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Using MEA for Primary Mathematics Classrooms (Eric Chan, 2008) 

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Using MEA for Primary Mathematics Classrooms (Eric Chan, 2008) 

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Session 2: Knowing the Curriculum and Instructional Strategies 

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Session 2: Knowing the Curriculum and Instructional Strategies 

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2023 FiDLHA Maths_Session 2_Knowing Curriculum and Strategies (full)

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1st:Whole class instructions
2nd:Break into different ability group for their respective tasks
3rd:Whole class come back for presentation of findings
LP: shares answers
MP: asking new questions based on the Pie Charts given.
HP: HP to show other graphs (done using excel or other tools). All to comment on how the different presentation helps in comparison of data etc.
All: Will discuss the questions together

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Pupils in LP and MP can proceed to do cutting of triangle and form into a straight line being 180 deg

Pupils in HP may decide how they would investigate that sum of angles equal 180 deg

activity extension : students may also investigate unknown angle in a triangle.

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1st: Whole class instructions
2nd: Break up to different ability group for respective tasks
3rd: Back to whole class
All: present and discuss answers
HP: Present the questions they have come up with
All: Discuss these alternative questions

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1a) Usage of learning stations (LPL/MPL/HPL)
1b) Usage of ePed
1c) Students to complete tasks based on a 'to-do list'
2) Students will do the activities at the same time.

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1) All the students will be given triangles and get them to cut the sides. LPL and MPL will try to show and arrange them together to form 180 degrees. HPL will show that an exterior angle is the sum of 2 interior angles.

2) These two activities will happen concurrently.

3) Get students to consolidate verbally

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1. Group students in a "homogenous" group (LP/MP/HP) into different learning stations
LP - Using the triangle cutouts/Geogebra with scalene/right angle triangle
MP/HP - Using the triangle cutouts/Geogebra with obtuse triangle, use different sizes of triangles
Students can choose the manipulatives.
2. Consolidate the learning as a class
All groups can share what they have found.

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Triangles:

HP: Get students to investigate if there can be 2 obtuse angles in a triangle.
HP: Get students to prove why sum of angles = 180 degrees without providing any manipulatives (e.g. they may use alternate angles)

LP: provide paper and get students to cut out different triangles to prove that sum of angles = 180 as they line up on a straight line.
Activity can also benefit HP who may have memorised the proof but not know why.

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LPLs: Give pictorial representations for students to make connections between decimals and fractions. Need not simplify.
MPLs: Give common decimals like 0.2, 0.25, 0.5, 0.125. Need to simplify.
HPLs: Give decimals more than 1 or recurring decimals.

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Differentiating Learner Outcomes (P6 Pie Charts)

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Differentiating Learner Outcomes (P6 Pie Charts)

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LPL - Reading and interpreting pie charts
MPL -  Formulate questions with given pie charts
HPL - Get students to compare the use of the different types of graphs - pie, bar, line, picture. In which situations, would the students choose to use which presentation of the data. They can also choose to present the data in the various forms - absolute values, percentages, fractions etc.

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P5: What is the sum of angles in a triangle? Can you prove it? Based on sum of angles in a rectangle, what would be the sum of angles in a triangle?
P6: Can you create a pie chart this information? What are the advantages and disadvantages of using pie chart as compared to other forms of pictorial chart like bar graph?

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Differentiating through the process or content.
Ask: What is the sum of angles in a triangle?
For those less ready:
Provide a scalene triangle.
Ask students cut out the vertices and place them adjacent to each other to show that the sum of angles is 180 degrees.
Repeat with an obtuse triangle.
Repeat with a triangle of a different size.

For those who are more ready:
Ask students to measure the angles of a triangle.
Ask them what they notice
Extension 1: Explore isosceles triangles and equilateral triangles.
Extension 2: Explore that alternate angles are equal.
Extension 3: Sum of 2 interior angles is equal to 1 exterior angle

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Activity 1: Differentiating Learner Outcomes 

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Activity 1: Differentiating Learner Outcomes 

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P4 Decimals : Converting decimals to fractions (decimals up to 3 decimal places)

P5 Triangles: Investigate and discover that the angle sum of any triangle is 180 degrees

P6 Pie Charts: Reading and interpreting data from pie charts

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Activity 2: Planning a Differentiated Lesson

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Activity 2: Planning a Differentiated Lesson

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1. What will the pupils do?
2. How will you organise the activities in class?
3. How will you facilitate learning as a whole class?

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P5 Triangles

Investigate sum of internal angles in a four-sided figure.
Further extension of properties of angles in a triangle to any polygon. Observation of the relationship between the sum of internal angles to the number of sides of the polygon.

(n-2) x 180

3 x 180 or 4 x 180

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Higher Order Thinking Questions.
Extension from the questions in the workbook - Thinking cap section.

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2023 FiDLHA 1 Maths_Session 1_ Knowing Our Learners (full)

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1. Some schools use the checklist as an additional interview to identify students for E2K.

