Readings for our Feb. 16 class on math education, equity and social justice

Here are our three readings for next week's class:

1) Latino/a parents' voices on teaching mathematics for social justice (Eric Gutstein)

2) The sociopolitical turn in mathematics education (Rochelle Gutiérrez)






3) Talking about teaching mathematics for social justice (David Stocker and Dave Wagner)

Five Grade 6 & Grade 9 word problems...but a little unfamiliar

(1) ஜென்னி $ 9.95 ஒவ்வொரு, 7 டி-ஷர்ட்டுகள், தன் ஏழு சகோதரர்கள் ஒவ்வொரு ஒரு வாங்கினார். காசாளர் தனது விற்பனை வரி கூடுதலாக $13.07 விதிக்கப்படும். அவர் ஒரு measely $ 7.28 கொண்டு கடையில் விட்டு. ஜென்னி எவ்வளவு பணம் ஆரம்பித்தீர்கள்? (Tamil)

 (2) Есть 22 золотых монет и 9 серебряных монет в коллекции монет Чарли. Каково отношение количества золотых монет на количество серебряных монет? (Russian)

(3) አንድ applesauce ኩባንያ ፖም 7 ላኩ አዘዘ. በእያንዳንዱ የጭነቱ ውስጥ 9.851 ሮማኖች ነበሩ. ምን ያህል ፖም ሁሉ ውስጥ ኩባንያ ትእዛዝ ነበር? (Amharic)

(4) Bíll fer frá A til B á hraða 40 mph þá skilar, með því að nota sömu leið, frá B til A á hraða 60 mph. Hvað er meðalhraðinn fyrir hringferð? (Icelandic)

(5) А прямоугольник далалық 300 шаршы метр аумақты және 80 метр периметрі бар. кен ұзындығы мен ені қандай? (KazakH)


(And the original word problems:)

(1) Jenny bought 7 t-shirts, one for each of her seven brothers, for $9.95 each. The cashier charged her an additional $13.07 in sales tax. She left the store with a measely $7.28. How much money did Jenny start with?

(2) There are 22 gold coins and 9 silver coins in Charlie's coin collection. What is the ratio of the number of gold coins to the number of silver coins?

(3) An applesauce company ordered 7 shipments of apples. There were 9,851 apples in each shipment. How many apples did the company order in all?

(4) A car travels from A to B at a speed of 40 mph then returns, using the same road, from B to A at a speed of 60 mph. What is the average speed for the round trip? 

(5) A rectangle field has an area of 300 square meters and a perimeter of 80 meters. What are the length and width of the field? 

The International Group of PME (the organization formerly known as Psychology of Mathematics Education)

Here is a link to the IGPME website.

You can create a log-in for yourself, and that will give you access to the full PDFs of the PME proceedings from 2013 and 2014, and 'print on demand' paid versions of the proceedings from 2015 and 2016.

I have hard copies of the proceedings for the PME conferences where I've presented -- and Cynthia Nicol has more. The UBC Library may have hard copies and/or electronic access to PME proceedings as well.

Through Google Scholar, you can access articles from the proceedings of PME conferences going way back. 

Readings on the language of mathematics/ multilingual math learners for our Feb. 9 class

(1) Moschkovich on learning math in two languages

(2)Schleppegrell: a research review on challenges of mathematical language

(3) Rowland: Hedges and vague language

'Something to think about': Mathematical problems from Mason, Burton & Stacey, Thinking Mathematically (2nd Edition)

It helps to be doing mathematical problem solving to get a sense of how it works for both learners and teachers.

As you work on these puzzles, note with your 'teacher bird' awareness how your 'learner bird' is engaging with the problem solving!

1) Thirty-one:
Two players alternately name a number from 1, 2, 3, 4 or 5. The first player to bring the combined total of all the numbers announced to 31 wins. what is the best number to announce if you go first?

- Try playing it!
-What do you need to record?
-What totals enable you to win in one move? Generalize!
-Can you find a strategy for playing that will guarantee you to win?

extend:
•What if 31 is changed to some other number?
•What if the permitted numbers are 1, 2, 3, 4, 5 and 6?
•What if there are 3 players?
•What if the permitted numbers are 1, 3, 5 or 2, 3, 7?


2) Sticky Angles:
Given a supply of sticks, all the same length, and a supply of angles all the same size, can you join the sticks together end to end at the given angle to make a closed ring?

-Have you tried it physically?
-Introduce a way of making a supply of angles!
-Have you stayed in the plane?
-Have you tried folding a strip of paper appropriately to mimic many sticks joined at the correct angle?
-Will your method always work, or is your angle special in some way?

extend:
•What is the shortest such sequence when it is possible?
•What length sequences are possible?
•Does it help to have more than one angle available, particularly when you are confined to the plane?

3) Sequence:
Write down a sequence of 0s and 1s. Underneath each consecutive pair write a 0 if they are the same and a 1 if not. Repeat this process until you are left with a single digit. Can you predict what the final digit will be?

-Specialize systematically.
-Allow your system to alter as you begin to see what is going on.
-Try to be systematic about patterns and not about lengths of sequences.
-Try working backwards from the final digit.
-Find a convincing argument to support your conjecture.

extend:
•Write down a sequence of 0s and 1s in a circle and proceed as before.
•Set your result in a more general context by using 0, 1 and 2 with some appropriate rule.

4) Milk crate
A certain square milk crate can hold 36 bottles of milk. Can you arrange 14 bottles in the crate so that each row and column has an even number of bottles?

-Depict the crate. Find a way to be able to manipulate bottle substitutes.
-Specialize to crates of other sizes
-How many bottles might there be in each row and column?
-Specializing to larger crates might help.
-Eventually you will deal with the 36-bottle crate, but what about square crates in general?
-Can you build up new arrangements from old ones?

extend:
•Try to place other numbers of bottles.
•Try rectangular crates.
•What is the largest/ smallest number of bottles that can be suitably arranged in a given crate?
•How many ways are there to place the bottles?

Some real-life workplace mathematical problem solving from the 90s (from Colours of Infinity)

In this older but nonetheless fascinating film on fractals, Colours of Infinity (featuring Benoit Mandelbrot, Arthur C. Clarke and Ian Stewart), Michael Barnsley talks about how he made a breakthrough in fractal image compression for video and computer images.

36:26 - 42:28.

YouTube video: Watch kids solve a word problem -- "How old is the shepherd?"

This is a replication of the famous "what is the name of the captain?" word problem -- a problem with misleading or insufficient information, and which many kids attempt to solve nonetheless.

"How old is the shepherd?" video

What do you think of this?