Professionalism and Participation in Mathematics Education Behaviours – In Schools, In Classrooms, and Beyond - Exploring Proportional Reasoning and its impact on mathematics teaching and learning through the Intermediate and Senior divisions - Relating theories of learning to the mathematics teaching of all students Practising designing, implementing and assessing programs for all learners Having the theoretical understanding and foundation necessary to design, implement and assess programs for all learners Professionalism and Participation in Mathematics Education Intermediate / Senior Mathematics Winter 2011 SESSION 5 – Jan 17, 2011

What Time is It? How do you know? MTMS April 2003 2 <15 min. Mind’s On> Clock Activity From Mathematics Teaching in the Middle School (April 2003; Volume 8) Materials Needed: cut-outs of clock templates. Facilitator Instructions: Distribute clock cut-outs to participants while running the PowerPoint slide. Instruct participants to determine the time displayed on the clock using the relationship between the minute hand and the hour hand keeping in mind that the 12 does not necessarily belong at the top. Correct Answer: 6:20 Debrief: Ask for volunteers to share their answers and strategies. Use document camera if available. Notice this problem is intriguing- no numbers must use the relationship between the minute hand and portion of an hour that it travelled, along with the relationship between the hour hand and the portion of an hour it travelled from one hour hand mark to the next. What Big Idea does this relationship elicit? Could be Big Idea 3: representing equal ratios of 1/3 using the hands of the clock How do you know? 2 MTMS April 2003 2

Questions and Queries Students Others New math? Is everyone able to learn math given enough time and support? … students across all ability levels How do I engage students who have turned off math? Hold interest? Some hate math? How do I anticipate their responses and get ready to respond? Should I expect students know all the math up to the curriculum of the previous grade? field trips? How can I set it up so they ask the questions? Others New math? Making connections between multiple areas of math? Math to self Math to world Math to other math Classroom Dynamics What do we say when students ask, “Why do we need this?” “How do we relate math to everyday life?”

Questions and Queries www.nctm.org Curriculum Lesson planning Expectations (overall, specific) Lesson goal(s) 3 part Instructional strategies Assessment for learning Assessment as learning Practice (assessment of learning) TIPS Grade 9 applied Unit 7 Overall / specific (before, THIS, after) Curriculum Is the history of curriculum development important? Do we have freedom to deviate from the curriculum? How has math curriculum changed since we were in school? Lesson plans How to make effective lesson plans and unit plans Make sure in the curriculum? Should one bring outside elements into the classroom? How do I use technology effectively in math class? Is using tech practical? Effective? Convince them a problem has multiple solutions? John’s lesson Grade 10 academic Overall / specific (before, THIS, after) www.nctm.org

Questions and Queries Instructional Strategies Assessment Which strategies reach students with different learning styles? How to make learning reach all students? And fun? How do we include different strategies into lesson plans? Do we plan differently for academic and applied classes? Emphasize group work – what kinds of groups? Assessment How does one assess? How does one evaluate? Marking test performance? Or marking critical thinking? Marks for homework? Assessment and evaluation for math courses? Knowing what to put on test? Best way to evaluate?

Agendas Jan 17 (2-198) – today SUPO meeting Professionalism and Participation Classroom Dynamics Proportional reasoning Open questions Parallel Tasks Jan 20 – Ed Commons Labs E-portfolio Lesson planning Expectations (overall, specific) Lesson goal(s) 3 part Instructional strategies Assessment for learning Assessment as learning Practice (assessment of learning) Teaching through the processes

Agendas Jan 21 – 2-286 Jan 24 – Ed Commons Labs 4 & 5 Assessment and Evaluation – success criteria Work on micro-teaching Jan 24 – Ed Commons Labs 4 & 5 Gizmoes

What else? What are we missing?

Instructional Strategy www.nctm.org

The SUPO Meeting Attendance Policies and Procedures Step away from the negative Attendance http://www.oise.utoronto.ca/supo/Teacher_Candidates/index.html Policies and Procedures http://www.oise.utoronto.ca/supo/Policies_Procedures/index.html Feedback Forms and Resources http://www.oise.utoronto.ca/supo/Forms_Resources/index.html Checklists LANDMINES Talking about… not in staffroom not in washroom not on telephone (publically) not in subways not at hockey games … Facebook raise privacy - Get off for 2 mo - use alias’

Professionalism and Participation

Classroom Dynamics – wiki http://oiseedu422.wikispaces.com/

Classroom Behaviour

Classroom Behaviour

Proportional Reasoning

Non-Numeric Problems that Encourage Proportional Thinking 1 2 3 4

Using Ratio Tables Cat Food Problem: Kittens have to eat a special kind of food. There are two stores that sell this kind of cat food. The cans are the same size and the same brand. Which one is the better deal? Show your work. Bob 12 cans for $15.00 Maria 20 cans for $23.00 Try this one with your group. Practise using a ratio table.

Ratio Tables extended When you step through the transitions in this slide you will see the following emerge. A ratio table can be used to track prices when you are aiming for unit cost. The first 3 transitions show manipulating the numbers for Bob’s prices unit you show a unit price of $1.25. Once you start that same process for Maria’s price, you see that the divisions will be messy to et to a unit cost … So ask, what number could you pick that is a multiple of both 12 and 20 that could be compared because the number of cans will be the same. The next bundle of transitions shows that 12 x 5 = 60 and 15 x 5 = 75 and then 20 x 3 = 60 and 23 x 3 = 69. Now, because we can compare the cost of 60 cans at either store, we can tell that Maria’s prices are lower. Capacity Building Series LNS, Communication in the Mathematics Classroom; Webcast Mathematics in Contexts; Cathy Fosnot, Investigating fractions, decimals, and percents: Grades 4-6. Portsmouth, NH: Heineman

Which mixture is the most “orangey”? Mix A 2 parts concentrate 3 parts water Mix B 1 parts concentrate 4 parts water Mix C 4 parts concentrate 8 parts water Mix D 3 parts concentrate 5 parts water

What do we value? Examine student solutions…

Thursday January 20 Education Commons E-Portfolio Lesson planning Expectations Lesson goal(s) 3 part Instructional strategies Assessment for learning Assessment as learning Practice (ass of learning) Teaching through the processes