My colleagues have long been frustrated sharing our work at conferences primarily because the work we do is complex and hard for people to understand thoroughly within the constraints of a conference session where we only have at most 75 minutes to work on an idea. So we contacted the organizers of the two NCTM […]

### Questions about Curriculum

Here are some questions that I ask myself whenever I read through a mathematics curriculum: • Does this curriculum assume that children will forget ideas over time? • Does this curriculum provide instructional supports that increase the odds that all children have access to it? • Does the curriculum assume all students are capable of […]

### Mathematical Representations

There is evidence that students who have access to and understand how to use different mathematical representations of the same mathematical concepts are more successful learning mathematics than students who only have access to one representation type. The issue is that mathematical representations are not intrinsically meaningful on their own. Some mathematical representations are completely […]

### Teaching to Big Ideas

On Big Mathematical Ideas, Cathy Fosnot writes: Underlying these strategies are big ideas. Big ideas are “the central, organizing ideas of mathematics—principles that define mathematical order”(Schifter and Fosnot 1993, 35). Big ideas are deeply connected to the structures of mathematics. They are also characteristic of shifts in learners’ reasoning—shifts in perspective, in logic, in […]

### A Task is Not a Lesson

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 […]