2. Schools also sometimes rely on teacher nominations.

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a) For one of the schools, the HAL checklist is effective in getting teachers' feedback about those who are talented in their class. It is not the only component. Their results, teachers' feedback and recommendation and interviews were taken into consideration.

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Usage of HAL checklist to identify students talent in Maths should be based on teacher observations and through students' work. Teacher/parents/self nominations need to be justified as well.

Using student portfolios of past work may not be accurate as we may not be aware of the support the student received when building the portfolio.

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1) Use Higher-order Problems (including certain Math Heuristics) to identify those pupils who are talented in Mathematics.
2) The checklist can be used as a further reference in selecting pupils for talent development programmes (e.g. E2K, Math Olympiads)
3) Give pupils problems that are cross-topics or even cross-subjects (to see if they are able apply their knowledge effectively).

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-use tasks to determine the extent of the characteristic
-assessing those who have done well as a basis for talent identification
-talent identification is also subjective when parents are proposing their own children who may not be up to the mark
- school banding of child - certain children may excel in only one subject - should the child go through talent identification for that strength subject?
- pupil interview on target group instead of whole cohort to identify the target 'gifted' children
- should class observation and feedback from teachers suffice instead of creating separate tasks or checklist
- variety of tasks in the classroom will be more holistic in identification of target group children

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Some of us are surprised that creativity is one of the 3 elements of giftedness in Renzulli's model

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Some of us are surprised that creativity is one of the 3 elements of giftedness in Renzulli's model

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-Renzulli's - some of us felt that the model is a bit simplistic

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-Renzulli's - some of us felt that the model is a bit simplistic

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Surprise - creativity in the Renzulli's model is something new to some of us and we also reinforced that creativity could be found in other domains.

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E2K - creativity, thinking out of the box
targeted programmes for HAL learners

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We all agree that having task commitment is crucial in ensuring that learners are productive and able to progress in their talent development

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Children are innately curious. Can we perhaps think of sharing HAL sharing resources for the whole cohort? We do wish to explore how more creativity can be incorporated into school programmes. Gagne's model focuses on inner and outer traits while Renzulli has 3 broad areas and houndstooth background (traits).

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Surprising that creativity is part of Renzulli's model. Do all gifted students necessarily have this creativity or intellectual curiosity?

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1) Renzulli's model - not all pupils may satisfy all three components (Ability, Creativity, Commitment).
2) Gagne's Model - Catalysts that are important, in terms of intrapersonal as well as environmental.
3) Some pupils could be HA, but because of certain environmental catalyst being missing, their potential may be hindered.

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We are important and can become mentors to our HAL. Concern: Most of our schools have limited resources to develop HALs, E2K and competitions. There is growing emphasis on thinking aloud, applications to daily life.

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Gagnes -
Importance of school - inculcating passion. Are we able to support students with programmes especially in cases where parents cannot support at home?

Students have to put in effort individually through hard work, dedication and willingness to achieve excellence.

Renzulli -
Creativity - more willing to explore a variety of answers compared to other students
Task commitment - necessary for students to put in effort but secondary to the other 2

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1) Some thought that giftedness was born and innate. Learning that giftedness can be helped developed into talents informs us that we can have more programmes in school.

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- renzulliis rings  -the various areas give play to the potential of a child
- Talent management Programme to join CCA
- Identifying of children based on results to participate in E2K
- Both models emphasise the potential of the child

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The Renzulli's 3-ring model that includes the houndstooth background suggests that one of the ways that we can create an environment to romance the students to love the subject proves a challenge especially when students' passion start to dwindle in the upper block. It seems that the non-routine questions such as the introduction of the golden ratio do not interest them as much as expected.

One question that we discussed was how to enthuse the girls as much as the boys.

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1) What surprised you about any of these models?
2) What resonated with you?
3) Which model(s) would be relevant to what your school is doing?

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Activity 2: Using the HAL Identification Checklist

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Activity 2: Using the HAL Identification Checklist

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1) Consider the HAL Checklist. How might you use the checklist to identify pupils who are talented in Maths in your class?
2) Consider the other ways of identification, i.e. using pupils’ portfolio (i.e. the work they did in the past, not necessarily graded), teacher nominations, parents nominations, pupil self-nominations). What are your thoughts on using these other modes when you select pupils for provisions?

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Students are usually selected for enrichment and competitions based on their results. The selection criteria does not consider the speed of the student since the selection is based on the exam grade.

The checklist articulates the criteria that a teacher can use to identify a student's ability, though the process of identifying a student as HA is not yet so formalised.

A last note... How accurate would it be to identify a student's ability based on attitude? A student may be very keen to try puzzles and non-routine questions but may not necessarily be considered a HA math learner.

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For our group, main selection is based on last year results; there is also cross-checking with subject teachers that the particular child is suitably chosen.

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For our group, main selection is based on last year results; there is also cross-checking with subject teachers that the particular child is suitably chosen.