Formative assessment

From Wikipedia, the free encyclopedia
Jump to: navigation, search

Formative assessment, including diagnostic testing, is a range of formal and informal assessment procedures conducted by teachers during the learning process in order to modify teaching and learning activities to improve student attainment.[1] It typically involves qualitative feedback (rather than scores) for both student and teacher that focuses on the details of content and performance.[2] It is commonly contrasted with summative assessment, which seeks to monitor educational outcomes, often for purposes of external accountability.[3]


Practice in a classroom is formative to the extent that evidence about student achievement is elicited, interpreted, and used by teachers, learners, or their peers, to make decisions about the next steps in instruction that are likely to be better, or better founded, than the decisions they would have taken in the absence of the evidence that was elicited.[4]

Origin of the term[edit]

Michael Scriven coined the terms formative and summative evaluation in 1967, and emphasized their differences both in terms of the goals of the information they seek and how the information is used.[5] For Scriven, formative evaluation gathered information to assess the effectiveness of a curriculum and guide school system choices as to which curriculum to adopt and how to improve it.[6] Benjamin Bloom took up the term in 1968 in the book Learning for Mastery to consider formative assessment as a tool for improving the teaching-learning process for students.[7] His subsequent 1971 book Handbook of Formative and Summative Evaluation, written with Thomas Hasting and George Madaus, showed how formative assessments could be linked to instructional units in a variety of content areas.[8] It is this approach that reflects the generally accepted meaning of the term today.[9] For both Scriven and Bloom, an assessment, whatever its other uses, is only formative if it is used to alter subsequent educational decisions.[6] Subsequently, however, Black and Wiliam have suggested this definition is too restrictive, since formative assessments may be used to provide evidence that the intended course of action was indeed appropriate. They propose that:

Practice in a classroom is formative to the extent that evidence about student achievement is elicited, interpreted, and used by teachers, learners, or their peers, to make decisions about the next steps in instruction that are likely to be better, or better founded, than the decisions they would have taken in the absence of the evidence that was elicited.[10]

Formative assessment vs. summative assessment[edit]

The type of assessment that people may be more familiar with is Summative assessment. The table below [11] shows some basic differences between the two types of assessment.

Summative Assessment Formative Assessment
Time At the end of a learning activity During a learning activity
Goal To make a decision To improve learning
Feedback Final judgement Return to material
Frame of Reference Sometimes normative (comparing each student

against all others); sometimes criterion

Always criterion (evaluating students according to the same criteria)

Rationale and practice[edit]

Formative assessment serves several purposes:

  • to provide feedback for teachers to modify subsequent learning activities and experiences;[2]
  • to identify and remediate group or individual deficiencies;[2]
  • to move focus away from achieving grades and onto learning processes, in order to increase self efficacy and reduce the negative impact of extrinsic motivation;[3]
  • to improve students' metacognitive awareness of how they learn.[3]
  • "frequent, ongoing assessment allows both for fine-tuning of instruction and student focus on progress."[12]

Characteristics of Formative Assessment:

According to Harlen and James (1997) formative assessment: - is essentially positive in intent, in that it is directed towards promoting learning; it is therefore part of teaching;

- it takes into account the progress of each individual, the effort put in and other aspects of learning which may be unspecified in the curriculum; in other words, it is not purely criterion-referenced;

-it has to take into account several instances in which certain skills and ideas are used and there will be inconsistencies as well as patterns in behaviour; such inconsistencies would be 'error' in summative evaluation, but in formative evaluation they provide diagnostic information;

- validity and usefulness are paramount in formative assessment and should take precedence over concerns for reliability;

- even more than assessment for other purposes, formative assessment requires that pupils have a central part in it; pupils have to be active in their own learning (teachers cannot learn for them) and unless they come to understand their strengths and weaknesses, and how they might deal with them, they will not make progress.[13]

Feedback is the central function of formative assessment. It typically involves a focus on the detailed content of what is being learnt,[2] rather than simply a test score or other measurement of how far a student is falling short of the expected standard.[14] Nicol and Macfarlane-Dick, synthesising from the literature, list seven principles of good feedback practice:

