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The psychologist/educationalist:
The topic:
Group members:
Time length if more than 5 mins:

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We've played the game (countdown from 100 to 0, 1-10 each time) last session.
Do you find any tips for wining the game?
How could this be used as an example of the assignment?

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Feel free to leave your group improvement of breathe, and your analysis of the 'breathe data'.
(e.g. Chi, from 6 times to 5 times + any comments)

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How do you perceive mathematical “instrumental and relational” understanding?
Does this relate to your experience of mathematics learning (or teaching)?

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1. Relational understanding is similar to instrumental understanding through learning a set of rules and being able to apply and manipulate it for a test. However, relational mathematics also involves knowing why the rule works and how it would connect to other rules.

2. Instrumental mathematics was experienced during GCSE and A-level Maths, as we had to memorise formulas and mathematics equations rather than learning how they were formed.

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instrumental math only focus on how to use formula and relational math will know how，why and where the formula come out.

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I think most of us experienced instrumental understanding at some point in a math class. When we did not know where a formula has come from but we just accepted that and used it.

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Instrumental math can be used wisely by learners when they face the math problems similar with samples given by teachers. But when learners are required to solve the advanced problem which build on their understanding of the formula, relational understanding is highly required.

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Instrumental understanding may be more suited to solving a problem when you have no foundation and learning how to solve it Relational understanding is for those who have some foundation to explore in more depth.

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For easy questions, instrumental maths works well. While facing hard questions, we need relational maths. For most of the maths questions in my life, I can solve them by using instrumental maths.

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relational understanding is were you know what to do and why. instrumental understanding is rules with out reasons

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I found instrumental learning interesting because it relates to personal experience in learning math.

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Anything not understood?

Any questions that came out of reading it?

Anything you disagreed with?

Anything you thought was interesting?

Any connections to other stuff so far?

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What are the positives and negatives of having an active role for learners in learning mathematics?

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How many different trains can be made of length =  5 ?

How do you know you have found them all?

Investigate for other lengths of train.(6? 7? 8?)

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We just discussed due to the pressure that teachers feel and due to the packed curriculum, it is not always possible to manage classes to be student-centred. However, I think the more the class is student-centred the more the students lean towards understanding relationally.

We also came up with this question:
We both agreed that students can learn better when they are given the opportunity to explore. However, is there a bit of an assumption that we all learn in the same way? If yes, isn't it a bit reductionist in that sense?

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-teaching is an art.
-maths improve your thinking process and u can use problem solving stages in real life as well

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Experiment with different numbers of green and black frogs.

Can you always swap the frogs over without having to move any frogs backwards?

Can you predict how many moves it will take you?

Can you swap the frogs over when the number of green and black frogs is not the same?

Can you predict how many moves it will take you?

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what you have learned in the drawing activity?

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what you have learned in the drawing activity?

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Anything you disagreed with?

Anything you thought was interesting?

Anything not understood?

Any questions that came out of reading it?

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Is the computer the same as playing with the frogs?

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Is the computer the same as playing with the frogs?

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- I think it is very similar to Alexander's dialogic teaching.
- Similar to the idea of scaffolding.
- ‘if an answer does not give rise to a new question from itself, it falls out of the dialogue’’ (Bakhtin, 1986, p. 168).
- The teacher has to be skilful to get the discussions going without intervening too much.
- It needs frequent practices to maximise the impact. (For both teachers and students)
- We discussed it makes the class more engaging.
- One question:
How much freedom should the teacher give to students?

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too easy???

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We need to be as precise as we can
Even small details are important

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Lets model/find some notation, be systematic, make a record/table/model, …

Pose new problems/extensions

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psychologist: Martin Hughes
Group Members: Jingyi Cao, Yu Jia, Xinlei Jin

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Martin Hughes- Steven, Kaiyuan Deng, Liuhong Guo, Yue Zha

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Martin Hughes- Steven, Kaiyuan Deng, Liuhong Guo, Yue Zha

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Do you panic at maths?

Julian

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Pyschologist: Rochel Gelman and Counting

Group member : Jingya Zhao&Xinyi Chen

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Jiahui Tong& Wanlin Zhang