1. Reflecting on Teaching and Learning Mathematics Seán Delaney Coláiste Mhuire Day 4

2. Overview of Day 4 Review of Day 3 Comment Cards Place Value Activities Video (Reinventing algorithms) Planning for Lab. Class Observation of Class Practical details about lab class

3. Review of Day 3 JOURNAL ENTRY DIVISION –Methods, meanings and estimation MINORITY GROUPS –Social issues; cultural issues; age appropriate v ability appropriate; attendance; language; outdated view. QUESTIONS –Are negative numbers positive and negative? http://mathforum.org/dr.math/faq/faq.integers.html http://mathforum.org/dr.math/faq/faq.integers.html –How do you introduce zero to children? –Who invented zero? PLACE VALUE –The decimal point, like the cat’s eyes in the middle of the road does not move; use of Dienes blocks for representing decimals –To multiply a number by 10 move each number one place value column to the left. Put a zero in the vacated column, if it is necessary to hold the value. –100 square

4. Comment Cards Would like some help with maths trails (examples if possible) Suggestions for discussion in preparing a whole-school plan for mathematics: –How can we use the content to develop the curriculum skills/children’s ability to think? –What are we doing well? What can we improve? –Others???

5. Activities for Teaching Place Value Hundred square activities Place value cards See handout with sample tasks Race to/from 50 (Ita’s house game) Proportional and non-proportional materials (Dienes, lollipop sticks, chain links, money, counters, abacus) Other ideas?

6. Video (Children reinvent algorithms) Term ‘Algorithm’ Agree/disagree Children encouraged to judge the correctness of their answers Notice ‘wait time’ View Video Reflect in journal: Learning benefits? Could it work here?

7. The Laboratory Class Idea from John Dewey (Christian Brothers) NOT a model lesson Provides material for discussion Video-tape

8. Place Value in 3 rd Class Explore and identify place value in whole numbers Read, write and order three-digit numbers Round whole numbers to the nearest ten or hundred Explore and identify place value in decimal numbers to one place of decimals

9. Planning the Lesson for the Lab Class Establish what the children know Genuine mathematics (e.g. not spending time on drawing or reading) Working on something that is ‘core’ Planning to anticipate individual differences Motivating the learners Seating arrangement Volunteer (a) to teach? (b) to videotape the class? Planning!Planning Lesson Plan from Deborah Ball’s Website (http://www- personal.umich.edu/~dball/)http://www- personal.umich.edu/~dball/ Consider lesson template. Lesson PlanLesson Plan

10. Observing Journal: What do you hope to learn from the lab class? What will you watch particularly closely? What do we know about the children? How do you think the children will respond to the lesson? Make notes in your journals during the lesson. They will form the raw material for our subsequent discussion

11. Practical Points Video Arrive a little later than usual (Lesson will begin at 9:50) Drift in and quietly take up seats! Try to be unobtrusive during lesson

12. Plan for Day 5 Lab Class Analysis of lab class Fraction problem(??) Simulation games in mathematics Review of week