There seems to be no question that, if you’re going to teach math (at least at the elementary level), you need manipulatives. Numerous studies have been conducted by educational researchers since the 1960s, and the evidence is overwhelming that using math manipulatives meaningfully with students of all ability levels in all grades greatly improves understanding and retention of math concepts.¹ Families who are new to Math-U-See®, however, often wonder if they can substitute another kind of manipulative for the recommended blocks. Cuisenaire rods, base ten blocks, linking cubes—can any of them take the place of the Math-U-See Integer Block Kit?

Many homeschooling parents begin in the early years by using everyday objects as math manipulatives. Their children learn to count using raisins, paper clips, buttons—whatever happens to be available. While using real objects is useful in learning to count and in relating math to solving real-world problems, challenges arise when children begin working with greater numbers and with more abstract mathematical concepts. Let’s face it—it’s tedious and time-consuming to count out 25 objects, let alone 60 or 300. Then, trying to put groups together to demonstrate addition only creates an even larger group that must be counted. It’s interesting to note that researchers who studied children using real objects for manipulatives found that the practice “distracts and prevents the child from making the relation between the manipulative and the mathematics concept it is meant to represent.”² Not too far down the educational path, children must switch to something more representational—a picture or a manipulative that stands for a mathematical idea.

This is where something like a Cuisenaire rod, base ten block, or a Math-U-See integer block comes in. Children use these manipulatives to represent numbers when performing calculations or demonstrating mathematical concepts. Generally students begin by associating a number with a manipulative. With base ten blocks or linking cubes, this is done simply by counting out the appropriate number of cubes. The difficulty with this approach is that it never encourages the child to subitize—to look at a small group of objects and know at a glance how many there are. Research has shown that this skill contributes to a student’s success in mathematics by enabling him to work with numbers efficiently and with understanding. While children certainly can be encouraged to view groups of cubes as distinct numbers, subitizing is more likely to occur when using a manipulative set that includes separate objects for each of the numbers from 1-9.

The most popular sets containing distinct manipulatives for the different numbers are Cuisenaire rods and Math-U-See integer blocks. There are several important differences between the two. The first and most obvious is that Cuisenaire rods do not include manipulatives for hundreds, which makes representing larger numbers impossible with the rods alone. Second, the Math-U-See integer blocks have raised ridges, while the Cuisenaire rods are smooth. While children should not be encouraged to count the ridges or use the blocks as a counting tool, visually seeing the ridges reinforces the number that the block represents and helps children make the transition from counting to subitizing more easily. Third, the Math-U-See blocks have depressions on the reverse side that enable students to visualize subtraction, inverse operations, and negative numbers—concepts that cannot be seen with Cuisenaire rods. Overall, more mathematical concepts can be demonstrated with Math-U-See integer blocks than can be shown with Cuisenaire rods or other manipulatives.

Research has also shown that mathematical learning is enhanced when the same manipulative is used consistently over a long period of time.² When used with the Algebra/Decimal inserts, the Math-U-See integer block kit can be used to demonstrate mathematical concepts from preschool through algebra. There is no need, for example, to move from counting bears to Cuisenaire rods to algebra tiles. Students can use the Math-U-See integer blocks consistently as representations of numbers as they progress through levels of math that become increasingly more abstract and complex.

Why purchase a set of Math-U-See integer blocks? Simply put, they are worth the investment. Not only do they meet all the criteria for effective math manipulatives, but they can also be used for multiple children over many years to teach a wide variety of concepts. Using the Math-U-See integer blocks will help your children truly “see”, understand, and appreciate math.

References

¹Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380.

²Laski, E. V., Jor’dan, J. R., Daoust, C., & Murray, A. K. (2015). What makes mathematics manipulatives effective? Lessons from cognitive science and Montessori education. SAGE Open, 5(2), 2158244015589588.