Triangulate That Data!

When we see a student struggling with a concept in math, what is our response? Sometimes we are able to help a student think through the problem or give some extra support that may be successful. That works when the child is working on the edge of their instructional level. Often as grades increase we see gaps in math achievement becoming greater. Even when a student has received additional support on a concept, they still seem to struggle and it is apparent that the building blocks of understanding are still developing. By identifying needs early and working side by side with the child to develop their understanding of numeracy promptly by meeting the child precisely where they are at, these gaps can be minimized.

In order to do this, conscientious assessment practice is essential. A student generated product is one step toward well-rounded assessment practice, but this gives only a limited picture of student understanding. To get a clear view of a student’s understanding we must also ask “How is this student thinking about this problem and why are they thinking this way?” The answers to when intervention is necessary and how to approach intervention appropriately are found in these answers. When we triangulate our data (Davies, 2000) a well-rounded picture of the student’s movement towards mastery is apparent. Observation and conversation give insight to a student’s thinking and lead us towards precise teaching.

In math, product is emphasized in many classrooms, often in the form of a written test or quiz, but for balanced assessment practice, observation and conversation are essential. Observation could be watching a student use concrete materials to solve a problem, or engaging in a learning game with a peer. From this standpoint the teacher can get a window into the student’s performance and see how a student strategizes about a problem. When conversation is added, the teacher can understand why a student approached a problem in this way. Following, the teacher may choose to engage in conversation with the intention of discovering up to which point the child is successful with their strategy and determine next steps to support the child in more efficient thinking.

An example may be something like this:

Written Product

Question:18 - 7 =

Student answer: 11

What we know: The student reached an accurate response,

What we don’t know: How did the student reach the correct response? Why did the student reach a correct response. Two aspects of fact fluency - flexibility and efficiency - are not assessed.

Although it is good practice to have students explain their thinking in writing, there is caution to be taken in assuming that the writing reflects 100% of the student’s thinking about a problem. In conversation, the teacher can probe further.


Question: 18 - 7

Student action: The student counts 18 blocks, then counts 7 from the whole group and pushes them to the side. They announce the answer as 11.

What we know:The student arrived at a correct response. The child understood subtraction as “take away”.

What we don’t know: Why the child arrived at the correct answer? This is the information needed to help the student develop further.


Question: 18-7

The student counts 18 blocks then counts 7 from the whole group and pushes them to the side. They announce the answer as 11.

The teacher asks “How did you know?”

A conversation with a student allows insight into thinking, which is what math is all about! By asking the student to talk about the strategy used, there may be several responses. In this case, the child may say “I subtracted 10 and added one”, “I subtracted 7 from 8 and then added ten and 1 more”, or “I counted up really fast”. Each of these responses gives a different insight into the thinking, and our goal is to support movement to more efficient and appropriate strategies. The conversation of math assessment can provide us with some answers that can help move students to the next stages of learning.

Time is of the essence in our classrooms! Products used as assessment are usually done as a whole class. In this way product assessments are tidy, convenient, and efficient. Conversations and observations take more time and can be complex. I would like to present some possibilities for including observation and conversation assessment in math class. Including these components is very flexible and is easily included in any style of math block as the teacher interacts with students regularly. The only shift may be that the teacher is now strategic in collecting data during interactions.

  1. During math workshop - during one rotation or one class do not schedule a group. Instead, visit with students as they are working or practicing through games and ask targeted questions to gain insight and make hypotheses about how a child is thinking about a concept.
  2. During math workshop meet with one group for the purpose of observation
  3. During math work stations or centres, invite students to a teacher centre on a predetermined schedule.
  4. Create a schedule for observation and conversation similar to how a schedule of reading conferences would be used.
  5. Sit side by side with a student during independent work time and have a guided conversation to determine thinking.

Teachers are so innovative and these few ideas are just a starting point! Conversation can easily be intentionally embedded into the fabric of the math block and the desire to create busy work so math interviews can be conducted or to push students farther in independent work than their stamina allows so the teacher can meet with individuals around reporting time is eliminated. The information collected can be ongoing and continually refreshed, and summative interview questions and observations can be included so there is no need to do it all at once, in fact, ongoing observation and conversation allows teachers to dig deeper in the moment and engage in the continual process of more precise flexible grouping by responding immediately to current, in depth data.

Observing and conversation are essential corners of the assessment triangle. Well rounded assessment in math provides a wealth of data to inform instruction for student success.

What creative ways have you seen to allow assessment conversation with kids in math? In what ways have conversations impacted your instruction?

Davies, A. (2000). Making classroom assessment work. Courtenay, BC: Connections Publishing.

Author: Kathleen Robertson