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 […]

### Ambitious Mathematics Curriculum

In an age where we can provide instantaneous access to high-quality encyclopedias and generate customized user-generated-playlists for a billion people on the fly, we should be able to provide curriculum with more ambitious goals and more customizable content than what is currently provided to teachers. The typical curriculum resources teachers have access to today are […]

### Instructional Routines as Formative Assessment

This article was rejected for publication so I decided to rework it and release it on my blog instead. Across the United States, there is a continued focus on the use of formative assessment to improve the conditions for students’ learning. One common theme is that teachers want more support in implementing formative assessment […]

### Expectations

In 1965 a pair of researchers, Robert Rosenthal and Lenore Jacobson, set out to study the Pygmalion Effect, which hypothesizes that if we hold high expectations for people’s performance, their performance will be better than if we hold low expectations. What they found was startling, especially for younger kids. Students who had been randomly selected […]

### The future of CLIME

CLIME (The Council for Technology in Math Education) is an affiliate of NCTM with the mission to: Empower math communities to improve the teaching and learning of math through the use of dynamic tools in a Web 2.0 world Last night members of CLIME and other interested people attended a meeting of CLIME to discuss […]

### Making Mathematical Ideas Explicit

If you or your students are going to talk about mathematical ideas in your class, it is critical that everyone understands the idea being discussed otherwise they are less likely to either remember it or be able to participate in the discussion. Every time you or your students make logical leaps when explaining mathematical ideas, […]