9. I Hate Answering Questions in Class: BUSTED

The Complaint:

 

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 opened 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 a 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, advocates  open ended questions in the maths classroom.

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

Concert in Toronto;

You have won tickets to a concert in Toronto but must plan your trip using flight times to arrive at the concert by 9pm.

Two Bike Race:

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.

1. Middle School Madness: BIG MATHS

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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 the National MathCon Competition.

Some of the best middle school maths posters can be found at MathsCareers, 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 instructions here!!!

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

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

Make some interesting cubes here.

Give students a variety of maths challenges they have to solve

like these Maths Mystery Box Challenges here.

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.

 

Crazy Ways to Make Middle School Maths Cool

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:

1. Defronting the Maths Classroom

2. Amazing German Maths Blog

3. m&ms and Exponential functions

4. Take a Mandelbrot Set Selfie

5. Best Fun with Algebra Ever

6. The Multi-legged Beast that Walks

7. Maths You Hold in Your Hand

8. Are you Maths Blind?

9. Real World Maths Selfies 

10. Magical Music Machine built with Maths

And don’t forget:

Maths News from around the World

7. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths

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.

This is what the graph should look like.

Bob the Beetle moves very fast and students have to use available tools eg. phones to calculate his speed.

You’ll find the answer here.

Safety Lecture: Do not flick at anyone. But it is fun.

 

8. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths.

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.

More Maths on or around you: 

*food snacks: nutrition information, calories, cost.

*medication: recommended dose, concentration eg. 5 mg, quantity, cost.

*room temperature: weather forecast.

*Light Bulbs: Watts, brightness (lumens, inverse quadratic function)

*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.

Leaning back on chair: Centre of Gravity. Watch out. 

Sharpening pencil: Circular motion, sharpness of blade reduces force needed. Why?

Pens, books dropping on floor: Good old gravity. Works every time. Quadratic fn.

Fonts: Size. Based on statistics for readability. Watch the small print.

Jewellery: Geometric shapes & patterns, but also symmetry of diamond facets, weight of diamonds in carats, purity of gold in carats (different carat).

Zips: Interlocking pattern hopefully not interlocking with your skin.

Heating: Flow rate, cost, vent locations.

Architecture: Of building involves length, height, area and cost. 

External Noise: Wall thickness. Sound proofing.

Rubbish: Recycling. Why do it?

Tights: You buy them using a height weight graph on the back of the packet. 

9. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths.

Here is a fabulous idea for prompting students to ‘see’ maths in the world. This activity was designed by Axelle Person Faughn, North Carolina University (Below).

The idea is simple.

Ask students to take pictures of maths they see in their lives. The photos below were taken by Axelle’s students.

Alternatively, you can give students an equation and ask them to find a picture representing that equation. Axelle gave Mathspig a slip of paper with the words ‘Demonstrate limits’. I sent back a picture of curly hair and a link to the equation of a helix.

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Is that pasta really a Sine Curve?

 

10. Funky, Fab and Fantastic. Yeah! That’s Middle School Maths.

Maths today is invisible.

It is hidden, most often, behind screens in computer code. But every so often some magical machine arrives that makes maths visible.

Look at the Marble Machine (below) by Wintergartan a Swedish folktronica band, then ask your students ‘what maths was involved making this machine?’

It didn’t just happen. Some suggestions below.

Maths involved:

*length of xylphone keys. These will be accurately measured to produce the correct note. Ditto width and thickness.

*rate of rotation of gears, wheels

*parabolic path of marble falling on xylophone keys

*ratios of gear wheels

*statistics. The marbles do not always bounce indentically off the keys. So the cup needs to be big enough to capture – what?- 99.99% of the bouncing marbles. I think less. You can count the number of marbles – ball bearings – that have escaped. You can see them on the floor at the end of the video. So you can calculate the % that escape.

*timing (Each element of the machine has to be timed to create the musical effect. Not chaos.)

*Engineering Maths: Strength of laminate. This will have been tested by the manufacturer. Laminates have a much greater tensile strength than one piece of wood.

*Computer Cutting: A program exists to accurately cut out those wheels from a laminate.

*Cost

*How do you buy 2,000 marbles (ball bearings)? Do you count them? You would buy them by weight.

*Any more suggestions?