Webinar

1
Mathematics and the NCEA realignmentPart three

• Webinar
• facilitated by
• Angela Jones
• and
• Anne Lawrence

2
Mathematics and the NCEA realignment

• AS 1.5
• Feedback on the standard and the task
• Implications for teaching and learning
• Supporting deeper thinking
• Understanding different levels of thinking
• Next steps

3
Mathematics and NCEA realignment
Introductions

• Angela Jones
• Senior adviser
• Secondary Outcomes Team
• Ministry of Education
• angela.jones_at_minedu.govt.nz
• Anne Lawrence
• Adviser in Numeracy, Mathematics Statistics
• Massey University College of Education
• a.lawrence_at_massey.ac.nz

4
AS 1.5 Apply measurement in solving problems

• Achieve
• Apply measurement in solving problems.
• Merit
• Apply measurement in solving problems,
• using relational thinking.
• Excellence
• Apply measurement in solving problems,
• using extended abstract thinking.

5
Achievement standard 1.4
Key skills and knowledge for 1.5

• Measurement includes the use of standard
  international metric units for length, area,
  capacity, mass, temperature, and time. Derived
  measures include density, speed and other rates
  such as unit cost or fuel consumption.
• Students will be expected to
• be familiar with perimeter, area and surface
  area, volume, metric units.
• convert between metric units, using decimals
• deduce and use formulae to find the perimeters
  and areas of polygons, and volumes of prisms
• find the perimeters and areas of circles and
  composite shapes and the volumes of prisms,
  including cylinders
• apply the relationships between units in the
  metric system
• calculate volumes, including prisms, pyramids,
  cones, and spheres, using formulae.

6
Achievement standard 1.4
Solving problems at A, M and E for 1.5

• Solving problems - using a range of methods
  solving problems, demonstrating knowledge of
  concepts, solutions usually require only one or
  two steps.
• Relational thinking - one or more of a logical
  sequence of steps connecting different concepts
  and representations demonstrating understanding
  of concepts forming and using a model, and
  relating findings to a context, or communicating
  thinking using appropriate mathematical
  statements.
• Extended abstract thinking - one or more of
  devising a strategy to investigate or solve a
  problem identifying relevant concepts in
  context developing a chain of logical reasoning
  forming a generalisation, and using correct
  mathematical statements, or communicating
  mathematical insight.
• Problems are situations that provide
  opportunities to apply knowledge or understanding
  of mathematical concepts. The situation will be
  set in a real-life or mathematical context.
• The phrase a range of methods indicates that
  there will be evidence of at least three
  different methods.

7
Achievement standard 1.4
What does excellence look like?
Student B
Student A
Student C
Student D
Student E
8
Supporting M and E thinking

• Students need to develop their own understanding
  of what A, M and E looks like.
• They need to
• Explore examples of A, M and E work
• Discuss student work (their own and others)
• Evaluate student work (their own and others)
• Is this at the M standard?
• What else is needed to make it to M?
• What could you take away and still have it M?

9
From Dan Meyer (US maths teacher)

• Dan Meyer Ted Talk - recommended viewing for all
  maths teachers
• http//www.youtube.com/watch?vBlvKW
• Questions to ask as you watch Dans talk
• What do you see as Dans key message(s)?
• What are the implications for the classroom?
• What are the key message(s) for you from Dans
  talk?

10
From Dan Meyer (US maths teacher)

• Dan Meyer Ted Talk
• http//www.youtube.com/watch?vBlvKW

11
Levels of thinking, NZC and NCEA
The NZC requires that deeper and more complex
thinking are rewarded along with more effective
communication of mathematical ideas and outcomes.
These are fundamental competencies to
mathematics. NCEA realignment supports this
focus. Students need to engage with activities
that provide the opportunity to develop numeric
reasoning, relational thinking and abstract
thinking in solving problems.
12
Rich mathematical activities

• Key questions
• What sorts of activities are appropriate?
• How do we support students to access these
  activities?
• What are appropriate levels of scaffolding?

13
Levels of demand

• Lower level demands
• Memorisation
• Procedures without connections
• Higher level demands
• Procedures with connections
• Doing mathematics
• Students of all abilities deserve tasks that
  demand higher level skills BUT teachers and
  students conspire to lower the cognitive demand
  of tasks!

14
Fuel for thought

• Which of the following would save more fuel?
• Replacing a compact car that gets 34 miles per
  gallon (MPG) with a hybrid that gets 54 MPG
• Replacing a sport utility vehicle (SUV) that gets
  18 MPG with a sedan that gets 28 MPG
• Both changes save the same amount of fuel.

15
Student responses

• Alex I see that the change from 34 to 54 MPG is
  an increase of 20 MPG, but the 18 to 28 MPG
  change is only a change of 10 MPG. So, replacing
  the compact car saves more fuel.
• Bo The change from 34 MPG to 54 MPG is an
  increase of about 59 while the change from 18 to
  28 MPG is an increase of only 56. So the
  compact car is a better choice.

16

• Chloe I thought about how much gas it would take
  to make a 100-mile trip.
• Compact car
• 100 miles/54MPG 1.85 gallons used
• 100 miles/34MPG 2.94 gallons used
• SUV
• 100 miles/28MPG 3.57 gallons used
• 100 miles/18MPG 5.56 gallons used
• The compact car saved 1.09 gallons while the SUV
  saved 1.99 gallons for every 100 miles. That
  means you actually save more gasoline by
  replacing the SUV.

17
Fuel for Thought
Using technology A general graph of what occurs
with different MPG amounts
What do you notice? Can you draw a conclusion?
18
Always, sometimes or never true?

• If two rectangles have the same perimeter, they
  have the same area.
• If two cubes have the same volume, they have the
  same surface area.

19
Putting your own spin on this

• Think about any topic
• Recast the content as questions that students can
  explore
• Resist the temptation to tell students the
  content. Believe that students can investigate
  and derive relationships and mathematical
  concepts.

20
Exploring activities

• Where would this activity fit?
• What is the level of demand?
• How can I extend the activity?
• How can I support students who are stuck?

21
Plan to get the most out of activities

• Use problems that have multiple entry points
• students at different levels of mathematical
  experience and with different interests all need
  to engage meaningfully in reasoning about a
  problem.
• Plan questions for when
• students get stuck
• students think they have the solution
• students are unable to extend the problem
  further.

22
An abundance of sources for rich tasks
http//www.shyamsundergupta.com/amicable.htm http
//micro.magnet.fsu.edu/primer/java/scienceopticsu
/powersof10/ http//www.curiousmath.com/index.php
?nameNewsfilearticlesid55 http//www.maths.s
urrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptia
n.html http//mathbits.com/virtualroberts/spacema
th/BottleTop/project.htm http//www.noao.edu/educ
ation/peppercorn/pcmain.html http//mathbits.com
/virtualroberts/spacemath/BottleTop/project.htm
23
Key implications

• Rich mathematical activities provide the
  opportunity for students to develop their
  thinking
• Sharing, examining and discussing student work
  develops students understanding of A, M and E

24
Next steps

• Discuss in your department
• Participate in the online forum
• Feedback
• Discussion, questions and comments
• Ideas for tasks
• Moderating assessment
• Look out for what is on offer next year

25
Next steps

• Discuss in your department
• Participate in the online forum
• Feedback
• Discussion, questions and comments
• Ideas for tasks
• Moderating assessment
• Look out for what is on offer next year