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1. Consider the HAL Checklist (Annex A). How might the checklist guide you to identify pupils to participate in a math talent development (TD) programme:

​Math Olympiad Competition​

E2K Mathematics Programme​

Math Expert @ Work

Inter-school Math Game Design Competition​

Others (you may suggest other math TD or enrichment programmes)​

2. What are some challenges or issues you may encounter in the identification process?​

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You have a class of pupils with varied readiness levels. You are going to teach a lesson based on one of the following CPPD topics and leaner outcomes. From your observations of their behaviours and their previous work, you anticipate that most pupils will progress well with the current CPPD learning outcomes, but some pupils may grasp the concepts very quickly. Choose any one of the topics and write differentiated learner outcomes to further challenge your high-ability learners in your class?

Note: if you prefer to present your group's discussion in a table form, feel free to type your response in ppt slide provided and upload it as an image.

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Please insert your group name e.g. Group 5 (based on your breakout room number) as the subject of the post, and jot down your group's discussion in the content of the post.

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1. Usually, subject teachers will identify the HAL students or asked about the suitability of the students to be in the programme. Sci E2K uses a similar checklist for identification.

Most of us have not seen this checklist applied.

2. Sometimes, students are identified but they are not keen to be in the programme and focus on the answers only. They are reluctant to share or present their thinking.

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(Qn 1)

Math teachers can use this checklist to capture inputs for fine grading after a rough initial cut. The initial cut could be from EOY results, as a proxy of baseline academic proficiency. Another data point for the initial cut is information from round 1 of the P3 GEP assessment.

This checklist helps to more objectively capture data to come up with the final namelist, for decision making at the departmental level.

(Qn 2)

This checklist needs not be floated out to all math teachers as a first cut, to streamline the workflow. It may be too overwhelming.

Other challenges: parental pressures to include their child (esp if performing at borderline band 1). This checklist better helps us internally make objective decisions (although this document is not parent - facing).

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Current indicators:

Year-end results

Teachers' inputs

P3 GEP list of HAL-identified students

Use of the checklist:

Having the checklist helps us not to just look at their academic performance (ability and aptitude), but their attitudes and disposition towards math

Challenges or issues identified

Good results in school-based curriculum is not necessarily correlated with mathematical problem solving (some students are drilled by parents)

Some have no interest in learning advanced concepts beyond the syllabus

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1. After first cut by assessment result, teachers will use the checklist to sieve out students who are considered gifted in Maths to have a smaller pool of students to consider for the TD programmes.

2. Teachers will need to understand the profiles of the students aside from assessment results. Challenge of shortlisting students for E2K and Olympiad > occurs at the start of the year where the teachers might not be too familiar with the students yet.

3. Difference between the questions from normal Maths curriculum and what is being offered at E2K/Olympiad so students and teachers teaching the students will not be able to observe if they have an aptitude for these kind of open questions (some students might feel too challenged by this and hence, turned off). Observed attitude towards learning mathematics by maths teacher could also have been hindered because of presence of enrichment/tuition classes.

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Problem solving abilities and attitude (point 13 & 15) lands itself well for the selection of students for E2K and MO.

Challenge: Students to choose between MA E2K and SCI E2K if they are selected for both. Due to constraints in the school's schedule.

Justifications to parents for selection of E2K students (as we are not allowed/supposed to share about the HAL list). These students may not be doing as well as those who are selected based on marks. The checklist can then come in handy to articulate some traits we are looking for.

In addition, we also refer to the list provided by GEP at the end of P3.

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The checklist can be categorised further.

For example, some of the points are necessary for participation in competitions (e.g. resilience, problem solving abilities).

2) The identification process could be observed across a few tasks. If it's only one particular task, some of the students may be on the losing end, for example those who lack interest in that topic or spatial awareness.

The students may be HALs, but may lack the mental stamina and the checklist may not be able to address that.

If the same student is identified for various competitions and programmes, it may add mental stress to these students.

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How to Apply the Checklist

Create a Clear Rubric: Ensure all teachers are aligned by developing a detailed rubric for consistent assessment. Break a task down into observable components. This helps teachers when making recommendations.

Challenges in Applying the Checklist

Subjectivity of Criteria: Traits like "elegant solution," "curiosity," "passion," and "intuition" are hard to measure and explain to parents.

Limited Challenging Questions: There may not be enough difficult questions to effectively distinguish varying levels of student understanding.

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1. Attitudes towards learning Maths allows teachers to look beyond a student's hard skills. Soft skills are just as important.

2. Subjectivity among teachers. Need some standardisation among teachers. Secondly, if the class is only exposed to the regular curriculum, the identification process may not accurate.

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Q1. It shows some characteristics of HAL students where are different from the rest. There are students who are not the top 10% of the cohort but show such characteristics. It allows for a more holistic observation of a child, that is not solely based on marks.

Q2.

Some of the indicators are difficult to observe, for example if the child reads Math books extensively.

Another characteristic of the children using a variety of representations to solve problems is vague. For example the use of Algebra to solve all questions.

The use of often, sometimes, rarely is subjective among teachers.

attitude towards math might depends on the types of Mathematics that are presented to them, routine math problems as compared to novel math problems. Children attitude Maths differs.

Teacher - student ratio. If the class is big with many students,teacher will have a difficult time analysing all of them in detail.

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1) Having different aspects of characteristics of HAL in the checklist enables schools to identify students who are suitable for such a TD programme. For instance, some students may be conceptually strong but may not demonstrate positive learning disposition and attitudes towards learning of Mathematics.