  1. It clarifies what good performance is (goals, criteria, expected standards);
  2. It facilitates the development of self-assessment in learning;
  3. It provides high quality information to students about their learning;
  4. It encourages teacher and peer dialogue around learning;
  5. It encourages positive motivational beliefs and self-esteem;
  6. It provides opportunities to close the gap between current and desired performance;
  7. It provides information to teachers that can be used to help shape teaching.[14][15]

Examples of formative assessment[edit]

The time between formative assessment and adjustments to learning can be a matter of seconds or a matter of months.[6] Some examples of formative assessment are:

  • A language teacher asks students to choose the best thesis statement from a selection; if all choose correctly she moves on; if only some do she may initiate a class discussion; if most answer incorrectly then she may review the work on thesis statements.[6]
  • A teacher asks her students to write down, in a brainstorm activity, all they know about how hot-air balloons work so that she can discover what students already know about the area of science she is intending to teach.[16]
  • A science supervisor looks at the previous year's student test results to help plan teacher workshops during the summer vacation, to address areas of weakness in student performance.[6]
  • A teacher documents student work and student conferences to help plan authentic activities to meet student needs [17]
  • Students could be given each one of three "traffic cards" to indicate the level at which they are understanding a concept during a lesson. Green means that the student is understanding the concept and the teacher can move on, yellow indicates that the instructor should slow down because the student is only somewhat understanding the concept, and red indicates that the student wishes that the teacher stops and explains a specific concept more clearly because they are not understanding it.[18]


Meta-analysis of studies into formative assessment have indicated significant learning gains where formative assessment is used, across all content areas, knowledge and skill types, and levels of education.[19] Educational researcher Robert J. Marzano states:

Recall the finding from Black and Wiliam’s (1998) synthesis of more than 250 studies that formative assessments, as opposed to summative ones, produce the more powerful effect on student learning. In his review of the research, Terrance Crooks (1988) reports that effects sizes for summative assessments are consistently lower than effect sizes for formative assessments. In short, it is formative assessment that has a strong research base supporting its impact on learning.[20]:9

While empirical evidence has shown the substantial impact formative assessment has in raising student achievement,[19] it is also “recognized as one of the most powerful ways to enhance student motivation.”[21] Believing in their ability to learn, contributing learning successes to individual efforts and abilities, emphasizing progress toward learning goals rather than letter grades, and evaluating “the nature of their thinking to identify strategies that improve understanding”[22] are all manners in which motivation is enhanced through an effective use of formative assessment.[21] However, for these gains to become evident formative assessment must (1) Clarify and share learning goals and success criteria; (2) Create effective classroom discussions and other tasks which demonstrate evidence of student understanding; (3) provide feedback which can and will be acted upon; (4) allow students to become instructional resources for one another; and (5) stimulate students to become owners of their own learning.[23]

Some researchers have concluded that standards-based assessments may be an effective way to “prescribe instruction and to ensure that no child is left behind”.[20]:13

The strongest evidence of improved learning gains comes from short-cycle (over seconds or minutes within a single lesson) formative assessment, and medium to long-term assessment where assessment is used to change the teacher's regular classroom practice.[6]


Understanding goals for learning[edit]

It is important for students to understand the goals and the criteria for success when learning in the classroom. Often teachers will introduce learning goals to their students before a lesson, but will not do an effective job in distinguishing between the end goals and what the students will be doing to achieve those goals.[18] "When teachers start from what it is they want students to know and design their instruction backward from that goal, then instruction is far more likely to be effective".[24] In a study done by Gray and Tall,[25] they found that 72 students between the ages of 7 and 13 had different experiences when learning in mathematics. The study showed that higher achieving students looked over mathematical ambiguities, while the lower achieving students tended to get stuck on these misunderstandings. An example of this [18] can be seen in the number . Although it is not explicitly stated, the operation between these two numbers is addition. If we look at the number , here the implied operation between and is multiplication. Finally if we take a look at the number , there is a completely different operation between the 6 and 1. The study showed that higher achieving students were able to look past this while other students were not.

