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Assessment for learning : Post 16 Level 2 : Mathematics-specific Pedagogy

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Post 16 Level 2
Assessment for learning
Question 1 of 3

1. How confident are you that you know and can use a range of assessment strategies to make learners' thinking explicit?

a. Activity One


Whole class questioning is an important part of Assessment for Learning (AfL). It enables a teacher to assess the understanding of all the learners in their class in ways that are both efficient and effective.

a) Watch this video Questioning whole groups and as you watch it, ask yourself:

  • What different types of question does the teacher use, and what are the advantages of each?
  • How does the teacher use the responses given by learners?
  • How does he ensure each learner is involved?
  • What do you think he is trying to achieve in each interaction?

Prompt 1.

Watch the ‘Reflections’ video in which you can hear the teacher reflecting on the whole group questioning session you have viewed.

b) What other assessment techniques could you use which would allow you to assess a whole group's thinking? Or if you only work with learners on a one-to-one basis what techniques can you use to assess that individual's thinking?



“Assessment for learning is the process of seeking and interpreting evidence for use by learners and their teachers to decide where the learners are in their learning, where they need to go and how best to get there”. Assessment Reform Group, 2002

“The effective use of formative assessment lessons depends on the quality of feedback given by teachers to students. One important way of moving students’ thinking forward is to prompt them to reconsider their reasoning by asking carefully chosen questions.” Mathematics Assessment Project

Whether you use questioning as in the video or another assessment technique, it is worth always remembering these rules:

  • Use “assessable” questions where the learners’ responses will influence your teaching and provide feedback to aid their learning.
  • If you are using an assessment task, complete it yourself (or ask a colleague to do it) to be sure that it is can be done in the time you will give the group or individual.
  • Plan how you will analyse your learners’ responses, will you look at individual questions and answers or will you group the questions into categories such as – everyone answered this well, some learners made mistakes in this answer, some learners appear to hold a misconception about…
  • After using a classroom assessment technique, talk about the results with the students so that they know both what you learned from the assessment and so what they should learn from the assessment and also what they should do about what they have learned!




The following are some examples of classroom assessment techniques that teachers use:

Minute Paper
Pose 1-2 questions in which learners identify the most significant things they have learned from a given lecture, discussion or assignment. The question can be very general or content-specific and their answers help you to determine if they are successfully identifying what you view as most important. Give learners about 1-2 minutes and ask them to write a response on an index card, or no more than a half page.

Muddiest Point
Ask your learners to answer: “What was the muddiest point in… (today’s lesson, the textbook explanation, the homework)?” Learners need to identify fairly quickly what they do not understand and articulate it.

Background Knowledge Probes
Create a short questionnaire to determine how much and what kind of relevant background knowledge students bring to your course. Your goal might be identifying what is familiar to them or determining their level of recall from prior related courses. Be sure to make the questionnaire anonymous and be clear that it is not a quiz and will not be graded.

Problem Recognition Tasks
Identify a set of problems that can clearly be solved better by one of the methods that you are teaching. Ask learners to identify by name which methods best fit which problems without actually solving the problems. This task works best when only one method can be used for each of the problems or one method is clearly best.

Documented Problem Solutions
Choose 1-3 problems and ask learners to write down all of the steps they take in solving them with an explanation of each step. Consider using this method as an assessment of problem solving skills at the beginning of the course or as a regular part of their homework.

Directed Paraphrasing
Select a method, concept or proof that learners have studied in some depth and identify a real audience to whom your learners should be able to explain this material in their own words (e.g. their classmates, Year 10/11 students, their parents). Provide guidelines about the length and purpose of the explanation.

Applications Cards
Identify a concept or topic your learners are studying and ask them to come up with 1-3 applications of the topic from everyday experience, other courses they are studying or current news events.

Learner-Generated Test Questions
A week or two prior to a test, begin to write general guidelines about the kinds of questions you plan to ask in the test. Share those guidelines with your learners and ask them to write and answer 1-2 questions like those they expect to see in the test.

Opinion Polls
When you believe that your learners may have pre-existing opinions about maths-related issues, construct a very short 2-4 item questionnaire to help uncover their opinions.

Group-Work Evaluations
Decide what you want to know about the group work, such as how well the group members worked together, how many actively participated most of the time, how many were well prepared for the group’s activity, or what the group could do to improve its effectiveness. Distribute a short 4-5 question evaluation form and be clear about the purpose (e.g. to improve group interactions and performance).


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