Scratch Programming in Mathematics

This year I have been experimenting with introducing programming to Mathematics classes, especially for Grade 6, who do not have programming in Design (nor did they in primary school). These are the tasks I have introduced so far, and some of the student responses.

Prime Number Checker

This is a starter program I explained in class, and set as a task to finish for homework: https://scratch.mit.edu/projects/184630994/#editor

Simple prime number tester.
Can you improve the algorithm, to make it more efficient?
Can you change the program so you don't have to keep clicking the green flag?
Can you make sure it doesn't add a prime to the list more than once?
How many prime numbers can you find between 100 and 1000?

This was successfully completed by two thirds of the class.

Leap Years

This was an optional question I added in to the existing assessment task here: https://docs.google.com/document/d/1D5s6gSlFkxGgB413xvYVIJrNUwS1TT4dcz8wUQLn2Mg/edit?usp=sharing

a. Write a program in Scratch to test whether a given year is a leap year or not.
b. Extend your program so that it will find all the leap years from 1900 to 2020. Check that it is working correctly.
c. Use your program to find interesting facts, (such as the final leap year of the millennium, or how many leap years there have been since the Gregorian calendar started. Use your imagination)

Three students opted to try this task. One didn't solve it, one had an incorrect implementation of the algorithm (the tricky 400, but not 100 rule), but the third student has the algorithm correct and concisely programmed, plus some nice useability scripting: https://scratch.mit.edu/projects/189135859/#editor

Electoral Systems

Again this is an addition to an existing assessment task, and one of the optional questions, here: https://docs.google.com/document/d/1q2MVJaBsYWIfeg6h7b81GoFw-FwOAFZpDLx1ByeBwHo/edit?usp=sharing

5. Write a program in Scratch to calculate the outcome of an election from the preferences of voters, by both the elimination method and the plurality method. Run your program many times, comparing the fairness of the results by the two systems. Extension: find out about the Borda count method, and add this into your program.

Students were provided with a starter program which creates random sets of voter preferences: https://scratch.mit.edu/projects/197219936/#editor

Reflection

The tasks have been well-received by students, and motivating for high-achievers. However, students who are less strong in mathematics find it difficult to implement the algorithm, or to break down the problem in a way that can be implemented with Scratch blocks. This isn't surprising, as programming involves high order thinking. The election task is coming up soon, so lets see how it goes.

New Standards

The old performance standards are being replaced by IB Standards and Practices:

• Standard C1: Collaborative planning
• Standard C2: Written curriculum
• Standard C3: Teaching and learning
• Standard C4: Assessment

New post labels reflect this change. They are: Collaboration, Curriculum, Teaching, Assessment.

Full checklist below.

C1: Collaborative Planning
Collaborative planning and reflection supports the implementation of the IB programme(s).
1. Collaborative planning and reflection addresses the requirements of the programme(s).
2. Collaborative planning and reflection takes place regularly and systematically.
3. Collaborative planning and reflection addresses vertical and horizontal articulation.
4. Collaborative planning and reflection ensures that all teachers have an overview of students’ learning experiences.
5. Collaborative planning and reflection is based on agreed expectations for student learning.
6. Collaborative planning and reflection incorporates differentiation for students’ learning needs and styles.
7. Collaborative planning and reflection is informed by assessment of student work and learning.
8. Collaborative planning and reflection recognizes that all teachers are responsible for language development of students.
9. Collaborative planning and reflection addresses the IB learner profile attributes.
Note: “Collaborative planning and reflection” is used as a single concept as the two processes are interdependent

C2: Written Curriculum
1. The written curriculum is comprehensive and aligns with the requirements of the programme(s).
2. The written curriculum is available to the school community.
3. The written curriculum builds on students’ previous learning experiences.
4. The written curriculum identifies the knowledge, concepts, skills and attitudes to be developed over time.
5. The written curriculum allows for meaningful student action in response to students’ own needs and the needs of others.
6. The written curriculum incorporates relevant experiences for students.
7. The written curriculum promotes students’ awareness of individual, local, national and world issues.
8. The written curriculum provides opportunities for reflection on human commonality, diversity and multiple perspectives.
9. The written curriculum is informed by current IB publications and is reviewed regularly to incorporate developments in the programme(s).
10. The written curriculum integrates the policies developed by the school to support the programme(s).
11. The written curriculum fosters development of the IB learner profile attributes.

C3: Teaching and Learning
1. Teaching and learning aligns with the requirements of the programme(s).
2. Teaching and learning engages students as inquirers and thinkers.
3. Teaching and learning builds on what students know and can do.
4. Teaching and learning promotes the understanding and practice of academic honesty.
5. Teaching and learning supports students to become actively responsible for their own learning.
6. Teaching and learning addresses human commonality, diversity and multiple perspectives.
7. Teaching and learning addresses the diversity of student language needs, including those for students learning in a language(s) other than mother tongue.
8. Teaching and learning demonstrates that all teachers are responsible for language development of students.
9. Teaching and learning uses a range and variety of strategies.
10. Teaching and learning differentiates instruction to meet students’ learning needs and styles.
11. Teaching and learning incorporates a range of resources, including information technologies.
12. Teaching and learning develops student attitudes and skills that allow for meaningful student action in response to students’ own needs and the needs of others.
13. Teaching and learning engages students in reflecting on how, what and why they are learning.
14. Teaching and learning fosters a stimulating learning environment based on understanding and respect.
15. Teaching and learning encourages students to demonstrate their learning in a variety of ways.
16. Teaching and learning develops the IB learner profile attributes.

C4: Assessment
1. Assessment at the school aligns with the requirements of the programme(s).
2. The school communicates its assessment philosophy, policy and procedures to the school community.
3. The school uses a range of strategies and tools to assess student learning.
4. The school provides students with feedback to inform and improve their learning.
5. The school has systems for recording student progress aligned with the assessment philosophy of the programme(s).
6. The school has systems for reporting student progress aligned with the assessment philosophy of the programme(s).
7. The school analyses assessment data to inform teaching and learning.
8. The school provides opportunities for students to participate in, and reflect on, the assessment of their work.
9. The school has systems in place to ensure that all students can demonstrate a consolidation of their learning through the completion of the PYP exhibition, the MYP personal project (or community project for programmes that end in MYP year 3 or 4), the DP extended essay and the CP reflective project, depending on the programme(s) offered.