Distractions from learning pt 2: Math Manipulatives

Maria Miller, author of Math Mammoth (a homeschool math curriculum), wrote a blog entry called The Value of Manipulatives.  She explains how Math Manipulatives can actually become a learning distraction. In my last post, Distractions From Learning, I explain that sometimes, attempts to draw students into a lesson can misfire, and actually serve as a distraction.  Mrs. Miller's post is a great example of math manipulatives distracting from the lesson.  Is teaching with math manipulatives a bad teaching strategy?

Math Manipulatives - what do they do?
Manipulatives show numbers visually and concretely.  You cannot hold 2, but you can hold two apples.  Manipulatives present Place Value: a ones place, tens place, hundreds place.  Higher level math continues with place value, into the decimal / fraction places and into thousands, millions, billions.  Manipulatives give the student something to touch and move around (manipulate).  When shifts happen in place value, this can be taught concretely, by showing the real shift in numbers.  Place value blocks are a common concrete representation of abstract concepts. 

When do manipulatives distract?
Many of us have seen the hundreds blocks get stacked into a house, complete with a tens block fence, and ones place people.  Our little students are not thinking about place value when erecting a tall skyscraper out of manipulatives!  When students ignore the lesson and explore the blocks creatively, the manipulatives did not enhance the math lesson: the manipulatives distracted.

Another distraction: when the student does not make the transition from concrete to abstract.  At some point, 2 apples and 2 apples can be understood abstractly as 2 + 2.  This stage of moving from concrete to abstract repeats with each new concept.  Remaining in the concrete phase means that the student still doesn't understand the connection between those 2 physical items and its representation.  A student can fall into this trap even in higher math.  Manipulatives should be a short phase before moving to the next phase.  The natural next step is a visual presentation on the page, and lastly, being able to work the abstract numbers.

Sometimes, using manipulatives with incredibly large numbers serves as a distraction.  In Maria Miller's blog post, she has a video of a child working a math problem using a pictoral representation of the numbers.  The numbers are in the thousands.  Shifting and counting these numbers becomes problematic because the sheer size of the numbers gets in the way.  Working the abstract numbers is faster and more reliable.  In teaching the concept of large numbers, a manipulative or pictoral representation can help show the student "hey, this is what is really happening, behind the scenes"; but hopefully the student will catch on and be able to bring this understanding with her in the next step: traditional algorithms.

Distractions from learning: when activities distract from the lesson

Many of my thoughts expressed on this blog have come from a book called Why Don't Students Like School by Daniel T. Willingham. One point he brings up in his book is: how is your student thinking about the information that is being presented? Often, our purpose in presenting a lesson is to get the student excited about the topic. Sometimes, our well intended purpose goes astray when the student focuses on the wrong thing. For instance, that hands-on lesson that involves making a map of Japan out of cookie dough? Were your students actually thinking about the geographical layout of Japan or were they thinking about licking their fingers or adding more blue to that ocean? That is one thing to consider when making lesson plans. What are your students really thinking about? Unit studies are well-known, well-liked method of learning in the homeschool world. When studying pioneer days, homeschool families may choose to hand dip their own candles or make a corn husk doll. I've heard of brave, endeavorous families building a full size wigwam in the backyard to add to their study of Native Americans. There are many fantastic, memorable projects to undertake as a homeschool family. However, sometimes these projects can be distractions from the real learning that takes place. How will you know if a hands-on project will be a distraction or will help cement the information in your student's mind?

Ask them later
One tale-tell way of knowing what your student really got out of the lesson is to ask them later. Have your child explain to a friend, your spouse arriving home after a full day of work, or a grandparent. Ask them: what did we do today? and why did we do that? If they can explain what happened and most importantly why it happened, the lesson was a success!

Watch their reaction
During the lesson, what is your student doing? Is he fully engrossed in what he is doing? Are his questions relating to the information you want him to learn? Or is he asking odd, unrelated questions? Is he fixated on playing with the materials or creating something that does not relate to the lesson? If you find that your student is distracted or is not relating the project with the information he needs to retain, then this particular activity did not meet its original purpose.

Trial and Error
So how do you know ahead of time that a lesson will focus your students' attention on the learning at hand? How can you steer clear of activities that serve as a distraction? A big answer to that is trial and error. If you repeatedly see activities turn into distractions, you'll need to ask yourself what was it about those activities that did not focus on the lesson? How did the topic veer away from the lesson? You can also ask yourself ahead of time, by running through the lesson in your mind: what is my student supposed to think about and does this lesson focus his attention on that?

In conclusion
Hands-on activities, projects, and unit studies can be a wonderful addition to school and homeschool learning. A parent or teacher needs to assess if the activities will help the student to learn the lesson or if the activity will serve as a distraction.