I’m going to start off on a negative note. I was totally unprepared for the teaching profession when I graduated from college. The college I attended was not much more than a large high school. My “Methods of Teaching Mathematics” was incorporated with methods of teaching science. In my college classes, I learned how to write detailed lesson plans (over some random subject), I learned how to use a copy machine, I learned the stages children go through, I learned behavior managment, I learned a lot of stuff. I learned a lot of stuff that didn’t really pertain to the actual teaching of mathematics. I wanted to learn how to actually teach fractions, how to actually teach solving equations, I wanted to know the best methods of teaching the things I was actually suppose to be doing. Unfortunately, I’ve had to learn that all by myself through trial and error. I want to apologize,tremedously, to the students I had my first few years. This is my eleventh year of teaching, and I finally feel like I’m making some progress. I actually want other people to come into my classroom and see the exciting things that we are doing. Before, I was afraid of people coming in and criticizing the way I teach. All of my career, I would order teacher resources looking for great lessons. It wasn’t until the beginning of last year that I really started finding the things I wanted and became confident in myself to actually start trying them out. In this new found teaching, I’ve learned the importance of using manipulatives in most everything that I do. The following are some research that has been done as well as some of the manipulatives I use.
Research indicates that lessons using manipulatives are more likely to help children achieve mathematically that lessons without manipulatives (Sowell 1989). Long-term use of concrete materials is positively related to increases in student mathematics achievement and improved attitudes toward mathematics (Grouws and Cebulla 2000). Using manipulaties also “helps students understand mathematical concepts and processes, increases thinking flexibility, provides tools for problem-solving, and can reduce math anxiety for some students” (The Education Alliance 2006).
Manipulatives can be anything that is not just a pencil and paper assignment. I use many different manipulatives in my classes. I use two-color counters for integers, I use homemade “tab” books for taking notes that are important, I use colored paper, I have multiple sets of different multi-sided dice, I use decks of cards, base 10 blocks, fraction bars, plus a lot more. My goal is to make every single lesson have some sort of manipulative incorporated with it. Manipulatives have to have meaning and be relevant to the lesson. Many times you can find lessons that have a whole lot of “fluff and fun”, but have very little to do with the actual mathematics you’re tyring to teach. I find that it is extremely important for your activities to keep all of the students engaged for the large majority of the time. When my students are working problems in a game, I most usually have all of the group working them to check the answers. I’ve seen lessons that look extremely cool, but if only one student out of the twenty-seven are actually engaged at a time then it’s not very efficient.
It is important to allow the students a little bit of time to explore the manipulatives. If I pass out dice, I usually give them a couple of minutes to play around with them. It is inevitable that they are going to roll the dice several times. If I give them this time, then they are more prepared to pay attention when I begin going over the rules and procedures of the activity.
It is important that each student have a set of the manipulatives themselves. Even if the students are in pairs or groups, I usually give each person a set. The whole point of the manipulative is to allow them to actually touch and move items around. If they are just watching someone else do it, it defeats the purpose. I understand that sometimes there may not be enough sets for each child, but I always try.
The most important part is that the students are enjoying the learning process. It is also important that the manipulatives are relevant to the concept being taught. When you see students who aren’t normally engaged in school lessons tend to perk up and be active learners with the hands-on lessons, you’ll see the importance of manipulatives.