: Uncovering Misconceptions: Harnessing Diagnostic Questions for Instant, High-Quality Feedback in the Classroom Sophie and Kirsty explore how we can use diagnostic questions in mathematics to uncover misconceptions

Sophie and Kirsty explore the importance of harnessing responsive teaching through the medium of diagnostic questions in maths lessons to support student learning outcomes.

Recommendation 1 of the EEF’s Improving Mathematics in Key Stage 2 and 3 guidance report indicates we should use assessment to build upon pupils’ existing knowledge and understanding. Diagnostic questions are a powerful tool for assessing student understanding in the classroom which is vital in the maths classroom to ensure that students have understood concepts before we build on them. They go beyond surface-level checks, helping teachers identify fundamental misconceptions which allow for adapting teaching to meet the needs of every student. In this post, we’ll explore the effective use of diagnostic questions in maths lessons and how they can drive meaningful learning.

A diagnostic question typically presents one correct answer alongside three carefully crafted incorrect answers, each designed to reveal specific misconceptions. These questions provide insight into students’ thought processes, offering teachers valuable information to shape their lessons.

The following diagnostic question, downloaded from the diagnostic question website (https://diagnosticquestions.com/), is an example of this.

Students who chose option B are correct but those who chose the other options reveal different misconceptions that help the teacher to move forward with the lesson. A student who chose option A may have confused perimeter and area and thinks they need to multiply by 4. A student who has chosen option C may have miscalculate 9 x 9 as 9 + 9 or misremembered 9 squared is 18 not 81. A student who has chosen D may not understand the geometric notation used to show equality of length but may understand the concept of area. In each of these instances whilst the misconceptions may be clear it is always worth digging deeper with students in the questioning after to make sure those misconceptions are not embedded further.

The example above, or any other diagnostic question, can be integrated at various points during a lesson:

• Start of the lesson/​topic: Gauge prior knowledge and identify gaps.
• Mid-lesson: Assess progress as students engage with new concepts.
• End of the lesson: Summarise class understanding and inform future teaching.
  
  

As indicated in recommendation 1 of the EEF guidance report, this allows the teacher to gather information about the students’ current level of understanding and using that to address misconceptions as well as make any necessary adaptations to the learning ahead.

For maximum impact, allow students 15 – 30 seconds of thinking time before they respond. Allowing students thinking time has numerous benefits (Stahl, 1994) but for this strategy it ensures a higher quantity and quality of answers which is vital in order for teachers to make decisions about the next stage of their lesson. However, this means that unlike other multiple-choice questions it is ideal if students do not have to do multiple stages of working out. In the example below, you will see how a question has been broken into just the first stage of the problem in order to allow students to make a choice in that 15 – 30 second thinking time. Responses can be collected through mini whiteboards, planners, hand signals, or online platforms. Importantly, ensure students answer independently without being influenced by their peers. Personally, I like to use mini whiteboards with my classes as students can write their thoughts and workings on the board which then helps me to see exactly what the misconception is.

The real power of diagnostic questions lies in how you respond to student answers. Here are five possible scenarios and strategies based upon the following example:

1. Everyone Gets It Right: Nearly 100% respond B

• Challenge students to explain their reasoning and why the incorrect answers are wrong.
  
  
• Consider a follow-up question to confirm understanding. This may be surface level such as ​‘any number to the power of 0 is 1’ or more in depth such as a proof using the index laws. The teacher can decide based on where the learning is going next whether students demonstrate the appropriate level of understanding for the next step in their learning.

2. Most Get It Right, a Few Struggle: 80 – 90% select B, some select C

• Use their answers to pinpoint misconceptions. If students are selecting C they are confusing 12 to the power of 0 with 12 x 0. You could address this as the teacher or ask a student to explain the misconception.
  
  
• Provide targeted intervention in the next stage of learning where this knowledge is necessary or pair struggling students with confident peers.

3. Mixed Responses: This may be a mixture of all 4 answers or 50:50 on two. Let’s consider 50:50 on option B and C.

• Ask students to justify their answers, ensuring they engage with multiple perspectives. This may be done as a paired task – convince you partner why B is correct or convince your partner why C is correct.
  
  
• Re-vote after discussion, hopefully the response changes to either scenario 1 or 2 as above. If now less get the answer correct refer to the scenarios below.

4. Most Get It Wrong, a Few Get It Right: Most C, some A, some B

• Assign the correct responders as ​“experts” to guide their peers if there are enough spread around the room.
  
  
• Have confident students explain their reasoning while you support others.
  
  
• Reteach the concept. In this case it may be worth getting students to check with their calculators and then trying with other numbers in order to re-discover the pattern.
  
  
• Re-vote and then reassess with another diagnostic question

5. Everyone Gets It Wrong:

• Use the insight gained to reteach the concept, targeting specific misconceptions that were revealed by the incorrect answers. As above this may involve using a calculator.
  
  
• Reassess understanding with another diagnostic question.

There is research evidence (Butterfield, Metcalfe, 2001) that states that when students confidently select an incorrect answer but later learn the correct one, they are more likely to retain the right information. This ​“hypercorrection effect” emphasises the importance of pairing diagnostic questions with constructive feedback (ibid). Therefore, it is vital that you challenge your classes to have 100% response rate.

Incorporating diagnostic questions into your teaching practice can transform the way you understand and address your students’ needs. By identifying misconceptions early and tailoring instruction accordingly, you can build a stronger foundation for mathematical success now and later in their learning journey.

References:

Barton (2007) Mr Barton Maths (Online)

Black, P., and Wiliam, D. (2001). ​‘Inside the Black Box: Raising Standards through Classroom Assessment’. The Phi Delta Kappan, Vol. 80, No. 2

Butterfield, B. and Metcalfe, J. (2001). ​‘Errors committed with high confidence are hypercorrected’. Journal of Experimental Psychology: Learning, Memory, and Cognition

Education Endowment Foundation. (2017) Improving Mathematics in Key Stage 2 and 3 (Online)

Stahl, R.J. (1994) Using ​‘Think-time’ and ​‘Wait-time’ skilfully in the classroom

William, D. (2007) Five Key Strategies for Effective Formative Assessment. National Council of Teachers of Mathematics

(A lot of the information shared is from Craig Barton and his website www.diagnosticquestions.com)