Another study done by White and Frederiksen [26] showed that when twelve 7th grade science classrooms were given time to reflect on what they deemed to be quality work, and how they thought they would be evaluated on their work, the gap between the high achieving students and the low achieving students was decreased.

One way to help with this is to offer students different examples of other students' work so they can evaluate the different pieces. By examining the different levels of work, students can start to differentiate between superior and inferior work.


There has been extensive research done on studying how students are affected by feedback. Kluger and DeNisi (1996) [27] reviewed over three thousand reports on feedback in schools, universities, and the workplace. Of these, only 131 of them were found to be scientifically rigorous and of those, 50 of the studies shows that feedback actually has negative effects on its recipients. This is due to the fact that feedback is often "ego-involving",[18] that is the feedback focuses on the individual student rather than the quality of the student's work. Feedback is often given in the form of some numerical or letter grade and that perpetuates students being compared to their peers. The studies previously mentioned showed that the most effective feedback for students is when they are not only told in which areas they need to improve, but also how to go about improving it.

It has been shown that leaving comments alongside grades is just as ineffective as giving solely a numerical/letter grade (Butler 1987, 1989).[28] This is due to the fact that students tend to look at their grade and disregard any comments that are given to them. The next thing students tend to do is to ask other students in the class for their grade, and they compare the grade to their own grade.


Questioning is an important part of the learning process and an even more important part is asking the right types of questions. Questions that promote discussion and student reflection make it easier for students to go on the right path to end up completing their learning goals. Here are some types of questions that are good to ask students:

  • What do you think of [student]'s answer?
  • What can we add to [student]'s explanation?
  • [Student] said this and [student] said that, but how can we combine these explanations into a complete answer?

Wait time[edit]

Wait time is the amount of time that is given to someone to answer a question that was posed. Rowe [29] went on to look at the outcomes of having longer wait times for students. These included:

  • answers were longer;
  • failure to respond decreased;
  • responses from students were more confident;
  • students challenged and/or improved the answers of other students;
  • more alternative explanations were offered.


Having students assess each other's work has been studied to have numerous benefits:[30]

  • When students know that they are going to be assessed by their peers, they tend to put more attention to detail in their work.
  • Students are able to speak to one another in a language that they are more comfortable with than they would be with an instructor. The insight of a fellow student might be more relatable than that of a teacher.
  • Students tend to accept constructive criticism more from a fellow student than from an instructor.
  • While students are in the process of peer-assessment, a teacher can more easily take command of the learning going on. The teacher can also stand on the sidelines and watch as the students continue to assess each other's work and may intervene at any time if need be.

In K–12[edit]

Formative assessment is valuable for day-to-day teaching when used to adapt instructional methods to meet students’ needs and for monitoring student progress toward learning goals. Further, it helps students monitor their own progress as they get feedback from the teacher and/or peers, allowing the opportunity to revise and refine their thinking. Formative assessment is also known as educative assessment, classroom assessment, or assessment for learning.


There are many ways to integrate formative assessment into K–12 classrooms. Although the key concepts of formative assessment such as constant feedback, modifying the instruction, and information about students' progress do not vary among different disciplines or levels, the methods or strategies may differ. For example, researchers developed generative activities (Stroup et al., 2004)[31] and model-eliciting activities (Lesh et al., 2000)[32] that can be used as formative assessment tools in mathematics and science classrooms. Others developed strategies computer-supported collaborative learning environments (Wang et al., 2004b).[33] More information about implication of formative assessment in specific areas is given below.


Formative assessment, or diagnostic testing as the National Board of Professional Teaching Standards argues, serves to create effective teaching curricula and classroom-specific evaluations.[34] By focusing on student-centered activities, a student is able to relate the material to his life and experiences. Students are encouraged to think critically and to develop analytical skills. This type of testing allows for a teacher's lesson plan to be clear, creative, and reflective of the curriculum (T.P Scot et al., 2009).[35]

Based on the Appalachian Education Laboratory (AEL), "diagnostic testing" emphasizes effective teaching practices while "considering learners' experiences and their unique conceptions" (T.P Scot et al., 2009).[36] Furthermore, it provides the framework for "efficient retrieval and application"(T.P Scot et al., 2009).[36] by urging students to take charge of their education. The implications of this type of testing,is developing a knowledgeable student with deep understanding of the information and then be able to account for a students' comprehension on a subject.

