Articles

Interactive whiteboard technology can enrich the learning and teaching experience. However, using this technology – and using it well – may seem a little overwhelming. These research-based tips will help make its introduction and ongoing use in your classroom easy and effective.

For many, algebra is a confusing jumble of symbols and equations. Until recently, this abstract area of mathematics was first introduced to students in high school, where it was often approached as a set of procedural rules for solving equations (Kilpatrick & Izsák, 2008). Developing algebraic thinking in the early school years provides a solid foundation for later algebra symbol work (Warren, 2008). Teaching children the big ideas (key concepts) of early algebra (Warren, 2008; explained below) through real-world problems helps them understand its rules and applications.

In general, this document presents a clear directive for a more consistent, challenging, concise, and connected mathematics curriculum for all students in grades K–12. It does away with the spiraling notion – that if we keep re-teaching the same concept every year, students will eventually “get it”. This is a positive step.

While we can debate about the order of topics, or the grade level chosen for any particular topic, the general outline seems sensible and achievable. For example, I was at first upset that I didn’t see algebra as a strand in grades K–5. However, a more careful look found at least four statements about algebraic properties and reasoning in each of these grades.

One of the criticisms that I have seen is that the skill development for addition and subtraction is too fast and too short. I maintain that we have not in the past taken time to CAREFULLY develop the concepts needed to maintain skill and fluency. If concepts are developed carefully, AND connected to procedures, procedural fluency will follow.

We have consistently underestimated what students can do at early grade levels. I believe that this document sets higher, but achievable goals. It is not perfect, but without something like this, we will not more forward.

Carol R. Findell, EdD
Clinical Associate Professor
Mathematics Education
Boston University

Note: This communication was originally sent to the National Governors Association Center for Best Practices and the Council of Chief State School Officers.

Have you ever played with dominoes? As well as being fun, domino games involve calculation and thinking strategies, which makes dominoes an ideal resource for teaching various aspects of mathematics. They can be used to develop number concepts, computation strategies, patterns and algebra, and chance and data. This sample activity shows how double-nine dot dominoes can be used to investigate addition involving three addends.

Representations of ten are used for teaching place value, number sense, and computation. However, many of the resources used for representing ten (frames, sticks, cubes, rods, and blocks) do not clearly show the individual ones within the number or effectively demonstrate three- and four-digit numbers. For example, all one thousand smaller cubes are not visible within a one thousand base-10 cube.

It is essential that all students are able to calculate mentally as well as with paper and pencil. Students can make mental calculations quickly and easily with the help of strategies. There are mental computation strategies for each of the four operations: addition, subtraction, multiplication, and division. Strategies for addition are explained here.

Number sense. Students need it to develop their mathematical skills and understanding. It is a key part of mathematics curricula. But what exactly is it? And how is it developed?

Classification charts show hierarchical relationships between categories of items, such as objects or concepts. As you move from the top of the chart to the bottom, the categories become more specific. What is true for an item at the top of the chart is also true for all connected objects or concepts below it. However, what is true for an item at the bottom of the chart may be, but is not necessarily, true for the higher concept.