A very common situation in many classrooms is that there is only one computer and it is usually attached to a projector. How can one meaningfully use technology under these circumstances? Here is a strategy that may help when you want students to use an interactive tool but either have limited access to […]

## Yearly Archives: 2017

### Responding to Student Mistakes

A while ago, I had something very similar to the following shared with me. The student was given the diagram and asked to find the measure of the angle marked with the question mark. The student has clearly made a mistake. Why did they do it? I asked on Twitter and here are some theories: Using […]

### Online Practice is Terrible Practice

One of the ways computers are being used in math education is to provide students with online practice. There are a bunch of serious problems with most of these programs. Here is one example from the Khan Academy (apparently at least one of the flaws outlined below no longer applies to the Khan Academy. […]

### 10 things that might actually disrupt US education

There’s a list being shared of ten things that will disrupt US education and I agree with Dan Willingham. My bold prediction: none of these 10 will disrupt education. None. https://t.co/pUAtmUOK7E — Daniel Willingham (@DTWillingham) October 16, 2017 In no particular order, here are ten things that might actually disrupt US education. Teachers […]

### A Conference Experiment

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 […]