Specific applications[edit]

The following are examples of application of formative assessment to content areas:

In math education[edit]

In math education, it is important for teachers to see how their students approach the problems and how much mathematical knowledge and at what level students use when solving the problems. That is, knowing how students think in the process of learning or problem solving makes it possible for teachers to help their students overcome conceptual difficulties and, in turn, improve learning. In that sense, formative assessment is diagnostic. To employ formative assessment in the classrooms, a teacher has to make sure that each student participates in the learning process by expressing their ideas; there is a trustful environment -in which students can provide each other with feedback; s/he (the teacher) provides students with feedback; and the instruction is modified according to students' needs. In math classes, thought revealing activities such as model-eliciting activities (MEAs) and generative activities provide good opportunities for covering these aspects of formative assessment.

Feedback examples[edit]

Here are some examples of possible feedback for students in math education:[18]

  • Student: "I just don't get it." Teacher: "Well, the first part is just like the last problem you did. Then we add one more variable. See if you can find out what it is, and I'll come back in a few minutes."
  • "There are 5 answers here that are incorrect. Try to find them and fix them."
  • "The answer to this question is... Can you find a way to work it out?"
  • "You've used substitution to solve all of these systems of equations. Can you use elimination now to solve them?"

Different approaches for feedback encourage pupils to reflect:[37]

  • "You used two different methods to solve these problems. Can you explain the advantages and disadvantages of each method?"
  • "You seem to have a good understanding of... Can you make up your own more difficult problem?"

Another method has students looking to each other to gain knowledge.

  • "You seem to be confusing sine and cosine. Talk to Katie about the differences with the two."
  • "Compare your work with Ali and write some advice to another student tackling this topic for the first time."

Formative assessment in second/foreign language education[edit]

As an ongoing assessment it focuses on the process, it helps teachers to check the current status of their students’ language ability, that is, they can know what the students know and what the students do not know. It also gives chances to students to participate in modifying or planning the upcoming classes (Bachman & Palmer, 1996).[38] Participation in their learning grows students’ motivation to learn the target language. It also raises students’ awareness on their target languages, which results in resetting their own goals. In consequence, it helps students to achieve their goals successfully as well as teachers be the facilitators to foster students’ target language ability.

In classroom, short quizzes, reflectionals journals, or portfolios could be used as a formative assessment (Cohen, 1994).[39]

Formative assessment in elementary education[edit]

In primary schools, it is used to inform the next steps of learning. Teachers and students both use formative assessments as a tool to make decisions based on data. Formative assessment occurs when teachers feed information back to students in ways that enable the student to learn better, or when students can engage in a similar, self-reflective process. The evidence shows that high quality formative assessment does have a powerful impact on student learning. Black and Wiliam (1998) report that studies of formative assessment show an effect size on standardized tests of between 0.4 and 0.7, larger than most known educational interventions. (The effect size is the ratio of the average improvement in test scores in the innovation to the range of scores of typical groups of pupils on the same tests; Black and Wiliam recognize that standardized tests are very limited measures of learning.) Formative assessment is particularly effective for students who have not done well in school, thus narrowing the gap between low and high achievers while raising overall achievement. Research examined by Black and Wiliam supports the conclusion that summative assessments tend to have a negative effect on student learning.

Activities that can be used as formative assessment tools in mathematics and science classrooms[edit]

Model-eliciting activities (MEAs)[edit]

Model-eliciting activities are based on real-life situations where students, working in small groups, present a mathematical model as a solution to a client’s need (Zawojewski & Carmona, 2001).[40] The problem design enables students to evaluate their solutions according to the needs of a client identified in the problem situation and sustain themselves in productive, progressively effective cycles of conceptualizing and problem solving. Model-eliciting activities (MEAs) are ideally structured to help students build their real-world sense of problem solving towards increasingly powerful mathematical constructs. What is especially useful for mathematics educators and researchers is the capacity of MEAs to make students’ thinking visible through their models and modeling cycles. Teachers do not prompt the use of particular mathematical concepts or their representational counterparts when presenting the problems. Instead, they choose activities that maximize the potential for students to develop the concepts that are the focal point in the curriculum by building on their early and intuitive ideas. The mathematical models emerge from the students’ interactions with the problem situation and learning is assessed via these emergent behaviors.

