Do Math Manipulatives Help Our Students Learn?
What are they?
A math manipulative is an object that is used in the teaching of mathematics that allows students to perceive the idea or concept they are learning through touching and moving the object. These manipulatives can range from anything like dice or money to pattern blocks, two-color counters, and even playing cards or dominoes.
What age groups?
All ages can benefit from the use of manipulatives while learning math. Math manipulatives are most commonly used in the early elementary ages or younger. Once students become more capable of abstracting concepts (older elementary, middle, and high school), teachers seem to have students spend more time doing math with paper and pencil, and less with hands on methods.
What are the benefits?
The use of manipulatives in the learning of mathematics allows students to represent math in multiple ways. More senses become engaged, including visual and tactile, which keeps a student more attentive. They are able to “see” math, which reinforces the conceptual understanding. This lays the groundwork for the mechanics that they will use later and allows the rules to be more meaningful and make sense, which in turn, will be less for them to “memorize”. Seeing math allows students to expand on ideas and uses of math in the world around them.
Why aren’t teachers using them?
Three reasons that math manipulatives are not used as often as they could, is time, money, and lack of knowledge. Developing the concept with a manipulative may require more time and so often, our teachers are burdened with getting through the material. While many math manipulatives on the market can be costly, not all manipulatives are expensive, but having enough for a class set could get pricey. Each math manipulative can be used to teach a variety of concepts. Often teachers may not know how to teach various concepts with these tools, and so they just do not get used. There are many companies out there that do trainings with their manipulative for teachers to learn.
This blog has an ultimate list of math manipulatives that can get you started!
I come across students daily who struggle in their academics, particularly in mathematics. For the students who are not trying or do not care, this message isn’t for you. Unfortunately, there is not much anyone can do to help someone who simply will not try or does not care. For all others, I see many students quietly failing their class as time continues to pass by. One bad grade after another accumulating. At some point, it may possibly be too late to undo! As I begin to understand and discover why this continues to happen to students who are “doing all the homework and still failing the tests”, what I have learned is the simple fact, you can do it, not always alone.
So, students, here are a few tips for you to win your math struggle…
- Do ALL of your homework. And furthermore, write it out on paper, step by step, even if that means you have to kill trees. Learning math means doing math and the paper is worth your learning!
- ALWAYS use answer keys while doing your homework. First, do the problem, then check your solution. Instant feedback is essential to correcting mistakes.
- After doing your homework, if there were types of problems that you didn’t understand or missed a lot of, ask for more practice problems from your teacher or find some on the internet or textbook.
- Okay, so you can do all of your homework? Does that really mean you are ready for that quiz or test? Not necessarily! Create a similar pre-quiz or test and TIME yourself and GRADE yourself. If you are going to make mistakes, make them on your practice quiz/test, not on the real one!
- Build a good working relationship with you teacher/professor. Visit tutorials and office hours. Let them know who you are and show them you are trying. If you are a college student, see if your university offers tutoring or a math lab.
- Create study groups with other students who care and are willing to work hard and want to succeed. Work problems together and check each other as you go.
- Write note cards with important notes/formulas as you go to keep everything in one place.
- And if you still need support, that’s okay! There’s MaThCliX!
You don’t “study” math, you DO it! Bottom line. Know your resources and use them. Others have gone before you and no one becomes a huge success all alone.
Tips for Students and Parents
And just like that, another summer is over and a new school year begins! Here are some tips for both parents and students to work together to ensure a successful school year.
1. Set goals: Write them out clearly and display them somewhere that you see them everyday
ex: I will complete my HW before I watch TV
2. Get organized: This includes finding a way to organize papers going back and forth from subject to subject. How are you going to know what your assignments are and when they are due?
3. Plan: What HW, tests, and quizzes do you have this week? How will you prepare for them? Make sure you plan out your study time.
4. Practice: This is how you learn! Make time each day to practice.
5. Get Help: Are you not understanding what you are supposed to be learning? Ask! Get help! Go to your teacher, parent, and of course, MaThCliX! That is what we are here for.
1. Make sure that you know how to communicate with your student’s teacher. Know when conferences are and plan to have a presence and be proactive in your student’s academics.
