (22) possible subnets.
|Network||Network (binary)||Broadcast address|
The RFC 950 specification recommended reserving the subnet values consisting of all zeros (see above) and all ones (broadcast), reducing the number of available subnets by two. However, due to the inefficiencies introduced by this convention it was abandoned for use on the public Internet, and is only relevant when dealing with legacy equipment that does not implement CIDR. The only reason not to use the all-zeroes subnet is that it is ambiguous when the prefix length is not available. RFC 950 itself did not make the use of the zero subnet illegal; it was however considered best practice by engineers.
CIDR-compliant routing protocols transmit both length and suffix. RFC 1878 provides a subnetting table with examples.
The remaining bits after the subnet bits are used for addressing hosts within the subnet. In the above example the subnet mask consists of 26 bits, leaving 6 bits for the host identifier. This allows for 62 host combinations (26−2).
The all-zeros value and all-ones values are reserved for the network address and broadcast address respectively. In systems that can handle CIDR a count of two is therefore subtracted from the host availability, rather than the subnet availability, making all 2n subnets available and removing a need to subtract two subnets.
For example, under CIDR /28 all 16 subnets are usable. Each broadcast, i.e. .15, .31, …, .255 comes off the client count, not the network, thus making the last subnet also usable.
In general the number of available hosts on a subnet is 2h−2, where h is the number of bits used for the host portion of the address. The number of available subnets is 2n, where n is the number of bits used for the network portion of the address. This is the RFC 1878 standard used by the IETF, the IEEE and COMPTIA.
RFC 3021 specifies an exception to this rule for 31-bit subnet masks, which means the host identifier is only one bit long for two permissible addresses. In such networks, usually point-to-point links, only two hosts (the end points) may be connected and a specification of network and broadcast addresses is not necessary.
A /24 network may be divided into the following subnets by increasing the subnet mask successively by one bit. This affects the total number of hosts that can be addressed in the /24 network (last column).
|Prefix size||Subnet mask||Available|
*only applicable for point-to-point links
Internet Protocol version 6
See also: IPv6 subnetting reference
The design of the IPv6 address space differs significantly from IPv4. The primary reason for subnetting in IPv4 is to improve efficiency in the utilization of the relatively small address space available, particularly to enterprises. No such limitations exist in IPv6, as the large address space available, even to end-users, is not a limiting factor.
An RFC 4291 compliant subnet always uses IPv6 addresses with 64 bits for the host portion. It therefore has a /64 routing prefix (128−64 = the 64 most significant bits). Although it is technically possible to use smaller subnets, they are impractical for local area networks based on Ethernet technology, because 64 bits are required for stateless address auto configuration. The Internet Engineering Task Force recommends the use of /127 subnets for point-to-point links, which consist of only two hosts.
IPv6 does not implement special address formats for broadcast traffic or network numbers, and thus all addresses in a subnet are valid host addresses. The all-zeroes address is reserved as the Subnet-Router anycast address.
The recommended allocation for an IPv6 customer site was an address space with a 48-bit (/48) prefix. However, this recommendation was revised to encourage smaller blocks, for example using 56-bit prefixes. Another common allocation is a /64 prefix for a residential customer network.
Subnetting in IPv6 is based on the concepts of variable-length subnet masking (VLSM) and the Classless Inter-Domain Routing methodology. It is used to route traffic between the global allocation spaces and within customer networks between subnets and the Internet at large.
- ^Jeffrey Mogul; Jon Postel (August 1985), Internet Standard Subnetting Procedure, IETF, pp. 1, 16, RFC 950
- ^RFC 1122, Requirements for Internet Hosts -- Communication Layers, Section 3.3.1, R. Braden, IETF (October 1989)
- ^RFC 4861, Neighbor Discovery for IP version 6 (IPv6), T. Narten et al. (September 2007)
- ^RFC 5942, IPv6 Subnet Model: The Relationship between Links and Subnet Prefixes, H. Singh, W. Beebee, E. Nordmark (July 2010)
- ^"Document ID 13711 - Subnet Zero and the All-Ones Subnet". Cisco Systems. 2005-08-10. Retrieved 2010-04-25.
- ^"Document ID 13711 - Subnet Zero and the All-Ones Subnet". Cisco Systems. 2005-08-10. Retrieved 2010-04-23.
- ^"Document ID 13711 - Subnet Zero and the All-Ones Subnet". Cisco Systems. 2005-08-10. Retrieved 2010-04-23.
- ^Jeffrey Mogul; Jon Postel (August 1985), Internet Standard Subnetting Procedure, IETF, p. 6, RFC 950,
- ^RFC 1878, Troy Pummill; Bill Manning (December 1995). "Variable Length Subnet Table For IPv4". IETF. RFC 1878. (Informational RFC, demoted to category Historic)
- ^RFC 4291, "IP Version 6 Addressing Architecture - section 2.5.1. Interface Identifiers". IETF. Retrieved 2011-02-13.
- ^RFC 4862, "IPv6 Stateless Address Autoconfiguration - section 5.5.3.(d) Router Advertisement Processing". IETF. Retrieved 2011-02-13.
- ^RFC 2464, "Transmission of IPv6 Packets over Ethernet Networks - section 4 Stateless Autoconfiguration". IETF.
- ^RFC 6164, "Using 127-Bit IPv6 Prefixes on Inter-Router Links". IETF.
- ^RFC 6547, "RFC 3627 to Historic Status". IETF.
- ^RFC 4291, "IP Version 6 Addressing Architecture - section 2 IPv6 Addressing". IETF.
- ^RFC 4291, "IP Version 6 Addressing Architecture - section 2.6.1 Required Anycast Address". IETF.
- ^"IPv6 Addressing Plans". ARIN IPv6 Wiki. Retrieved 2010-04-25.
- ^"IPv6 Address Assignment to End Sites". IETF. Retrieved 11 November 2013.
- RFC 1812 Requirements for IPv4 Routers
- RFC 917 Utility of subnets of Internet networks
- RFC 1101 DNS Encodings of Network Names and Other Type
- Blank, Andrew G. TCP/IP Foundations Technology Fundamentals for IT Success. San Francisco, London: Sybex, Copyright 2004.
- Lammle, Todd. CCNA Cisco Certified Network Associate Study Guide 5th Edition. San Francisco, London: Sybex, Copyright 2005.
- Groth, David and Toby Skandier. Network + Study Guide, 4th Edition. San Francisco, London: Wiley Publishing, Inc., Copyright 2005.
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