“Do you have to use the blocks all the time?”
“Isn’t my child too old to play with blocks?”
If you are using or considering Math-U-See, one of these questions has likely crossed your mind. While some of us may be familiar with hands-on learning, most parents have not had any training on the use of manipulatives. So let’s examine the whys and whens of manipulative use with Math-U-See.
In addition to direct teaching and illustration of mathematical concepts, Math-U-See manipulatives have many other applications. They can be used for various games and activities, from “Race to 100” to measuring and estimation. The integer blocks make a wonderful building block substitute. This sort of free exploration with the blocks should be encouraged, as it helps to develop foundational mathematical concepts. Additionally, Seefeldt and Waskik suggest children be provided with opportunities to work with manipulatives without predetermined goals because “(t)hese experiences help children think about their world in alternative ways and help them understand that there are multiple ways to solve problems.” (Source) Not only does this free play help children become familiar with the blocks, but it also encourages that same creative spirit when using manipulatives for more advanced concepts.
Math-U-See builds on this foundation through the intentional use of manipulatives based on research. According to mathematician Z. P. Dienes, “Children whose mathematical learning is firmly grounded in manipulative experiences will be more likely to bridge the gap between the world in which they live and the abstract world of mathematics.” (Source) This ability of manipulatives to help students move from concrete experiences to abstract reasoning is so powerful that it has a tremendous impact on student achievement. In fact, according to Wenglinsky, “When students are exposed to hands-on learning on a weekly rather than a monthly basis, they prove to be 72% of a grade level ahead in mathematics and 40% of a grade level ahead in science.” (Source) The mental images your child develops from the manipulatives can serve as an important bridge as she moves from the concrete to the abstract. Not only will students have a better grasp on abstract concepts with manipulative use, but they will remember them better, too.
Fortunately, throughout the Math-U-See program, clues are provided as to when manipulative use is essential, optional, or should be avoided. The first of these clues comes from the video lesson. Are manipulatives used in the presentation of the lesson? If so, that is a strong indication that they should be used in the teaching, exploration, and mastery process. You can also check for graphics of the manipulatives in the Instruction Manual for the lesson. For most concepts, there should be a natural progression from concrete exploration to abstract application. The instructions on the worksheets and tests will typically guide you regarding the anticipated use of manipulatives. Directions such as, “Build, write, and say” would indicate manipulatives are necessary. Instructions to, “Solve for the unknown. Use the blocks if needed,” would leave that option to the student. Simply seeing a direction to “Solve” signals that the concept should be mastered to the point that the student is able to work with just the written symbols.
Sometimes a student will argue, “But I don’t need the blocks!” Often challenging the student to “prove it” can resolve the issue. Can the student teach the concept back through building, writing, and saying and show the ability to apply the concept? If so, then he may have in fact reached a point of mastery for that particular concept where manipulative use is no longer necessary. However, the manipulatives would then be incorporated again for the next new concept, following the guidelines mentioned previously.
It is important to remember manipulatives are not just for young children; they are tools that are used by all ages. Consider the flight simulators used by pilots or mannequins and robots used by medical students. These are just large manipulatives that permit adult learners to practice concepts. In “Manipulatives: The Missing Link in High School Math,” Marilyn Curtain-Phillips indicates, “Most learners, whether adults or children, will master mathematical concepts and skills more readily, if they are presented first in concrete, pictorial and symbols.” (Source) The benefits of manipulatives for learners of all ages is a basis for Math-U-See’s incorporation of them from Primer all the way through Algebra 1.