PowerPoint Presentation - Valuing mental computation online - before you start

1
Valuing Mental Computation Online Before you
start
2
Focus for mental computation
With mental computation the focus is twofold

• students explaining their own mental strategies
• students listening to and evaluating, in their
  own minds, the methods other students are using.
• Your questioning needs to facilitate this.

3
Explaining mental methods

• When explanation and justification are central
  components of mental computation, students learn
  far more than arithmetic.
• They learn what constitutes a mathematical
  argument and they learn to think and reason
  mathematically.

4
Valuing Mental Computation Online

• Recording student responses

5
Recording student responses

• It is important to record student responses so
  that all students can see the thinking.
• It is important not to judge the methods students
  offer.
• Students will be able to see the variety of
  methods and may choose to try a different one
  next time.

6
Recording student responses

• The way you record the student responses so that
  all students can visualise the thinking will
  depend on the method.
• The empty number line is a useful tool when the
  student begins with one of the numbers and deals
  with the second number in parts.
• Recording the steps is better when the student
  partitions both numbers and then recombines.

7
Problem 52 17

• I took 10 from the 52 to give me 42. Then I took
  away 2 more gives me 40. I have 5 more to take
  away gives 35. Lawrence
• First I took away the 2. Then I took away the 10.
  Then I took away the other 5. My answer is 35.
  Denzel
• I started at 17 and added 3 to make 20 and then
  30 more makes 50 and I need 2 more to get to 52.
  My answer is 33 , 35.Kate
• First I take 10 from 50 to get 40. Then I take 7
  from 2 to get 5 down. My answer is 35. Dominique

8
Problem 52 17

• I took 10 from the 52 to give me 42. Then I took
  away 2 more gives me 40. I have 5 more to take
  away gives 35. Lawrence

-10
-5
-2
52
42
40
35
9
Problem 52 17

• First I took away the 2. Then I took away the 10.
  Then I took away the other 5. My answer is 35.
  Denzel

-10
-5
-2
52
50
40
35
10
Problem 52 17

• I started at 17 and added 3 to make 20 and then
  30 more makes 50 and I need 2 more to get to 52.
  My answer is 33 , 35. Kate

33 , 35
30
3
2
17
20
50
52
11
Problem 52 17

• First I take 10 from 50 to get 40. Then I take 7
  from 2 to get 5 down. My answer is 35. Dominique

35
12
The empty number line

• can also be used for larger numbers
• 300 158

150
8
300
150
142
13
The empty number line

• 300 158

160
300
140
142
2
14
Partitioning each number
23 38

• Can be recorded as
• 20 30 50
• 3 8 11
• 50 11 61

15
Partitioning each number
23 38

• or in diagrammatic form

16

• Mental computation helps to develop an
  understanding of place value.

17
Using models of place value

• The current approach to developing written
  algorithms is through forming a place value
  rationale of trading.
• This begins with models of place value
• bundling
• multi attribute blocks (MAB, Dienes)
• place value charts.

18
Limits of models of place value

• The sense of numbers students need is more than
  reading the positional tag of a numeral.
• Activities using trading with models of place
  value do not always translate into understanding
  of place value and we see

19
Limits of models of place value

• An over-reliance on the linguistic tags approach
  leads to problems when the student breaks the
  number into parts.

• Instead of 2 in the tens column and 3 in the
  units column, 23 needs to be seen as a composite
  20 and 3 or 10 and 13.

20
Developing models for place value

• Mental computation practices often preserve the
  relative value of the parts of the numbers that
  are being operated on.
• That is, hundreds are treated as hundreds and
  tens are treated as tens.

21
Developing models for place value

• In written algorithms, the relative values are
  set aside and digits are manipulated as though
  they were units.
• Mental computation is more likely to be
  meaning-based than written algorithms which are
  rule-based.

22

• PC users close the new browser window to return
  to the website.
• Mac users - quit PowerPoint to return.