Looking At Mathematical Connections

 Last time,  I spoke about connecting certain equations with different situations.  Today, I’m looking at making mathematical connections.  If you look at most math textbooks, there doesn’t seem to be any connections between sections or chapters in general so students see each topic as unique and unrelated to anything else they’ve studied.  If one looks at the world enough, math is connected and interrelated.  

As teachers, we need to teach students that there is connectivity in math otherwise students will not see it and will continue to struggle.  If you look at everything in math, you will see there are connections between and within strands, subjects, the real world, the past, and the future.  If you were to create a picture of the connections, it might resemble a spider web.

Let’s start by looking at the connections with the strands.  There is a connection among rational numbers, fractions, decimals, ratios, proportions, percentages, and measurement.  Or direct variation, arithmetic sequences, and linear equations.  We need to find the connections and share them with our students.

Then to show connections between math and other subjects, one can explore vocabulary and concentrate on words that mean one thing generally but have a specific meaning in math such as product or look at similar words such as hundreds and hundredths that are similar but are different.  Another thing to look at is the idea that certain things can be spoken of differently such as dividing by four is the same thing as multiplying by one-fourth.

Of course there is connecting between the past, present, and future. For instance, if you show students how to multiply binomials using a vertical set up just like you do for 12 x 36 so instead of place values of 100’s, 10’s, and 1’s you use x^2, x, and ones.  When I’ve introduced it this way, rather than beginning with the foil, students have seen the immediate connection. For students who learned to multiply using the lattice method, students found they could easily use it with binomial multiplication.  

Then if one can take what is being taught right now and connect it with something a student might run into the future, it adds another dimension to the learning process.  This might take the form of sharing when they will use it again in future classes or in the real world.  One example is the use of area.  Once students are familiar with finding area, extend it a bit to show that certain products such as paint are labeled as covering so much area per gallon.  Assign them a task to find the number of cans of paint is needed to cover the walls in a room.  This provides students with a chance to see how they might use it in their lives in the future.

The last example shows the connection between the area formula and its application in a real world situation.  Students need to see how the abstract math they learn in school is applied outside of the classroom.  One visual way to do this is to set a bulletin board up with one section devoted to each topic.  Then as a topic is taught, add it onto the board and connect to other sections till you have what looks like a spider web.  As new things are taught, you might need to change items out each time.  Let me know what you think, I’d love to hear.  Have a great day.