Maths Teaching & Planning�Maths Experiences, Tasks (& Problems)
30 April 2020
Rob Proffitt-White
“
Building a Synergy with School Vision & Values
Learners at The Centre
Valuing Every Individual
Community Engagement
Procedural Fluency is achieved by providing representative examples followed by repetitious practice
Conceptual Understanding is developed through clear and interactive explanations and representational tasks, that encourage communication between Student/Teacher, Student/Student
Adaptive Reasoning and Strategic Competence comes about from working on tasks that require them to make and justify choices, integrate ideas, plan strategies, explain thinking.
It is about doing mathematics and it is not possible to engage students through the actions of explanations and worked examples.
Task Types: Sustaining Inquiry with variety
Teachers use a game, model, example or explanation that elaborates the mathematics
Representational
Students investigate specific mathematical content with multiple solutions and pathways
Open Ended
Teacher situates maths with cultural responsiveness to engage students, but motive is explicitly mathematical
Contextual
Covering multiple domains within maths or across subject areas. Duration over days or weeks
Contextual 2
Interdisciplinary
Investigations
UDL: Engagement, Representation, Action & Expression
Representational, Contextual & Open Ended
Evidence based checklist for tasks
Above all tasks should have a mathematical focus, be challenging for the learner, promote thinking and justification, provoke insights into the structure of mathematics and insights into strategies or methods for solving problems
(Anthony and Walshaw, 2009)
Difference: Contextual are not “word problems”
In typical word problems, the context is not intended to motivate students or help them make sense of the world particularly, but largely provides what Maier (1991) called school problems coated with a thin veneer of ‘real world’ associations.
They are usually closed
They are quickly solved (better suited to independent tasks not group inquiry)
They are usually simple routine (only 1 or 2 steps to reach the answer)
E.g You purchase something for $32.50; how much change would you get from a $50 note?
These can still be part of our repertoire.
By adding “show two ways you can solve this” will foster adaptive reasoning and conceptual understanding.
By doing this they can become a simple representational task
Representational
Chocolate bars are presented on plates at the front of the room.
10 students leave the room, and one by one come back in.
As they return they are asked to decide which plate to stand in front of so they get the most amount of chocolate when it is divided up at the end.
Before each of the final two students re-enter and make their choice of where to stand, the class, as a group, discusses where they think each of the last two should go, and why?
Representational
Game in pairs. They take turns moving a single counter
around a maze. They start with say 100 and are given a
choice of alternate moves to make
with associated mathematical operations to perform
on the number (you can use a calculator)
A running record is kept for proof of calculations
The player with the lowest number when counter
reaches the finish is the winner.
It develops number sense, estimation,
Strategic competence and adaptive
Reasoning. Students can be creative and
Design their own game boards.
It can be adapted Level 1 to Level 5 students.
Before each of the final two students re-enter and make their choice of where to stand, the class, as a group, discusses where they think each of the last two should go, and why?
Open Ended - Content Specific
A person wrote a sentence which contained only five words
The average number of letters in each word is 4.
What might the sentence have been?
Extension:
None of the words in the sentence actually had for letters
Enabler:
How many different sentences can you make that have a total of 25 letters.
Contextual
Coins from different countries.
Students are given a collection of coins/notes from different countries.
Exchange rates are up on the board ( better if technology allows them to investigate this)
Students investigate and compare the value of international currencies in relation to the
New Zealand dollar.
LAUNCH: Experiences with travel overseas, foreign currency, (bringing it in from home)
Issue a set amount of coins per group.
Eg explicit expectations: draw and label coins in local and NZ value, what could you buy?
Before each of the final two students re-enter and make their choice of where to stand, the class, as a group, discusses where they think each of the last two should go, and why?
Contextual
Coins from different countries.
Students are given a collection of coins/notes from different countries.
Exchange rates are up on the board ( better if technology allows them to investigate this)
Students investigate and compare the value of international currencies in relation to the
New Zealand dollar.
LAUNCH: Experiences with travel overseas, foreign currency, (bringing it in from home)
Issue a set amount of coins per group.
Eg explicit expectations: draw and label coins in local and NZ value, what could you buy?
Before each of the final two students re-enter and make their choice of where to stand, the class, as a group, discusses where they think each of the last two should go, and why?
Contextual: Extended
Idea: How many people can stand in your classroom?
Add Context: Imagine we have opportunity to put on a concert to raise funds for [ ]. How many tickets could we sell if we held it in this room?
Here the context provides a motivation for what follows and dictates the mathematical decisions that the students make in finding a solution
The planning and anticipation stage with the team will relate the content to relevant NZ elaborations to be taught and developed.
Eg area, estimation, measurement
Our students must choose to engage; affective
Some are motivated by Performance Orientation;
Seek social affirmation as goal of their effort
Avoid risk and challenge
Anxious of failure
Some are motivated by Mastery Orientation;
Seek to understand the content
Evaluate success by transferring content
Believe effort leads to success regardless of failure along the way