Welcome back again!

1. Welcome back again! Sept 29, 2014

2. Today’s Plan • Class summaries • Homework (achievement chart) • Go over your feed back • My notions of teaching and learning (enactivism) • Interpretation of last class from my perspective of learning and teaching • Teaching strategies/lesson planning • Division of fractions

3. Feed back (what you want) • Lesson planning • More structure-uncomfortable (lecturing?/sit-tell-do?) • Less discussion-more opportunities to learn • More videos (especially of model teaching) • More range of grade topics (9-12) • Teaching strategies for struggling students • More teaching strategies • Resources of activities for the the I/S level • New techniques: smart board, applets, etc. • Student choice (students ask questions about things that relate to their practicum experiences)-Let’s plan for teaching together? • Course summary (video online) • My quietness (please let me know when you can’t hear) • Moderated marking (7/8 want it, mandatory?)

4. Notions of teaching and learning (enactivism) • Enactivism is a theory of cognition • Flavor of constructivism but has different focuses • What is constructivism? • Teaching and student learning co-emerge/couple • Build on students prior knowledge and experiences (NCTM principle) • My students play an important role in the direction of each class • I’ve taught the same class several times but it’s never the same because of the responses/interests/backgrounds of students • Basically, I never know exactly how students will respond or react. I need to listen and react.

5. Framed by Enactivism • a theory of cognition or philosophy that has become popular amongst Canadian mathematics education researchers (Ernest 2007). • Enactivism finds it roots/origins in biology and has co-emergence as a central idea (Li, Clark & Winchester, 2010). • A living system (learner/class of students, etc.) and its environment co-emerge and couple as they interact. • “[A]ll of our understandings are situated in and co-emerge with complex webs of experience, and so we can never discern the direct causes of any particular action” (Sumara and Davis p 412). • Teaching, in this framework, can not be predetermined as it emerges through the interactions of the teacher and learners. A teacher cannot predetermine how a lesson will run as one cannot completely predict how a learner/(or learners) will react to their environment/a piece of mathematics. Cognition occurs in the possibility of shared actions.

6. What do I really mean? What does a classroom with these sensibilities look like? (NCTM principles in action 2014) • http://www.nctm.org/uploadedFiles/Standards_and_Focal_Points/Principles_to_Action/PtAExecutiveSummary.pdf

7. What does lesson planning look like from an enactivists perspective? • The big question is: • What is the difference between lesson planning and planning for teaching?

8. Let’s look at a document from the Ontario Literacy and Numeracy Secretariat(pg. 7 http://www.curriculum.org/secretariat/coplanning/files/CoPlanningGuide.pdf)

9. Where do we select problems from? • NCTM, nrich, edugains, talk to each other, go to conferences, talk to me, talk with other teachers of mathematics. • Let’s look at NCTM

10. During the lesson • Ask in the moment questions that promote student’s understanding. (including asking students to compare their thinking). • Examples from this class • Observe very tentatively to decide what to draw students attention to during whole group discussion. • Examples from this class • Select students work to sequence, highlight and summarize

11. The big thing…During the lesson • You need to take up students thinking to build on their prior knowledge! • What does this mean? Taking up student thinking involves an ongoing, cyclical, continuous process where students share what they think, teachers listen to student thinking, teachers make in the moment decisions about how to support and direct students’ attention

12. What does enactivismmean for my math classes? (teaching on the fly) • I don’t go toclass with nothing! • I have a list of possible problems based on the curriculum and my interests. I’ve done the math and anticipated student responses. • Rarely do we cover all of them or in the order you find them in my notes • I often do make up questions to assist in understanding (we’ll talk about this throughout the course with specific instances from my classroom)

13. What does this mean for your lesson plans? • How many practicing teachers have lesson plans? • You will be expected to use one…Here’s a bunch of different templates that you can use: http://www.oise.utoronto.ca/supo/Forms_Resources/Lesson_Plan_Templates/index.html

14. Complex instruction • http://nrich.maths.org/7013

15. My adaptation of complex instruction • Students are given specific roles based on the strengths • Facilitator, Recorder/Reporter, Resource Manager, Understanding coordinator • Assessment (Daily assignments to be handed in at the end of class many questions come from the list I come to class with) • Careful be conscious of time etc. • Group Assessment (actually individual assessment) • Students are taking a crucial role in each lesson and each assessment task

16. Division of fractions • Craft a word problem that involves the division of fractions (the denominator of the divisor fraction can not equal 1)

17. Ribbon question • You have six meters of ribbon. Each bow requires 5/6 of a meter. How many bows can you make? How much is left over? • Anticipate student responses

18. Thanks for engaging!

19. References • Li, Q., Clark, B., & Winchester, I. (2010). Instructional design and technology grounded in enactivism: A paradigm shift? British Journal of Educational Technology, 41, (3): 403–19. • Sumara, D & DAVIS, B. (1997). Enactivist Theory and Community Learning: toward a complexified understanding of action research, Educational Action Research, Volume 5, No. 3, 403-427.