Go Figure!

Put a LID on It! Using plastic lids as a teaching tool

There are so many things we consider to be trash, when in reality, they are perfect treasures for the classroom. One that I often use is plastic lids from things like peanut canisters, Pringles, coffee cans, margarine tubs, etc. These lids can be made into stencils to use when completing a picture graph.

Students must first of all understand what a picture graph is. A pictorial or picture graph uses pictures to represent numerical facts. Sometimes it is referred to as a representational graph. Each symbol or picture used on the graph represents a unit decided by the student or teacher. Each symbol could represent one, two, or whatever number you want. This type of graph is used when the data being gathered is small or approximate figures are being used, and you want to make simple comparisons.

Here is what you do to make ready-made picture graph stencils.

Choose the size of lid that you want and turn it over. Then trace a pattern on the plastic lid. Make sure you are using the bottom of the lid so the rim does not interfere when the children use it to trace.
To make the stencil, cut out the pattern using an Exacto knife. You might choose to do zoo animals: a zebra, a lion, a bear, an elephant or a giraffe.
Have a large sheet of paper ready with a question on it such as: “What is your favorite zoo animal?”
The students then select the stencil (picture) that is their favorite animal and trace it in the correct row on the graph.

Below is a sample of this type of graph. It is entitled, What is Your Favorite Season? A leaf is used for fall; a snowflake represents winter; a flower denotes spring, and the sun is for summer. Notice at the bottom of the graph that each tracing will represent one student.

You could craft stencils for modes of transportation, geometric shapes, pets, weather, etc. The list is infinite. But what if you don't want to or don't have time to make all of those stencils? Then save the strips that are left when you punch out shapes using a die press. They are instant stencils!

If you are interested in additional graphing ideas, check out the resource entitled: Graphing Without Paper or Pencil. You might also like Milk Lid Math. This four page handout contains numerous math activities that utilize a free manipulative.

Helping Students to Think Mathematically

What does it mean to think mathematically?

It means using math vocabulary, language and symbols to describe or interpret mathematical concepts, procedures and to discover relationships among ideas. Therefore when a student problem solves, they use previous knowledge, skills, and understanding of concepts to solve a problem. This process might include formulating problems, applying a variety of strategies, or interpreting results.

What can we do to help our students become better mathematical thinkers?

We can teach and model problem solving strategies. We can remember and plan our lessons to involve the three stages of conceptual development: concrete, pictorial, and abstract. We can have the students talk or write about how they got an answer either with the class or with a partner. We can use writing in the mathematics classroom (such as math journals) to allow the students to practice expository writing and show their understanding. We can exhibit math word walls and have the students use the glossary in their book to write and define terms.

We can also create a positive and safe classroom atmosphere for problem solving...

By being enthusiastic and allowing the students to take risks without consequences. By emphasizing the process as well as the answer, the students may be willing to try unconventional or different ways to solve the problem. I always tell my students that there isn't just one right way to get an answer which surprises many of them. In fact, this is one of the posters that hangs in my classroom.

As math teachers, let's continue to emphasize problem solving so that all students will acquire confidence in using mathematics meaningfully. But most of all, let's have fun while we are doing it!

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If you are interested in having a math dictionary for your students, check out A Simple Math Dictionary. It is a 30 page student dictionary that uses easy and clear definitions as well as formulas and examples so that students can learn and understand new math words without difficulty or cumbersome language. Most definitions include diagrams and/or illustrations for the visual learner. Over 300 common math terms are organized alphabetically for quick reference.

Defeating Negative Self-Talk

One of the biggest problems with the college students I teach is their math anxiety level. Math anxiety is the felling of tension and anxiety that interferes with the manipulation of numbers and the solving of math problems during tests. In other words - mathphobia! This is a learned condition, not something they are born with and is in no way related to how smart a student is. In my Conquering College class, we have been looking at causes for anxiety which include bad experiences, teacher and/peer embarrassment and humiliation, or being shamed by family members. We've been looking at ways to reduce math anxiety such as short term relaxation as well as long term techniques and managing negative self-talk.

For many of my students, a song is the best way of remembering. I found an old nonsense song by Roger Miller entitled, You Can't Roller Skate in a Buffalo Herd. First we read over the words. Next we watched a video on You Tube and then we actually sang the song. I replaced the words "But Ya can be happy if you've a mind to" with "But ya can be positive if you put your mind to it."

You Can’t Roller Skate in a Buffalo Herd

By Roger Miller