When to Introduce the Calculator

When Should Students be Introduced to Calculators?  I am sure that this topic could spark an interesting debate. Well, I certainly have no interest in debating, but, I would like to bring to light, my professional belief on this topic, after working with math students for almost 20 years.

First, I would like to explain theoretical mathematics as doing math independent of the world.  It uses reasoning, proof, and abstract concepts to establish truth upon truth.  While things going on in the world around us may inspire a theoretical mathematician with new ideas, the study of theoretical mathematics does not depend on the world around us.  So, some might argue that if math does not have a direct “real-world application”, then it is useless.  This is not true since even applied mathematicians draw on theoretical mathematics to solve problems related to the the world.

Research has shown that students receiving more instruction in theoretical math do better overall because they build a mathematical foundation that will allow them to extrapolate math to other real-world situations.  If math is just taught for a specific application, then the student will not be able to transfer that knowledge to another context.  Theoretical mathematics does not change. It is simply, truth.

Now, let’s get back to the calculators! What is the purpose/role of calculators in mathematics?  To make it simple, calculators are used to speed up extensive calculations involved in real-world problems.  The problem is that students who haven’t developed a strong math foundation are using these calculators for much smaller calculations that they should be doing by hand, to strengthen their grasp of numbers, or even in their head in some cases.  When students do computations by hand, they develop a feel for number patterns and a respect for mathematics.  They build a foundation of mathematics that will be evergreen, and thus withstand the test of time and any changing technology.

Consider this example:  I watched an advanced 9th grader go to her calculator to compute 105-90.  A person with a strong sense of numbers would likely “mentally” compute this by knowing that from 90, it’s 10 more to 100 and then 5 more past 100 so the difference is just 10+5 =15.  Once this skill is developed, it is certainly quicker to state this difference without a calculator!  Just in case you think this example is too “complicated”, what about watching a student perform 13-9 on a calculator?  That is not what a calculator was invented to be used for!

So, what am I suggesting?  I am suggesting that calculators aren’t really needed until a student has a solid grasp of number sense.  So solid, they won’t “forget” how to do basic arithmetic on all numbers, including integers, fractions, and decimals. So, when is this?  Well, clearly it will vary from student to student, but in general, I would go as far as to suggest not allowing calculators until at least precalculus.  And even then, limiting their use.  Even the AP Calculus exam and the SAT have “no calculator” sections!

I say to all math teachers, let’s put the pencils in student’s hands and give them lots of paper and let them DO MaTh!  There is no shortcut or tricks to learning math.  Each student has to walk the road and allow their brain to make the connections.

 

Back-to-School Success

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.

Students

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.

Parents

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! 

Math Manipulatives

Math ManipulativesDo 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!

You Can Do It, Not Always Alone

aloneI 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…

  1. 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!
  2. ALWAYS use answer keys while doing your homework.  First, do the problem, then check your solution.  Instant feedback is essential to correcting mistakes.
  3. 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.
  4. 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!
  5. 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.
  6. 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.
  7. Write note cards with important notes/formulas as you go to keep everything in one place.
  8. 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.