How do we design our Math Class?

I have been doing a lot of reflecting about math, in particular thinking about different types of math class situations, and considering what kinds of questions we need to ask to help students develop conceptual knowledge.

In our math classes it is important to provide students with cognitively demanding tasks. Rich tasks are great examples of this. Rich tasks provide multiple entry points AND multiple strategies that students can come to a solution.

When we are planning our math classes, we can consider the following situations that we may be providing for our students. Next, we can think about what feedback we need to make the student learning more conceptual.


Situation #1 – Students are engaged in lessons that focus on basic knowledge, and procedures. Students need to get to a correct answer vs gaining a conceptual understanding of the strategies used. Students therefore are unable to make connections to deeper math concepts.

Key Questions:

  • What do we do to help students develop conceptual knowledge?
  • What supports need to be in place to help make this happen?

Situation #2 – students engage in more complex tasks, but then the tasks turn into procedural tasks, thus the students don’t get experience with increasingly difficult and complex tasks

Key Questions

  • How do we keep students engaged with a task, and allow them to experience increased cognitive demands and go through the ‘fits and starts’ that learners go through?

Situation #3 – Students may engage in rich tasks, with multiple entry points and multiple solution paths, however, they are unable to engage in a whole class discussion about different types of strategies.  

Key Questions

  • What steps can we take to conduct a whole class discussion?
  • How do we structure the strategies in a way that helps students to make the best connections?
  • What do we want students to get out of our whole class discussions?

Situation #4 – Students are engaged in rich tasks, with multiple entry points, multiple solution paths. Students are choosing from a variety of strategies and honing in new ones. They are able to explain why they chose a certain strategy. They are given time to explore their various strategies, and time to explain their reasoning. Whole class discussions allow for students to explore different strategies, and consider the efficiency of the strategies. Students make deeper connections, learn from peers and apply the new learning to a new task or ‘exit ticket’.

Key Questions:

  • How do we push our learning and the learning of our students in this type of a situation?

The questions can really help to guide our  thinking into how we are going to design our math class.

I would love to hear your ideas,

Deborah McCallum

Copyright, 2017


Educational Administration Quarterly

Vol 53, Issue 3, pp. 475 – 516

First Published January 31, 2017

Question Matrix for Instructional Design

How do you organize all of the curriculum pieces together?

How do you organize all of the curriculum pieces together?

This is a Question Matrix I created to help to explore the curriculum based on important questions we need to be asking ourselves when designing our programs. It was inspired by the work of Dillon (2009). It is very big and complicated – perhaps quite impractical – but it is also very organized and comprehensive. A cumbersome, yet reflective tool to use while planning and designing your curriculum.

The same questions are along each axis, but interconnect in different ways:

Teacher – who?

Student – Who?

Subject – What?

Milieu – Where and When? 

Goal – Why? What is the point?

Activity – How?

Result – When? 


Please find a printable version here: Question Matrix

Deborah McCallum

c 2016



Dillon, J. T. (2009). The questions of curriculum. Journal of Curriculum Studies, 41(3), 343-359. doi:10.1080/00220270802433261
What are the basic things that compose curriculum, and what are the questions that may be posed about these things? Joseph Schwab’s conception of curriculum is used to introduce a scheme of questions concerning the nature, elements, and practice of curriculum. Formulations of questions by other curriculum theorists are reviewed and analysed in light of this scheme, and the various uses of such questions are described. How far the questions prove to enhance thinking and acting in the domain of curriculum is the ultimate criterion of the usefulness of the questions. The answer to this final test question, as to the others, is to be found in the circumstances of practice