1. SBED 1259 Teaching Methods Mathematics 2017
Friday 27 JAN Test 1
Friday 3 FEBR Assignment
Friday 10 FEBR Test 2
Monday 13 FEBR Micro teaching
Wednesday 15 FEBR Micro teaching
Friday 17 FEBR Last lecture

2. Principles to actions Chapter: Effective Teaching and Learning
USA
Principles to actions
Ensuring mathematical success for all
Chapter: Effective Teaching and Learning
Establish mathematic goals to focus learning (pp 12-16)
Implement tasks that promote reasoning and problem solving
Use and connect mathematical representations
Facilitate meaningful mathematical discourse
Pose purposeful questions
Build procedural fluency from conceptual understanding
Support productive strugle in learning mathematics
Elicit and use evidence of student thinking
Book title:

3. Implement tasks that promote reasoning and problem solving
Mathematical tasks can range from routine exercises to complex challenging problems
Not all tasks provide the same opportunities for student thinking and learning
Student-learning is greatest when tasks encourage high-level student thinking and reasoning. Student-learning is least when tasks are routinely procedural in nature
Tasks with high cognitive demand are the most diffiucult to implement in the classroom. These are often transformed into less demanding tasks during instruction.

4. Implementent tasks that promote reasoning and problem solving
A taxonomy of mathematical tasks based on the kind and level of thinking required to solve them.
Lower-level demands (memorization)
Lower-level demands (procedures without connections)
Higher-level demands (procedures with connections)
Higher-level demands (doing mathematics, mathematical reasoning))

5. Connections to underlying ideas
Lower – level tasks
Memorization
What are the rules for solving equations?
What are the rules for divisjon of fractions?
Procedures without connections
2x = 10
x + 1 = 6
1 2 : =
Connections to underlying ideas

6. Higher – level tasks Procedures with connections Find one halve of 1/3
Find 1/3 divided by 2
Doing Mathematics
Create a real world problem where you need to divide fractions
Your monthly limit for use of smart phone is TzS How many SMS-messages can you send per month before you reach the limit if you need to pay a basic fee of TzS 50,000 per month and TzS 100 per SMS-message?

7. Open and closed mathematics
Adults and students , when presented with «real world» mathematical situations, do not use school-learned mathematical methods or procedures but instead use their own invented methods.
… that students are unable to use school-learned methods and rules because they do not fully understand them.
Boaler, J. (1998). Open and closed mathematics: Student Experiences and Understandings. Journal for Research in Mathematics Education, 29 (1) pp 41-62

8. Open and closed mathematics
Closed mathematics: use of traditional low-level tasks
Open mathematics: process-based, tasks of higher-level
Students who learned mathematics in an open, project-based environment developed conceptual understanding that yielded advantages in a range of assessments and situations.
Boaler, J. (1998). Open and closed mathematics: Student Experiences and Understandings. Journal for Research in Mathematics Education, 29 (1) pp 41-62

9. Implementent tasks that promote reasoning and problem solving
No more place for low-level tasks ?
No more place for practicing skills (procedures) in mathematics classrooms?
Yes, we need both low-level tasks and high-level tasks

10. High level tasks ?
Low-level tasks

11. Higher – level tasks Procedures with connections Find one half of 1/3
Find 1/3 divided by 2
Doing Mathematics (Mathematical reasoning)
Is one third of 1/2 the same as one half of 1/3?
Why is 1/3 divided by 2 the same as 1/3 x 1/2?

12. Lower – level tasks 1 2 : 1 3 = Higher – level tasks
Procedures without connections
2x = 10
x + 1 = 6
1 2 : =
Higher – level tasks
Explain
Is x the same as x ? Why (not)?
Is : the same as : ? Why (not)?

13. An example: Learning about fractions and decimal fractions
2 periodes
What is a fraction? What is a decimal fraction?
How can we compare fractions and decimal fractions and how can we find out which fraction is the greatest one?
How do fractions and decimal fractions relate?

14. An example: Learning about fractions and decimal fractions
Warming-up activity
Learning activity 1
Learning activity 2
Learning activity 3
Summarizing

15. ? 1 𝟑 𝟒 An example: Learning about fractions and decimal fractions
Warming-up activity ? 1

16. An example: Learning about fractions and decimal fractions
Warming-up activity
Learning activity 1
1. Explain to another learner why your fraction
is greater than one half
is less than one half
2. Make a drawing that illustrates your fraction
3. Refer to something in real life that represents your fraction

17. An example: Learning about fractions and decimal fractions
Warming-up activity
Learning activity 2: learners receive a new fraction
1. Compare your fractions . Explain to another which of your fractions is the greatest one, and why
2. Make a drawing that illustrates your fractions and shows which one is greatest

18. An example: Learning about fractions and decimal fractions
Warming-up activity
Learning activity 3: learners receive a decimal fraction
1. Compare your fractions. Can you arrange them from smallest to biggest? Explain to another why you have arranged them like this

19. An example: Learning about fractions and decimal fractions
Summarizing
How can we compare fractions? Greater than … , smaller than …?
How do we compare fractions and decimal fractions?
How can we transfer from fractions to decimal fractions , and the other way around?

20. An example: Learning about fractions and decimal fractions
How to expand/extend …..

21. An example: Learning about fractions and decimal fractions
When should we do this activity in the classroom?
As an introduction to fractions and decimal fractions ?
As a summary?
Other …?

22. WHAT DO YOU THINK?
It will become = 6 times smaller
If we halve the length of each of the sides of the box, then the volume will be halved.
I think that the new volume of the box will be 1/3
I think the volume of the smaller box will be 1/8 of the volume of the bigger box

23. Yes or no, or maybe? 1 All numbers are fractions 8
The numerator is bigger than the denominator in an improper fraction 2
Every fraction is smaller than 1 9
The numerator is bigger than the denominator in a proper fraction 3
49/21 is in its simplest form 10
1/6 is double 1/3 4
To simplify a fraction, divide by 2 11
0.33 is greater than 1/3 5
Doubling the top and bottom of a fraction makes it twice as big 12
Adding the tops and bottoms of two fractions gives their sum 6
The larger the denominator the bigger the fraction 13
Some fractions are odd numbers 7
Multiplying by a fraction makes a number smaller 14
Fractions are always less than zero
Yes or no, or maybe?