Minset in Mathematics - End of Year

 

Students were shown several videos from the Stanford EdX course "How to Learn Math: for Students" over the course of the school year.

At the end of the year (June) they were given the same survey questions that they had answered before watching anything (August).

The questions are taken from the online course itself, and I have identified three categories in which to group them. The questions were not asked in this order.

The scale used is 

1: strongly agree

2: somewhat agree

3: somewhat disagree

4: strongly disagree

The numbers are percentage of grades 7 and 8 students.

 

Attitude Towards Mathematics

Not a great change in the distribution, still roughly 60% of students enjoy maths and don't find it boring, but only 30-40% enjoy being challenged to solve difficult problems. A slight shift towards a more positive attitude was observed on all questions of this type.

 Nature of Mathematics

 The message of the online course was mostly targeting the misconceptions commonly held that mathematics is difficult for most people and that there isn't much they can do about it.

It is clear from the responses here that the message was well-received by students and we can see a definite shift towards more positive attitudes.

 

Perception of Ability

Half of students expressed negative self-perception of mathematical ability in most such questions, though they believe they can do well, if they make enough effort. This confidence has grown since the beginning of the year, again influenced by the message of the videos, it seems. There was a video about growth mindset and likening mathematical to sporting ability in terms of the benefits of training.

Mindset in Mathematics

Grades 7 and 8 were surveyed using the introductory questions from the Stanford EdX course "How to Learn Math: for Students". There were 22 responses. E-mail addresses were collected to facilitate possible targeted follow-up. Students were told that this was to help my study (I showed them the course), and to answer honestly.

The questions fall into three broad categories - attitude towards maths (enjoy or not), perception of ability, and opinion about the nature of maths.

Summary

Roughly 60% of students enjoy maths and don't find it boring, though only 30-40% enjoy being challenged to solve difficult problems.

40-50% of students believe there are people who are naturally good at mathematics, and that there isn't much you can do to become one of them. Presumably they feel that more effort would enable them to do well without becoming a maths person.

40-50% of students characterised mathematics as a subject where it was important to remember methods, though most also saw it as creative and with many interconnected ideas.

50-60% of students expressed negative self-perception of mathematical ability in most such questions, though 60% believe they can do well, rising to a massive 90% who believe they can do well if they make enough effort. This is quite a surprise to me, and very encouraging.

 

Overall, roughly half of respondents feel positively about mathematics, and do not agree with the typical negative stereotype answers that might dominate in a western classroom. The next step is to target the other half.

Vote-counting Programs

The Election task has been completed, and four students opted to try the programming question. To recap, these were the instructions:

5. Write a program in Scratch to calculate the outcome of an election from the preferences of voters, by the plurality method. Then try to use the Borda count method (see below). Run your program many times, comparing the fairness of the results by the two systems. Extension: try to add the elimination method into your program.

I provided a starter program which casts random votes and puts them into a list.

https://scratch.mit.edu/projects/197219936/

The students had to write a script to parse the list and add up the votes. This involves creating and incrementing variables, followed by some if-else logic, and was achieved by all. Applying the Borda count method is quite a bit more difficult, and students asked me for help. I had to teach a double-loop algorithm, whereby elements of a list are looped over while the list itself is looped through. Following this, Borda count was successfully achieved.

One student who was absent came back with a working program written with Dad, which was nice to see! Another student hadn't realised there was a starter program, and wrote everything from scratch, and very well, too! The programs are below:

• https://scratch.mit.edu/projects/203946553/
• https://scratch.mit.edu/projects/203946227/
• https://scratch.mit.edu/projects/203946958/
• https://scratch.mit.edu/projects/203946137/

Reflection

This task was quite challenging, but was well-received by students, and I was impressed by their interest and perseverance. While writing a model answer, I noticed that the elimination method is much harder to implement, and I will drop this from a future version.

It occurred to me that this would also be a good spreadsheet task, and next time I might offer that as an alternative among the optional questions. It is of concern to me that students coming up to IB diploma Chemistry don't have much experience of using spreadsheets since we switched to MYP Design, with most of it taught by English and Art teachers.

Performance Goals 2018

Two SMART goals based on a specific standard and connected to an ATL skill, and separated into impact on learning and impact on practice. At least one based on Inquiry Reflection.

Goal 1 C3.13. Teaching and learning engages students in reflecting on how, what and why they are learning.

Students in grades 6 and 7 Mathematics will write a guided reflection at the end of each unit. My task is to prepare the guidance and give feedback on student reflections. Guidelines and student reflections will provide evidence of completion of this goal.

Goal 2 C2.Introduction of Computer Programming to the Mathematics curriculum.

Each unit in grades 6 and 7 Mathematics will include examples of the application of computer programs to solve mathematical problems, and provide opportunities for students to learn how to program. Task descriptions, programs written for teaching, and student responses will provide evidence for the completion of this goal.

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.

24h acid hydrolysis

Needing to hydrolyse some protein foods down to amino acids by boiling for 24h in 6M HCl, I came up with a new "invention".

Place four 100ml conical flasks full of water into a 2l Japanese water boiler, about half-full, so as not to cause the flasks to float. Having four of them means they can't tip over anyway.

Then place your hydrolysis solution in a boiling tube into one of the flasks (or do up to four at once). I stoppered it with a one-hole stopper, to prevent too much water dripping into the tube and diluting the HCl or causing it to overflow.

I set the boiler to 90^oC, not 98, to reduce the amount of bumping.

It works really well, and is so much safer than using a normal water bath.

Thiosulphate - Acid in a reasonable time

Struggling to get a simple thiosulphate - hydrochloric rate of reaction practical to work in a handful of minutes, trial and error brings me to this conculsion

0.1M sodium thiosulphate  + 1.0M hydrochloric acid + water in equal volumes gives about 6 minutes to obscure a cross at 20^oC, or about 2 minutes to max out a turbidity sensor at the same temp.

Student Surveys - Mathematics

I gave the mid-year survey to all of my students last week. Here are the results for my mathematics classes in grades 6 and 7. Almost 100% response, because I held off giving the survey until the end of the week, when several students returned from sickness.

Again I used the standard school survey, with ratings from 1 (strongly disagree) to 4 (strongly agree), and I plotted the results onto a net on a scale of 2 to 4. Click the image to view.

Student Surveys - IT

Mid-Year survey given to all students as a Google form, to complete anonymously.
Questions are answered on a scale of 1(strongly disagree) to 4(strongly agree)