9. I Hate Answering Questions in Front of the Class

The Cause:

Students worry about getting the answer wrong in front of the class because they believe that maths answers are always either RIGHT or WRONG.

The Solution:

The maths we need in the REAL world often involves open ended questions. Think of finding directions on Google Maps. What is the best way to get from A to B? One route might be shorter but include tollways another might involve longer distances but less traffic.

Text book problems are often repetitive with RIGHT answers at the back of the book. But in the real world maths problems nearly always involve THINKING. eg. A building design might require specific engineering maths. Now add costing! That’s an open question. There are many options. Maybe the costing will then change the engineering. Build 20 stories instead of 25.

Thinking Outside the box in Education: Info and Toolbox: here

Prof Peter Liljedahl, Faculty of Edu, Simon Fraser Uni, Canada, advocatesopen ended questions in the maths classroom.

Here are some of his examples for Year 7 -9 (Download pdf file at the link):

You are in a bike race and have to use a street bike and trail bike, but one bike must be left somewhere on the route.You travel at different speeds depending on which bike you use. What route do you take? (A basic map is included.)

Something inspiring:

Maths is often about playing around with answers. This is how play led a class of 12 year olds to produce a peer reviewed research paper published in a science journal.

Community Maths can involve the school community or the wider, local community. The aim is to get maths out of the classroom and make it a hands-on experience.

Set up displays, posters, demonstrations or art/maths projects in your school library, gym or school yard or take some interesting maths to the local library, strip mall, town hall, local gardens or shopping mall. It will mean planning the project, collecting the materials and making a phone call to the local, say, librarian, but libraries, for instance, welcome community involvement.

Here are just some community maths project ideas.

MATHS POSTERS

Major maths conferences around the world have poster displays. So why not a display of students maths posters in your school library or local library or even a nearby shopping mall. And students should be present at allocated times to explain their poster to other students, parents or members of the public.

Roosevelt Middle School students Jacob Klausner and Oliver Adelson WEST ORANGE, NJ, who were finalists heading to theNational MathCon Competition.

Some of the best middle school maths posters can be found atMathsCareers, UK. Here are some posters from the 2016 competitions.

Winner 9 – 11 years Maths Poster Competition

Fatimah Patel Preston Girls High School

Runner Up 9 – 11 years Maths Poster Competition

Maja Kowalska McAuley Catholic High School

Winner 12-13 years Maths and Music Poster Competition

Laeticia Junanto Bancrofts School

MATHS DEMONSTRATIONS

Maths students can construct displays that involve interesting maths. The most amazing maths dispalys Mathspig has seen were at the 13e Salon Culture & Jeux Mathematique in Paris. Here is LAGA Phd student Attouchi @ the 13e Salon Culture & Jeux Mathematique in Paris.

She was showing students how to use a graph to create anamorphic projections. More detailed instructionshere!!!

Palestinian Maths teacher Daina Taimina has many zany ideas. You’ll more Creative Maths ideashere.

Mentalist Maths … OK. This may include some Card Tricks … but they’re amazing. You’ll find 10 amazing Mentalist Math Trickshere.

Or let students explore some of the inspiring maths websites and pick a project. You will love the amazing German website IMAGINARY. It’s in English and has some fascinating videos!!!!!

Perhaps students could construct double pendulum like this one demonstrated at the MiMa-Museum, Oberwolfach, Germany. Mathspig can’t stop watching it. Fascinating!!!!!!! The double pendulum has some demanding trigonometry, but at the middle school level the 2D graph traced by the lower pendulum is fascinating enough (Below). And maths can provide equations for this movement. That’s impressive.

I started my maths workshop in Hamburg by stirring up some friendly rivalry. And what better way to do this than by using statistics.

Which is the biggest country?

Australia is 21.5 times the area of Germany. So I counted off 22 workshop participants and pointed to one saying ‘Your’re Germany! Ha!’ Here’s another way to compare areas:

Which country has the largest population?

Germany has 3.5 times the population of Australia.

But the really interesting questions are:

Who drinks more beer?

Who eats more meat?

Here are the answers to these and other interesting questions from the introduction to my workshop with apologies to Brisbane and Perth:

Here are some amazing ways to make middle school maths AMAZING:

The Maths Mystery Box is a great treasure chest to take into maths classes. It can be used an an extension exercise or to engage some disengaged students.

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The IDEA is to use concrete objects and write a maths problem to go with the object. (See examples below) The appeal of the MATHS MYSTERY BOX is that it involves CONCRETE THINKING, sort of. All text books involve ABSTRACT thinking, which some students do not like.

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A student picks a maths problem from the box. A problem can be simple or complex. But it is not just a maths problem. The student gets to hold an object in their hand. They have to devise their own method of approach. And they must be resourceful. ie. use equipment at hand eg. their phone as a stop watch. Students like this activity. Even maths teachers like this activity as Mathspig found out at her workshop in Hamburg.

One reason why students think maths is a waste of time is because they do not see it in their world. It’s not just middle school students. We are all maths blind.

Here is the challenge. At the beginning of your next maths class:

Ask your students what ‘mathsy’ thing they have on them and see what happens. Mathspig started her ICME 13 Workshop with that question and maths teachers from around the world struggled to answer. Here is what happened.

More ideas below.

Note: I missed the significance of ‘Standing on the Shoulders of Giants’ Quote. It was from the great mathematician Sir Isaac Newton, 1776.

*Flooring: Wood (parallel lines), carpet (tessellations), coefficient of friction (Don’t want people to slip in the wet).

*Windows, doors: Hinges (Fulcrum, Effort as a Hyperbolic function), opening/closing door is an equation of a circle, angles, fly screens (pattern), windows (pulleys sometimes), handles (knob or lever impacts on effort)

Table/desk/chair: Based on statistics to fit majority of students.