Embedded Files
Warm up:
Goat Maths from the ABC - https://www.abc.net.au/education/topic-goat-maths/102180130
Let's all start with https://www.abc.net.au/education/goat-maths-mega-crashers/102463790 Mega Crashers. Work in 2s.
Working and thinking mathematically
Working and thinking mathematically
Remember that Working Mathematically is a strand of the NSW Syllabus for Mathematics and is also present in the Australian Curriculum as 4 separate sub-strands.
In NSW it includes:
communicating
problem solving
reasoning
understanding
fluency
all of which are described in the learning models on the previous pages.
Let's look at how we develop these critical skills which support students to investigate maths problems, use the language of maths, justify their ideas and findings, question their processes and answers and build the necessary understanding to be numerate adults. What do we do?
- Building understanding
1a. Rathmell's Triangle - building understanding
1a. Rathmell's Triangle - building understanding
When teaching and supporting students we need to use concrete objects and representations and correct maths language - a great teaching model for developing skills and understanding in the early stages of number and counting is Rathmell's Triangle (Piaget, Discovery learning, Constructivism)
Watch this video about the importance of using concrete materials (objects) and pictures in early numeracy learning. Click on this link or click on the video to the right and use the Pin code SMPDWL (copy the pin before you click on the link). 15:03 mins
Children need to count collections of all different types of objects!
After watching the video make sure you understand that when you remove concrete materials for counting the child is dealing with abstract ideas and understandings.
Start a discussion: what happens if you move to written computation methods too quickly?
1b. How and when do we move students from using concrete materials to working with abstract ideas
1b. How and when do we move students from using concrete materials to working with abstract ideas
1. Good concrete activity is good mental activity
2. Why Teach Mathematics with Manipulatives?
3. Manipulatives in the Primary Classroom
4. From Objects and Images to Mathematical Ideas
5. Concrete-to-Representational-to-Abstract (C-R-A) Instruction
6. Refer back to the video of Rathmell's Triangle (above)
1c. Other examples of building understanding
1c. Other examples of building understanding
When students are exposed to ideas presented:
in different ways for enough time and
with enough opportunities to practice and internalise those ideas,
they develop understanding and they develop fluency. They know how to approach problems, they develop automaticity in elements such as adding, subtracting, multiplying and dividing and they build up a repertoire of strategies with which they can tackle problems.
Extra
Watch and listen to these videos from the link below about the importance of building understanding and fluency with numbers:
using a hands-on approach to represent numbers (resource S6181) - 13:15
using structured patterns to develop number combinations (resource S6189) - 19:15
using a hands-on approach to represent 10s and 1s (resource S6182) - 10:13
teaching number 0-9 (resource S6192) - (you have watched this already) - 15:03
To access the videos, copy this Pin code IXNBCV.
Click on this link and paste in the Pin code you copied.
Consider: are all these strategies Maths or numeracy?
2. Questioning to support communicating, build understanding, support problem solving and support reasoning
2. Questioning to support communicating, build understanding, support problem solving and support reasoning
2a. We need to ask questions - we need to ask ‘Why?’ We need to ask ‘How?’
2a. We need to ask questions - we need to ask ‘Why?’ We need to ask ‘How?’
Why did you count in fives?
Why did you start to count at ten, not one?
Why did you put aside the two lollies left over after sharing them out / dividing them up?
How did you get that answer?
How did you work that out? Was there another strategy you could have used?
2b. Types of questions to ask
2b. Types of questions to ask
Maths/Numeracy Questions - Stage of lesson questionsThe sample questions on the left are questions that you use at particular stages of a lesson.
They are taken from https://nrich.maths.org/10341
Activity: Questioning (stage of the lesson questions)
Activity: Questioning (stage of the lesson questions)
Play the game Strike it Out with a partner. Watch the video (left) and then before you start playing, brainstorm some questions you might ask the students from the 'Particular stages of the lesson' questions.
Play the game. There is more about the game here https://nrich.maths.org/strike-it-out/note .
When you finish playing, brainstorm some end of the lesson questions you might ask students who had played the game.
Consider: is this activity Maths or numeracy?
The sample questions on the right are questions that you use to encourage different levels of thinking.
They are taken from https://nrich.maths.org/10341
Maths/Numeracy Questions - Levels of thinking questionsActivity: Questioning (Levels of thinking questions)
Activity: Questioning (Levels of thinking questions)
Do the activity The Add and Take-away Path from https://nrich.maths.org/7281/note with a partner. Read about the activity and then brainstorm some questions you might ask before you start. Undertake the activity and then brainstorm some questions you might ask. Make up a new path each and see if you would add any questions. Give some examples of some questions you could use to guide/challenge your partner's creation of a path and vice versa.
Consider: is this activity Maths or numeracy?
Maths/Numeracy Questions - Mathematical skills questionsThe sample questions on the left are questions that you use to encourage different types of mathematical skills.
They are taken from https://nrich.maths.org/10341
Activity: Questioning (Mathematical skills questions)
Activity: Questioning (Mathematical skills questions)
Read the activity School Fair Necklaces from https://nrich.maths.org/9692/note with a partner. Brainstorm some questions about this activity before you start. Do the activity and then brainstorm some questions you might ask at the end.
Consider: is this activity Maths or numeracy?
Discussion:
Discussion:
How did your questions improve your thinking on the puzzle.?
How did they encourage the processes described in Working Mathematically?
Which elements of Working Mathematically did they particularly support?
3. Language and body language (communicating, reasoning)
3. Language and body language (communicating, reasoning)
There are two main types of language we consider as we learn to work with children in this area:
the language used in asking questions, setting expectations and encouraging independence and
the language of maths / numeracy itself.
Read the article Developing a Classroom Culture That Supports a Problem-solving Approach to Mathematics.
It asks you to consider the following aspects of how you support maths / numeracy learning and use language with the students you are working with. It is written for classroom teachers but it has some excellent learnings for you in your support role. As you consider each question in the article, think about which aspects of your support strategies you might want to work on. The article describes a range of strategies for each.
I know that students need to be communicating in maths/numeracy lessons but who does the talking when I am working with students?
What questions do I ask?
Who answers the questions?
How well do I listen to the students’ answers and seek to understand what they are saying?
How well do I encourage conversations about maths in the students I am working with?
What do I do with the students’ answers?
How do I facilitate the learning?
How confident are the students to take a risk, to try out ideas, to make mistakes?
What does my body language communicate?
Activity - Planning for communication using great resources from NSW for thinking mathematically by Stage
Activity - Planning for communication using great resources from NSW for thinking mathematically by Stage
Go to one of the sites below for the stage of students you are working with or want to work with. Look at one activity and consider:
What questions would you ask?
What maths specific language would you be using?
How would you encourage the students to explore the ideas presented?
https://sites.google.com/education.nsw.gov.au/get-mathematical-early-stage-1/early-stage-1-home
https://sites.google.com/education.nsw.gov.au/get-mathematical-stage-1/stage-1-home
https://sites.google.com/education.nsw.gov.au/get-mathematical-stage-2/stage-2-home
https://sites.google.com/education.nsw.gov.au/get-mathematical-stage-3/stage-3-home
Share with the group.
5. Maths language and dictionaries
5. Maths language and dictionaries
Use the following links to brush up on your maths language if unsure:
6. Activity: building our language
6. Activity: building our language
Open this word document on Vocabulary and language in Mathematics from NSW Maths Syllabus.
Summarise in your books.
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