Generative activities[edit]

In a generative activity, students are asked to come up with outcomes that are mathematically same. Students can arrive at the responses or build responses from this sameness in a wide range of ways. The sameness gives coherence to the task and allows it to be an "organizational unit for performing a specific function." (Stroup et al., 2004)

Other activities can also be used as the means of formative assessment as long as they ensure the participation of every student, make students' thoughts visible to each other and to the teacher, promote feedback to revise and refine thinking. In addition, as a complementary to all of these is to modify and adapt instruction through the information gathered by those activities.

Formative assessment in computer-supported learning[edit]

Many academics are seeking to diversify assessment tasks, broaden the range of skills assessed and provide students with more timely and informative feedback on their progress. Others are wishing to meet student expectations for more flexible delivery and to generate efficiencies in assessment that can ease academic staff workloads. The move to on-line and computer based assessment is a natural outcome of the increasing use of information and communication technologies to enhance learning. As more students seek flexibility in their courses, it seems inevitable there will be growing expectations for flexible assessment as well. When implementing online and computer-based instruction, it is recommended that a structured framework or model be used to guide the assessment.

Formative assessment in UK education[edit]

In the UK education system, formative assessment (or assessment for learning) has been a key aspect of the agenda for personalised learning. The Working Group on 14–19 Reform led by Sir Mike Tomlinson, recommended that assessment of learners be refocused to be more teacher-led and less reliant on external assessment, putting learners at the heart of the assessment process.[41]

The UK government has stated[42] that personalised learning depends on teachers knowing the strengths and weaknesses of individual learners, and that a key means of achieving this is through formative assessment, involving high quality feedback to learners included within every teaching session.[43]

The Assessment Reform Group has set out the following 10 principles for formative assessment.[44]

Learning should:

  • be part of effective planning of teaching and learning
  • focus on how students learning attitude
  • be recognised as central to classroom practice
  • be regarded as a key professional skill for teachers
  • be sensitive and constructive because any assessment has an emotional impact
  • take account of the importance of learner motivation
  • promote commitment to learning goals and a shared understanding of the criteria by which they are assessed
  • enable learners to receive constructive guidance about how to improve
  • develop learners’ capacity for self-assessment so that they can become reflective and self-managing
  • recognise the full range of achievements of all learners

Benefits of formative assessments for teachers (Boston, 2002)[edit]

  • Teachers are able to determine what standards students already know and to what degree.
  • Teachers can decide what minor modifications or major changes in instruction they need to make so that all students can succeed in upcoming instruction and on subsequent assessments.
  • Teachers can create appropriate lessons and activities for groups of learners or individual students.
  • Teachers can inform students about their current progress in order to help them set goals for improvement.[45]

Benefits for students[edit]

  • Students are more motivated to learn.
  • Students take responsibility for their own learning.
  • Students can become users of assessment alongside the teacher.
  • Students learn valuable lifelong skills such as self-evaluation, self-assessment, and goal setting.
  • Students become more adept at self-assessment[46][47][48]

See also[edit]


