READING
· Developing Understanding in Mathematics
· Letters to a Young Mathematician
TEACHING EXPLORATIONS
1. Consistently use visibly random grouping assignments with the same group of students for the next two weeks.
2. Spend as much time as possible with your students working on vertically non-permanent surfaces.
3. Pay attention to the way students ask questions and the reasons for them asking.
4. Pay attention to your teaching and the way you are inclined to react to students' questions and behaviours.
Written JOURNAL
1. Reflect on your experiences from this weekend and give a thoughtful and detailed response to the following questions:
· What is mathematics?
· What does it mean to do mathematics?
· What does it mean to learn mathematics?
2. Referring to your answers to the above questions respond to the following question:
· What does it mean to teach mathematics?
3. What are your thoughts to the assigned readings?
4. Based on your TEACHING EXPLORATIONS what have you learned about yourself, your teaching, and your students?
Problem solving portfolio – the following are eligible problems for your portfolio
· Mother – Daughter Tea Party Problem
There is a mother-daughter tea that will be attended by 20 mother-daughter pairs, including the hosts. The rules of conduct are very strict; the host mother-daughter will greet everyone, all the guest mothers will greet everyone, and all the guest daughters will greet all the mothers only. How many greetings will there be?
· Palindromes Problem
Consider a two digit number – for example 84. 84 is not a palindrome. So, reverse the digits and add it to the original number – 84+48=132. Repeat this process until the sum becomes a palindrome. 132+231=363. The number of times the process is repeated determines the depth of the palindrome. For 84, the depth is 2. Find the depth of all two digit numbers.
THINGS TO REMEMBER
· the following problem MUST be completed before weekend #2 (rough work is fine)
Consider the following number pattern: 1, 2, 3, 5, 8 where each number is the sum of the two numbers before it. The first two numbers (1, 2) are called the seed numbers and they are responsible for generating the rest of the number pattern. I am interested in the fifth number – I want it to be equal to 100. Find all the seed numbers (whole numbers) that will make the fifth number 100.
· use the wiki to keep a daily record of how your teaching explorations is unfolding in your teaching.