2. Check grades! Even if your student is old enough to check their own grades, it never hurts to have a parent checking, too. Know when progress reports and report cards are due. If you see grades dropping, intervene quickly!
3. Make sure your student is doing the success tips for students. Ask them how they are doing each one.
4. Find out about what student’s are learning each week so that you can help or get help, as needed. Find out about tutorials, teacher websites, and recommended resources.
5. Bring your student to MaThCliX!
When I was a graduate student, I was very serious about my work and committed to making A’s and doing my best. While taking a graph theory course, I remember working hard daily to learn and Learnunderstand the many proofs coming at us each week. I knew that I would never be able to reproduce any of these proofs on a test if I didn’t learn them and understand each step involved. To help me with this endeavor, I purchased the poster-sized Post-It Notes and carefully wrote out each proof in different colors. I hung them all over my apartment walls; they became my wall art for the time being. I studied them day and night as I spent time at home. I practiced writing them out on my own to see if I truly understood it and to discover what I might not understand. I think it is safe to say that I put forth a great amount of time, effort, and sacrifice. However, it paid off because I made very high A’s on all four tests and was exempt from having to take the final exam! In addition, I can honestly say I learned the content of the course.
I currently teach college algebra and while helping my students get prepared for their upcoming test, I was telling my students the above story about my efforts in graph theory. I was using it to demonstrate that to learn something we must work and put forth effort. Afterwards, one student even made the comment, “You’re like someone on the Big Bang Theory or something!”. Of course I laughed and took that as a compliment.
It occurred to me, at that very moment, that there are so many students out there who haven’t a clue what it means to work hard. It may sound simple, but for me, it was one of those “a ha” moments—-Learning requires time, effort, and sacrifice and it is every bit worth our time, effort, and sacrifice! The knowledge and experience that we gain and the discipline it takes to acquire it is invaluable and can build our character in ways nothing else could. I look back on my college days of hard work and stress and many moments of confusion and cherish it as a special time that shaped who I am today.
I encourage all students working towards a worthy goal to know that it will all be worth it in the end! Keep going!
When working with students I often get asked the question, “How do you know all of this?” or “How do you do math so well?”. I feel the answer to these and similar questions is just as simple as it is for anyone learning to do anything. When you study something thoroughly enough, you begin to piece everything together as one whole truth, if you will. In other words, when we focus on math as one whole truth and refrain from getting caught up or lost in the steps and procedures and forget what we learned, we begin to understand how each lesson (or piece of truth) is preparatory for the next. Think of it as a cake with infinite layers and each layer necessary before the next. If a layer is missed, then the next layer will not fit quite right.
I am not sure why, but I notice far too often, that students “learn” math, take a test, and then forget it. When you show them or discuss a concept that they already “learned”, they often act like they have no clue what you are talking about. At some point, they must approach math as a whole subject and put the lessons together.
For example, think of a knitting a sweater. One might knit an arm, front, back, etc. At some point, in order for the end result to actually be a sweater, it must be all pieced together.
Or, one can compare it to learning to drive. A new driver might study operating car controls, learning laws and road signs, parking techniques, interstate travel, backroads, night-time driving, etc. Any one of these lessons standing alone will not create a skilled driver. Nor will doing any of these things just once or twice. It’s in the actual piecing together of the skills and practice of driving in each area, that one becomes a skilled driver.
So it is with mathematics. To my elementary students, learn what you are doing now very well, because you will never stop using it in the progression of your mathematics study. Middle school students, what you are learning now is preparatory for high school mathematics. High school students, by now I hope that you are starting to piece together this beautiful subject of truth called mathematics! What you are learning is a culmination of all of your earlier years and preparatory for you to advance in further mathematics. There is always more to discover and learn and the further we go, we begin to see the subject as one whole truth. Our perspective and understanding is enhanced.
Thus, I would suggest as a final answer to these opening questions is that I have learned to understand math and not just memorize it. So, I approach it by applying all truth that I know and putting the question in context, then solving. I have spent much time doing and practicing and that is “how I know all of this”! Anyone else can, too.