  1. ^ Crooks,, T. (2001). "The Validity of Formative Assessments". British Educational Research Association Annual Conference, University of Leeds, September 13–15, 2001. 
  2. ^ a b c d Huhta, Ari (2010). "Diagnostic and Formative Assessment". In Spolsky, Bernard; Hult, Francis M. The Handbook of Educational Linguistics. Oxford, UK: Blackwell. pp. 469–482. 
  3. ^ a b c Shepard, Lorrie A. (2005). "Formative assessment: Caveat emptor" (PDF). ETS Invitational Conference The Future of Assessment: Shaping Teaching and Learning, New York, October 10–11, 2005. Retrieved 25 August 2011. 
  4. ^ Black, Paul; Wiliam, Dylan (2009). "Developing the Theory of Formative Assessment, Educational Assessment, Evaluation and Accountability". 21 (1): 5–31. 
  5. ^ Scriven, Michael (1967). "The methodology of evaluation". In Stake, R. E. Curriculum evaluation. Chicago: Rand McNally. American Educational Research Association (monograph series on evaluation, no. 1. 
  6. ^ a b c d e f Wiliam, Dylan (2006). "Formative assessment: getting the focus right". Educational Assessment. 11: 283–289. doi:10.1080/10627197.2006.9652993. 
  7. ^ Bloom, Benjamin S. (1968). Learning for mastery. Los Angeles, USA: University of California press. 
  8. ^ Bloom,, Benjamin S.; Hasting, Thomas; Madaus, George (1971). Handbook of formative and summative evaluation of student learning. New York, USA: McGraw-Hill. 
  9. ^ Black, Paul; Wiliam, Dylan (2003). "'In praise of educational research': formative assessment". British Educational Research Journal. 29 (5): 623–637. doi:10.1080/0141192032000133721. 
  10. ^ Black, Paul; Wiliam, Dylan (2009). "Developing the theory of formative assessment". Educational Assessment, Evaluation and Accountability. 21 (1): 5–31. doi:10.1007/s11092-008-9068-5. 
  11. ^ R. Pr ́egent, Charting your course: How to prepare to teach more effectively, Atwood, 2000.
  12. ^ Cauley, K, M.; McMillan, J. H. (2010). "Formative Assessment Techniques". The Clearing House. 83 (1). 
  13. ^ Wynne Harlen & Mary James (1997) Assessment and Learning: differences and relationships between formative and summative assessment, Assessment in Education: Principles, Policy & Practice, 4:3, 365-379
  14. ^ a b Nicol, David; Macfarlane-Dick, Debra (2005). Rethinking Formative Assessment in HE: a theoretical model and seven principles of good feedback practice. Quality Assurance Agency for Higher Education. 
  15. ^ Nicol, David J.; Macfarlane-Dick, Debra (2006). "Formative assessment and self-regulated learning: a model and seven principles of good practice". Studies in Higher Education. 31 (2): 199–218. doi:10.1080/03075070600572090. 
  16. ^ Cowie, Bronwen; Bell, Beverley (1999). "A model of formative assessment in science education". Assessment in Education. 6: 101–116. doi:10.1080/09695949993026. 
  17. ^ Buldu 2009
  18. ^ a b c d e ORDER, IN. "Five “Key Strategies” for Effective Formative Assessment." (2007).
  19. ^ a b Black, Paul; Wiliam, Dylan (1998). "Assessment and classroom learning". Assessment in Education: Principles, Policy & Practice. 5 (1). 
  20. ^ a b Marzano, R. J. (2006). Classroom assessments and grading that work. Alexandria, VA: Association for Supervision and Curriculum Development.
  21. ^ a b Cauley, Kathleen; McMillan, James (2010). "Formative assessment techniques to support student motivation and achievement". The Clearing House: A Journal of Educational Strategies, Issues and Ideas. 83 (1): 1–6. 
  22. ^ McMillan, James; Hearn, Jessica (2008). "Student Self-assessment: The Key to Stronger Student Motivation and Higher Achievement". Educational Horizons. 87 (1): 40–49. 
  23. ^ Wiliam, Dylan; Thompson, M (2008). "Integrating Assessment with Instruction: What will it take to make it work?". In C. A. Dwyer. The Future of Assessment: Shaping Teaching and Learning. Routledge. pp. 53–82. 
  24. ^ Wiggins, Grant, and Jay McTighe. Understanding by Design. New York: Prentice Hall, 2000.
  25. ^ Gray, Eddie M., and David O. Tall. “Duality, Ambiguity, and Flexibility: A ‘Proceptual’ View of Simple Arithmetic.” Journal for Research in Mathematics Education 25 (March 1994): 116–40.
