Mathematics and the NCEA realignment Part three. Webinar facilitated by Angela Jones and Anne Lawrence. Mathematics and the NCEA realignment. AS 1.5 Feedback on the standard and the task Implications for teaching and learning Supporting deeper thinking
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Apply measurement in solving problems.
Apply measurement in solving problems,
using relational thinking.
Apply measurement in solving problems,
using extended abstract thinking.
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.
Key skills and knowledge for 1.5Achievement standard 1.4
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.
Solvingproblems at A, M and E for 1.5Achievement standard 1.4
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?
Questions to ask as you watch Dan’s talk:
What do you see as Dan’s key message(s)?
What are the implications for the classroom?
What are the key message(s) for you from Dan’s talk?From Dan Meyer (US maths teacher)
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.
Lower level demands:
Procedures without connections
Higher level demands
Procedures with connections
“Students of all abilities deserve tasks that demand higher level skills BUT teachers and students conspire to lower the cognitive demand of tasks!”
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.Student responses
100 miles/54MPG = 1.85 gallons used
100 miles/34MPG = 2.94 gallons used
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.
A general graph of what occurs with different MPG amounts…
What do you notice? Can you draw a conclusion?
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.
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.
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.