Day 5 - Saturday, January 31

FIELDS INSTITUTE FORUM

Ann Kajander - Tears, trials, and transformations: the requirement of deep teacher knowledge in mathematics education.

Teacher specific knowledge about mathematics process and specific content knowledge makes a difference in student success.

A specific connection needs to be made between the hands on to the more conceptual.

Finding an answer is not enough in teacher preparation, we need to have flexible content knowledge and be open to a variety of solutions.

"If you want to see kids thinking, you have to keep the task open."

Considering imposing a mandatory math exam for teacher candidates.

Evidence that incoming teacher candidates had virtually no conceptual understanding of elementary mathematics regardless of what curriculum experience they have.

Common content knowledge , specific content knowledge, pedagogical content knowledge.

There needs to be a shift in teacher education programs that puts more emphasis on mathematical pedagogy and content knowledge. 

Joyce Mgombelo - Rethinking the use and availaboof resources in mathematics teaching and learning 

International research and development projects- Tanzania 

Focusing on evidence based and gender sensitive mathematics teaching and learning practices

Extend our notions of resources beyond material objects to include human and cultural resources such as language and time

Learners canbe used as resource for teaching mathematics

Use the outside environment 

Have students generate problems

Yasmine Abtahi - "A quarter wouldn't be that":Mathematical tools and the emergence of ZPD

Manipulatives help learning and progress

Physical properties of tools helps develop understanding of concepts 

Researchideas.ca

Chester Weatherby - Streaming protocols for university level mathematics: The effects of placement tests on first-year calculus achievements 

Preliminary results suggest it is not an effective measure of future success for students those who met the initial criteria.

Richard Barwell - Researching language in mathematics education 

Context and experience are key.  Needs to be culturally relevant.

What restrictions does the instructor bring.

Structure of the problem

Interpretation of text

Interaction of teacher and students

Interaction is students with students

Classroom norms

Multiple languages and ways of talking

Language policy

Curriculum

Point of view interpretation (post-Structuralist)

Societal discourses of mathematical teaching and learning

Language is fluid and changing.

It can stratified and stratifying

CRRP is essential 

Discursive demands of a math lesson - multiple speaker interaction (following multiple voices, recognizing speaker); frequent clarification of meaning; raising the stakes (question answer sequence puts additional pressure)

Language tensions in a math lessons - use of mother tongue; mathematical word problems (unfamiliar contexts, ideologies); students' mathematical explanations (requirements of certain kind English)

Researcher Description- subjective, choice of the researcher 

Newspaper Reporting - framing 

We need to use a critical approach when teaching mathematics 

Day 4 - Tuesday, January 27

NASTY VERSION - you can decide to keep the number or have your opponent put it in a particular cell. Can further adapt by having an option for one discard. 

Games can provide opportunities for students to use strategy.  LOW THRESHOLD, HIGH CEILING TASK - easy access utmost of potential.  

Http://you cubed.stanford.edu/tasks/. Has examples of these particular tasks.

What are the characteristics of a mathematically literate student?

How can students develop problem posing strategies?

Ever Wonder What they Motice?  By Annie Fetter (Google search)

Day 3 - Tuesday, January 21

Using Guess & Check

Effective use of Guess & Check shows reasoning for the second guess.  Why did you make your second guess?  Will give you an idea about the strength of a student's reasoning.

To have students learn a new strategy, we need to be intentional in our instruction. Run a complete 3 part math lesson, share strategies and annotate solutions completely to unpack the solutions.  We need to purposefully plan our consolidation to attain our learning goals. If students don't own a strategy, they won't use it.

 

Day 2 - Saturday, January 17/15

Why doesn't it belong?

REASONING 

It is important to get students to explain their answers and support their reasoning.

Open ended questioning and discussion of results.  Presents opportunities to take up thinking.  Hearing other types of thinking broadens our understanding and thinking on the topic. 

Smith and Stein, 2011. "As we move into the second decade of the 21st century one thing is clear,... we need students who can thunk, reason, and engage in problem solving."

"If...Then"

If one of these doesn't belong then...

Relating proportion to problem solving.

5 Practices - Peg Smith

Learn the 5 practices for facilitating effective inquiry-oriented classrooms:
Anticipating what students will do--what strategies they will use--in solving a problem
Monitoring their work as they approach the problem in class
Selecting students whose strategies are worth discussing in class
Sequencing those students' presentations to maximize their potential to increase students' learning
Connecting the strategies and ideas in a way that helps students understand the mathematics learned

Consistent use of details to explain thinking and in-depth analysis of text.

Leaves and Caterpillars problem lesson study - Google search on topic.  Can find examples of student work and lesson studies.

How to communicate thinking during problem solving must be taught - sharing solutions in consolidation helps students develop strategies to explain her thinking and boosts students' ability to ask questions about work and the thinking involved.

THREE PART MATH LESSON

• The entire lesson should take between 45 and 69 minutes.
• If the lesson doesn't go the way you expected, go back to your before and see where it went wrong.
• "Communication the Math Classroom" - Capacity Building Series
• Ontario Mathematics Gazette - centre of magazine has a BANSHO board plan.
• To make sure everyone is solving the same problem establish the problem criteria,
• What information will we use to solve the problem?
• Include examples of specific strategies you want students to use when solving the problem. e.g. If goal is to use T-chart lay that out.

When do we teach the number ZERO.  When we speak zero we often say "oh".  E.g. 401, 905, 305 Milverton Blvd.

CLOZE Strategy

We can use a reading strategy where we reason to find the missing word, CLOZE, to find the missing number.

Can also use the technique to work on use of appropriate units.

COUNTING

Counting by halves

Before going to solve problem establish Problem Criteria- what do you know?  What do you need to find?

Day 1 - Tuesday, January 13