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1. For competitions like Math Olympiad, we can also look out for students who learn new math concepts and processes quickly, which means they show ability to understand concepts quickly. This also means that they can and are able to handle questions of a higher difficulty as well. Linking of math topics would land nicely into making connections among math concepts, and this also lands itself in place for programmes like e2k, where cross-knowledge of topics would be appropriate.

2. The ownership of doing math outside of math class - the criteria of doing math puzzles and logic problems would be also a good indicator of choosing of students for activities like e2k mathematics programme. However, we do also need to take note that this can also be a challenge in the identification process as we also need to identify the difference between high ability students and student who can perform at a high level academically.

3. Another challenge could be that some students are soft spoken and more reserved. This could result in not being able to identify these students, as in the checklist, if the student is unable to vocalise his or her curiosity in learning new math concepts, then they might not be identified as a high ability learner.

4. Subjectivity in teacher judgement also falls in place. From a teacher to a teacher, there exists abias as well.

5. The scope of the checklist could be a bit narrow. For example, spatial thinking or reasoning is not explicitly mentioned in the checklist, so that could result in the choice of students being a bit narrow.

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1. The list provides characteristics based on:

A - Affective

B - Behavioural

C - Cognitive

2. Challenges

Attitudes towards learning of Mathematics may not reflect that all HAL enjoy solving Math problems or puzzles

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Selection process in our schs

exam results

GEP results

teachers' observation

past competition results (e.g. Olympaid. etc)

Checklist is useful for teachers unsure of selection process.

Challenges

checklist can be subjective and parents can questioned teachers' observation

exam results may 'penalise' students who are not inclined to 'pen and paper' tasks

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Primary 5

Using knowledge about angle sum of triangle

Outcome: By extending on their understanding - to investigate the properties of polygons with more than three sides, exploring how the sum of the interior angles increases with the number of sides.

Challenge: Using a triangle, students will also explore and explain the relationship between the angle sum of a triangle and the general formula for the sum of interior angles of any polygon (i.e., (n−2)×180∘)

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P5 Triangles

Cpdd: Investigate and discover the angle sum of any triangle is 180 degrees.

Differentiated learner outcomes:

Find the interior sum of n-sided polygons

From the interior sum of triangles, generalise to find the pattern relating n to the interior angle sum of any n-sided polygon

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P5 Triangles

High Ability Learner

Give them different types of triangles, let them measure the angles on their own using protractor

Come up with different methods to prove that the angle sum of any triangle is 180o.

Get students to think why is having an angle sum of 180o important in our daily life.

Average ability learner: the angles are provided instead

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P5 Triangles:

To apply the concept of triangles in real world scenarios.

-Students to design a structure using the angle sum property

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P5 Triangles

High Ability Learner

Give them different types of triangles, let them measure the angles on their own using protractor

Come up with different methods to prove that the angle sum of any triangle is 180o.

Get students to think why is having an angle sum of 180o important in our daily life.

Average ability learner: the angles are provided instead

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P5/P6 Percentage

Application of percentages in real world context

Students to source for real world articles/posters/advertisements involving discounts

Working with percentages that come with decimals

Students can come up with multi-step word problems based on the articles/posters/advertisements they have found

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Differentiated learner outcome:

working backwards to find original price

getting students to explain how the increase works and why it must be based on original and not new final price.

give a worthwhile task to let students figure out if discount is "cheaper" if purchased in bulk or in single unit.

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P5 Angles

HAL will be asked to prove the following properties:

1) Corresponding angles are equal when a transversal cuts through 2 parallel lines

2) Alternate angles are equal when a transversal cuts through 2 parallel lines

3) Interior angles are supplementary

4) Exterior angle of triangle is equal to the sum of the opposite interior angles of the triangle.

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DI Outcome 1: Percentage

Students will understand how the same absolute change can result in different percentage changes depending on the base value.

They will apply this understanding to real-life contexts such as rising costs, inflation, and income growth.
For example: Although Switzerland's average income increased by a larger amount than Singapore's, Singapore showed a higher percentage increase because the starting income was lower.

Students will develop the ability to interpret and compare growth meaningfully by considering both absolute and percentage changes.

DI Outcome 2: Percentage

Students will explore and calculate different types of discounts, additive and multiplicative methods.

Example (Additive): A store offers 20% off plus an extra 10% off – total discount = 30%.

Example (Multiplicative): A store offers 20% off, then an additional 10% off the discounted price. Total discount ≠ 30%.

DI Outcome 3: Percentage

Students will compare costs of living and item prices across different countries or cities using real-world data.

They will apply percentage and ratio reasoning to understand affordability and value.

DI Outcome 4: Decimals

They will learn the relationship between fractions and decimal forms, and discover patterns in why some decimals terminate (e.g., 0.5) and some recur (e.g., 0.333…).

DI Outcome 5: Angles

DI: They will look for patterns and derive general rules such as:

Angle sum of a polygon = (n - 2) × 180°, where n = number of sides.

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1. To draw any kind of triangle and cut out the angles. put the angles on a straight lin. What do you observe?

2. Why is there no obtuse right angled triangle? Explain.

3. Why is there no equilateral isosceles triangle? Explain.

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P6 Percentage

Outcomes:

Extend the concept of percentage - investigate the interests earned

Tasks:

Give students a table of interest rates offered by 2 banks. The table will show the interest rates based on different tiered of deposits.

Students to determine which bank to deposit the given sum of money by working out the interest gained.