Math Word Problems – why are they so hard for so many students?

I’m working with a range of students, boys and girls, young adults in their early teens and adult learners, my age and up, those who want to improve their grade from a B to an A, and those who want to “just pass the course”.  However, I am repeatedly faced with an unresolved question – what make math word problems a category so many of them fear and dislike?

On the surface, these questions can be technically easy. Some can be solved by a single equation and most, when compared to the other questions on a given exam or worksheet , involve less calculations and mathematical manipulation. So why then are they considered harder?

My thinking on this question is still evolving – I think the answer is complex. However, I’ve been able to identify two reoccurring themes.

One theme is the lack of skills to translate the information in the question – which is stated in words and sentences and in English to the mathematical language of expressions, equations, constants, and variables. These are skills that can be developed and I work hard with my students to do exactly that – create a “Dictionary” that enables them to read English and write Math, pick clues from the way the problem is written, and move back and forth between the two languages.

The second theme has more profound implications. The way math is taught in the US (at least in Montgomery County Maryland – where most of my students obtained their mathematical education) seem to curtail imaginative thinking for these students. The student reads the problem and then either comes up with a way to solve it or gives up. This approach is detrimental and prevents the student from succeeding solving problems they nether seen before. To overcome this obstacle I work with my students on what I call “friendly encounters”. I tell the students that when they come across a problem they have no idea how to solve they should engage with it. This can be done by rephrasing the problem in simpler terms, drawing a diagram, plugging in numbers (miniature deduction process), and other techniques.

Over time, I would like to think, my students develop their own paths to successfully engage word problems. However, I am feeling sorry for the many other students out there who are reluctant to solve word problems due to lack of proper guidance and hope the information and insight I shared with them here will help them better cope with this type of Math problems.

Hanan

What is Math?

What is math?

Good question. Mathematics, according to Merriam-Webster dictionary,  is “the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.” There are several good definitions, however, none can briefly encompass all the aspects and meanings we attribute to mathematics. I have tried, though.

Here is my definition:

Mathematics is a language devised by humans to describe quantities and the relations observed between these quantities. This dialogue facilitates our understanding of the world.

Once you accept the approach, ‘math is a language’, an alternate path to it will open for you. The, so often encountered, approach that in order to learn math you need to learn a boring series of mechanical operations will be exchanged by a view of a dialogue between people (you and your teacher, you and your classmates, or you and the author of your math textbook).

I view math as a form of communication between individuals speaking the same language. The unique and universal feature of the mathematical speech allows an exchange of ideas and tools between individuals. It is not surprising then that the math done in China, Russia, Korea, Australia, Brazil, and the US is in essence the same. Not only that, we can understand the mathematical calculations done by ancient cultures (like the Mayans, Greeks, Romans, Ottomans, Egyptians, Slavs, etc.) while we encounter difficulties in understanding their spoken and written languages.

Start of the School year

Now, as in every year around late August to early September, we transition from the summer activities to the back-to-school frenzy.

Yet again, school buses travel the streets and gather students to their assigned schools. Students carry their books and backpacks back and forth. They meet their new teachers, take exams, hopefully do their assigned homework, and in the process learn the skills they will need for the 21st century. For many, this is a hard job. Sometimes they need support and assistance. There is no shame in asking for help when you need it.

My recommendation to all parents is to track their children’s performance and to require daily feedback that is detailed (not just the typical teenage “OK”). For parents of MCPS students: Edline is a great tool – and  it helps you keep track of how your child did on each individual task. You’ll be surprised how many graded homework  assignments are to be handed in during the school year. Be proactive – contact your children’s teachers, encourage your kid to meet with his or her teacher during lunch breaks to review and strengthen understanding, encourage him or her to take advantage of the free tutoring offered by many honor societies within the school, engage and join study groups, and spend time reviewing the material.

I know this will be a great year and am looking forward to help my students attain their educational goals.

-Dr. G.

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Math4Teens is in the process of updating content for the 2012-2013 school year.

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Math4Teens is all about making math accessible, understandable, and fun.

Dr. G. founded Math4Teens with a simple premise guiding his teaching philosophy:

Math=Language

 

Dr. G. considers Math as a human form of communication. This language is used when communicating properties of quantities, the relations between such entities, and the tools to process them.
Like learning a second language, the acquisition of mathematical skills is strongly facilitated by its use in interaction between the student and the tutor. See more in the Blog section.