  26. ^ White, Barbara Y., and John R. Frederiksen. “Inquiry, Modeling, and Metacognition: Making Science Accessible to All Students.” Cognition and Instruction 16, no. 1 (1998): 3–118.
  27. ^ Kluger, Avraham N., and Angelo DeNisi. “The Effects of Feedback Interventions on Performance: A Historical Review, a Metaanalysis, and a Preliminary Feedback Intervention Theory.” Psychological Bulletin 119, no. 2 (1996): 254–84.
  28. ^ Butler, Ruth. “Task-Involving and Ego-Involving Properties of Evaluation: Effects of Different Feedback Conditions on Motivational Perceptions, Interest and Performance.” Journal of Educational Psychology 79, no. 4 (1987): 474–82.
  29. ^ Mary Budd Rowe, Wait-time and rewards as instructional variables, their influence on language, logic, and fate control: Part one-wait-time, Journal of Research in Science Teaching 11 (1974), no. 2, 81–94.
  30. ^ P. Black and D. Wiliam, Inside the black box: Raising standards through classroom assessment, Depart- ment of education & professional studies, GL Assessment, 2006.
  31. ^ Stroup, W. M., Ares, N., & Hurford, A. C. (2004). A taxonomy of generative activity design supported by next generation classroom networks. Paper presented at the Proceedings of the twenty-sixth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Toronto, Ontario, Canada.
  32. ^ Lesh, R., Hoover, M., Hole, B., Kelly, E., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591-645). Mahaway, NJ: Lawrence Erlbaum.
  33. ^ Wang, T.H. (2007). What strategies are effective for formative assessment in an e-learning environment? Journal of Computer Assisted Learning. 23(3), 171–186.
  34. ^
  35. ^ Scot, Tammy Pandina, Carolyn M. Callahan, and Jill Urquhart. "Paint-by-Number Teachers and Cookie-Cutter Students: The Unintended Effects of High-Stakes Testing on the Education of Gifted Students." Roeper Review: A Journal on Gifted Education 31.1 (2009): 40-52. Web. 30 Oct. 2012 url=
  36. ^ a b Scot, Tammy Pandina, Carolyn M. Callahan, and Jill Urquhart. "Paint-by-Number Teachers and Cookie-Cutter Students: The Unintended Effects of High-Stakes Testing on the Education of Gifted Students." Roeper Review: A Journal on Gifted Education 31.1 (2009): 40-52. Web. 30 Oct. 2012
  37. ^ Hodgen, Jeremy, and Dylan Wiliam. Mathematics inside the Black Box: Assessment for Learning in the Mathematics Classroom. London: NFER-Nelson, 2006.
  38. ^ Bachman. L.F. & Palmer A.S. (1996). Language Testing in Practice. Oxford University Press.
  39. ^ Cohen. A. (1994). Assessing Language Ability in the Classroom. Heinle & Heinle Publishers.
  40. ^ Zawojewski, J., & Carmona, G. (2001). A developmental and social perspective on problem solving strategies. In R. Speiser & C. Walter (Eds.), Proceedings of the twenty-third annual meeting of the North American chapter of the international group for the psychology of mathematics education. Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
  41. ^ Jones, Dr Cheryl A, Assessment for Learning, Learning and Skills Development Agency (now the Learning and Skills Network) (2005), p.1
  42. ^ A national conversation about personalised learning – a summary of the DfES discussion pamphlet, Department for Education and Skills (2005), p.8
  43. ^ Duckett, Ian and Brooke, Di, Learning and Skills Network (2007), p.1
  44. ^ Assessment for Learning: 10 research-based principles to guide classroom practice, Assessment Reform Group (2002), p.2
  45. ^ Boston, Carol (2002). The concept of formative assessment. Practical Assessment, Research & Evaluation, 8(9).
  46. ^ Cooper & Cowrie (2010). Collaborative Research of Assessment for Learning; Teaching and Teacher Education 26
  47. ^ Marzano, Robert J. (2003). What works in schools: Translating research into action. Alexandria, VA: ASCD.
  48. ^ Stiggins, R.J., Arter, J.A., Chappius, J. & Chappius, S. (2006). Classroom assessment for student learning: Doing it right-using it well. Portland, OR: Educational Testing Service.

External links[edit]