Posted by: a | July 13, 2011

Don’t just memorize—Build connections!

Some students approach school as though it’s a game of memorizing new information, writing it down on a test page and then forgetting about it forever. How can you move beyond this, to make your learning more valuable and long-lasting?

One answer is to build connections. Think of your brain as a big spiderweb of ideas, thoughts and memories. When you drop a new concept in, the more strands you can stick to it, the more likely you are to retain it, and the easier it will be to find. Instead of thinking about new information in isolation, find out how it connects to what you already know.

Consider these strategies:

Find parallels

New mathematical concepts can seem mysterious, but often they are just the same methods you already know applied to more complex situations.

For example, if you stop and think about what’s really happening when you multiply numbers like 97 x 86 (something you already know), you might notice that you are using the same principles when you learn how to multiply binomials like (x-2)(3x+4) (new knowledge built on the old!).

Check out Vi Hart’s explanation with doodles.

Make sense of numbers

Too often we gloss over large numbers without fully processing their relative size. Try to consider them in terms of the familiar.

Canada’s federal debt is $560 billion. I’ve never earned a billion dollars, but I have earned minimum wage. A bit of googling and a quick calculation shows that if all Canadians worked full-time at minimum wage, it would take close to a year to earn $560 billion.

The Great Wall of China spans 8800km. How much of Canada would that cover?

Make analogies

Map a new process or idea onto something simpler or more familiar.

Learning about cell-structure in biology? Think of each cell as a factory, with each cellular component representing a particular job or location.

Photo credit: Luc Viatour © GFDL

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Responses

  1. I currently teach at a PYP school in China. Today, traditional Chinese education is all about memorization. Students learn numbers and time tables from a young age and can recite with ease. However, when asked to apply their skills with number to a word problem or real life situation, they can appear lost. Simply presenting the question in a different way than what they are used to can trigger mass confusion. This is something of a problem when I have students transferring from such a system into my inquiry based math classroom. However, I believe learning math through inquiry is another great way for students to develop valuable and long-lasting mathematical fluency.

    In my school, we call the subject mathematical literacy – aiming to ensure students become math literate in the real world. This is largely accomplished through investigating math topics and applying it to their lives. It is also accomplished through a lot of differentiation, which is great, but as all teachers know, can present more prep work. Learning math through inquiry usually takes students a while to grasp and it definitely helps if they have been exposed to it from a young age.

    A great website I use for reference is : http://www.inquirymaths.com
    It provides teacher resources and prompts to teach math through inquiry. It is aimed at the middle school and up level, but can be adjusted to suit primary level students as well.

    Here is a quick example of teaching math through inquiry in a grade 1 classroom on the topic of time and clocks. Start with a prompt. It can be a question, image, object, etc. What can you do in 1 second? 1 minute? 1 hour? Right away students are making connections between the topic and their daily lives. Test what students say to see if they are correct and draw connections between things that take a similar amount of time. They can then move into predicting as well. They can be given tasks to do such as bouncing a ball, counting to ten, etc. and time how long it takes them and make connections to what other people are testing. When investigating the clock, do not tell students there are 60 seconds in a minute, have students discover that information through comparing different clocks and hands, and finding patterns. Scheduling is also a great tool to relate time to their lives. Teaching math in this way can be resource heavy and require more planning time, but the benefits in terms of retention and ability to apply concepts learned to their lives and other learning will help to develop more well-rounded students.

  2. This is so important! Making connections to the real world answers: “so when am I ever going to use this?” Our new curriculum in BC involves a lot of those connections as part of the big ideas and competencies. In Math, I have always tried to make connections and to give them a close to authentic situation (ex. researching buying a car new or used, vs leasing and all the costs that go with it, etc.) Where I struggle in Math is connecting the abstract to the real world? When the answer to “so when am I ever going to use this?” is, never.


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