Reflecting on Teaching and Learning Mathematics

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  outdated view.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
  
• How do you introduce zero to children?
• Who invented zero?
• PLACE VALUE
• The decimal point, like the cats 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/childrens 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 (Itas 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 3rd 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!
• Lesson Plan from Deborah Balls Website
  (http//www-personal.umich.edu/dball/)
• Consider lesson template. Lesson 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 950)
• 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