Does this image represent a lesson or a task? I’ve noticed that opinions are split on this question with some people calling the image above a task and others calling it a lesson. In my opinion, unless an image like this includes a description of how the teachers and students will interact […]

### Why Inquiry Fails

Here are at least six problems that often make inquiry-based lessons fail. Some Problems Students have too much information to process when attempting to solve a problem which can quickly overwhelm their working memory. When given a new problem type, students do not always have all of the prerequisite knowledge necessary to approach […]

### Teaching Two Courses on Instructional Routines

This spring I’m going to be co-teaching two courses with Kaitlin Ruggiero on instructional routines. Learn more here Learn more here The first course will focus on using the instructional routine, Contemplate then Calculate, as a tool for learning how to use the 5 Practices for Orchestrating Productive Mathematical Discussions. The second course will […]

### Five traps of technology

“Mathematics is not done with a computer. Mathematics is not done with pencil and paper. Mathematics is done with the brain.” ~ An anonymous participant of the Computer Based Mathematics Summit, London, 2011 The heart of mathematics education is ensuring that students develop both knowledge of mathematics (here is a definition of mathematics) […]

### Just Google It

In an age where fake news is beginning to dominate the media consumed by millions of people around the world and Google’s results are being gamed by racist organizations, claiming that students don’t need to know anything because “they can just Google it” is irresponsible at best and negligent at worst. Students (and adults) are […]

### Is Teacher Marking Necessary?

Teachers do a lot of marking of student work. But is it necessary? In this comprehensive review of the literature on feedback, corrective feedback (example shown below) without mechanisms for correcting that feedback were found, unsurprisingly, to have little impact on student learning in most cases. Unfortunately, there is also good evidence […]

### Moving beyond CUBES and keywords

It is well known that children often struggle to solve word problems in mathematics. One strategy that is used to support students with having access to word problems is called CUBES. Another is to have students identify all of the keywords in the problem. (Update: Margie Pearse wrote a longer response to these same two […]

### Writing Curriculum

An experiment Let’s try a little experiment. Take a look at the following network graphs and think about what is different for each graph and what is the same for each graph. Now look at this matrices associated with these network graphs. Which network graph do you think goes […]

### The difference between performance and learning

When my son was initially learning about fraction notation, he told me the following, right at the end of a class. My son: Daddy, 1/3 is the same as 3/4. Me: Why is that? My son: The 3 in the denominator tells you how many quarters there are in the fraction. Strictly […]

### Conceptual Understanding, Procedural Fluency, and Application

My colleague Liz created this graphic which nicely summarizes our project’s position on the relationship between conceptual understanding, procedural fluency, and application. The balance between conceptual understanding, procedural fluency, and application depends on your goals with your students and those goals should depend on what you know about your students. This is why […]