Title: The national mathematics curriculum as a stimulus to better teaching and learning of mathematics
1The national mathematics curriculum as a stimulus
to better teaching and learning of mathematics
- Peter Sullivan
- Monash University
2Overview
- Goals of the mathematics curriculum
- Key decisions
- Definitions
- Assessment
- Using the teaching of fractions to exemplify the
points about the curriculum
3The curriculum needs to foster
- development of expert mathematicians
- expert users of mathematics in the professions
- a workforce capable of meeting all numeracy
requirements - citizens able to use the mathematics they need
4Some of the key decisions
- mathematics success creates opportunities and all
should have access to those opportunities - inclusive for all to end of year 9 (and
compulsory in year 10)
5- the curriculum will be clear and succinct, and
this is about pedagogy - currently teachers feel they have to rush from
one topic to the next, and this is bad for
teaching - all students can be challenged within basic
topics, including the advanced students
6Numeracy
- There are some who see numeracy as a separate
subject - There are some who think numeracy does not exist
- There will be a numeracy continuum within
mathematics as well as including references to
numeracy aspects of other subjects in
mathematics, and to numeracy in history, English
and science
7Three content strands (nouns)
- Number and algebra
- Measurement and geometry
- Statistics and probability
8Expectations for proficiency (verbs)
- Understanding
- Fluency
- Problem solving
- Reasoning
9To give an example
- Why choose fractions?
- How can it be described simply?
- What is the nature of the learning?
- What sorts of activities can we consider?
10Why would I talk about fractions to a group of
secondary teachers?
- In the 2007 Victorian Year 9 AIM assessment, the
following question was posed - Carol eats 1/3 of the pizza. Theresa eats 1/4 of
the pizza. How much is left for Peter? (it was a
write in answer) - What percentage of SA Year 9 students would get
that correct? - Less than one quarter of Year 8/9 Students could
work out a/5 a/10
11What else do we know about teaching fractions
- Takes up a lot of time
- Students dont seem to improve much (about 10
improvement in year 8, for example) - The topic serves to alienate some students
- We use confusing models (shape and number), and
sometimes we dont connect them well
12The fractions curriculum (my view)
- Definitions and language
- Rational numbers (Counting in fractions)
- Equivalence
- Addition and subtraction
- Converting and comparing
- As an operator
- Multiplication and division
13The Victorian upper primary curriculum
- Students use decimals, ratios and percentages to
find equivalent representations of common
fractions (for example, 3/4 9/12 0.75 75
3 4 6 8). They explain and use mental and
written algorithms for the addition, subtraction,
multiplication and division of natural numbers
(positive whole numbers). They add, subtract, and
multiply fractions and decimals (to two decimal
places) and apply these operations in practical
contexts, including the use of money. They use
estimates for computations and apply criteria to
determine if estimates are reasonable or not. - Progression point 4.25
- knowledge of decimal and percentage equivalents
for1/2, 1/4, 3/4, 1/3, 2/3 expression of single
digit decimals as fractions in simplest form and
conversion between ratio, fraction, decimal and
percentage forms division of fractions using
multiplication by the inverse
14Teaching ideas
15We count before we operate
- Race to 10, start at 0, counting by 1 or 2
- Race to 3, start at 0, counting by ½ or ¼
- Race to 3, start at 0, counting by 1/6 or 1/3
16Different ways to write the one fraction
- In a group, ½ of the people were Crows
supporters. How many people might be in the room
and how many are Crows supporters. Please write
it like this
Crows
People
17Different ways to write the one fraction
- In a group, 1/3 of the people were Port
supporters. How many people might be in the room
and how many are Port supporters. Please write it
like this
Port
People
18- What is the smallest group size common to both?
19Addition
- Why cant we add like we used to?
- What types of addition are there?
20What cant we add like this
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23 24Types of addition
25To illustrate how easy questions can be
interesting
26The following is a description of an idea that
might be used as the basis of a lesson
or
27A question for you
- Please work out the answer
28Some solution methods
- Finding common denominators
- Using a calculator to divide numerator by
denominator to convert to decimals - the residual needed to build 200/300 and 201/301
to the whole - the first fraction requires 100/300
- the second fraction requires 100/301,
- because the 301ths are smaller parts, the
residual needed is smaller.
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30The sugar rule
gt
So long as b ? 0, a lt b
31- A teacher in the United States used a basketball
analogy to give a convincing alternative
strategy. He argued that we could think of
200/300 as a basketball players free throw
success rate. In moving to 201/301, the
basketball player has had one more throw, which
was successful. His average must therefore have
improved, and so 201/301 must be larger.
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33- It is possible to engage with simple topics in
sophisticated ways
34Conclusion
- The process of writing will allow input
- Let us think about the big ideas and how to
express them in ways that will inform teaching