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+Maths teaching course for teachers and parents
“Somehow, it’s okay for people to chuckle about not being good at math. Yet, if I said, “I never learned to read,” they’d say I was an illiterate dolt.”
-Neil deGrasse Tyson, American astrophysicist and author
(Reposted from the GenWise Substack. Find more fascinating blogs here: https://genwise.substack.com/)
Some years ago, our team was talking to students in a school about their favourite subjects when one child piped in saying, “I love studying Maths because I have to remember less! In other subjects, I have to remember so many things”. We thought this was such a great insight from the perspective of a child! We believe that every child can and should feel this way about Maths. In our work on training Maths teachers, we have started to see this happen- when the teacher understands and teaches Maths in a particular way, almost all children start seeing the connections, making learning Maths much easier and more fun.
In this post, GenWise mentors, Sowmya Jatesan and Jayasree Subramanian, share their thoughts on what needs to change about Maths teaching to make this happen. They also share details of our upcoming online course on teaching Maths this way- the course is open to schoolteachers as well as parents who are interested in teaching Maths. Details of the course are available here and those interested can register here.
There is one batch targeting grades 3-5 and another batch targeting grades 6-8. If you have any queries, you can contact Sowmya on sowmya@genwise.in or +91-9606810163.
The video below shares one example of how Maths learning can be easier and make sense. We share another example in detail in the main post.
Teaching Maths for Foundational Understanding
Every teacher who loves mathematics and is committed to making the subject understandable and enjoyable to students can become a great Maths teacher. To become such a good teacher though, she also needs to understand the topics she is teaching at a much deeper level. When she understands topics at this level, she is able to help students understand core principles and associations between concepts. When a student gains this kind of foundational understanding, he is not afraid of Maths and does not have to struggle much because he has to ‘remember less’.
For example, a student whose teacher has taught him multiplication shortcuts is quick at multiplying a number by 10 or multiples of 10 because he ‘remembers that he must add the same number of zeroes’ (e.g. 73 x 100= 7300). But if he is not familiar with the concept of place value and where decimals are placed on the number line, he may give answers such as 0.73 x 100 = 0.7300, when working with decimals.
In contrast, a student whose teacher has taught him the core principles and connected the concepts, realizes that 0.73 is a number close to 1 on the number line, and when made ‘100 times larger’ (multiplied by 100) has to be a number near 100 on the number line. Thus, even if this student initially makes a mistake by applying a rule blindly and writes 0.7300, he checks the reasonableness of his answer and corrects it. In contrast, the student who knows only shortcuts and rules, does not even think in terms of whether something is reasonable or not. Check out the next sub-section for a more detailed elaboration of the contrast between the two students.
For a teacher to teach core principles in the manner outlined above, she must be exposed to concepts at a much deeper level and spend time honing her classroom and instructional practices over a few years. Every committed teacher can become a great Maths teacher if this path is followed. This takes time, but shortcuts to teacher development do not work and only make things worse in the long run.
Learning Methods vs Learning Core Principles- an Example
Consider these two cases:
Case 1:
Arnav is a grade 4 student. Arnav’s grade 3 teacher has given them a lot of practice with Multiplication facts and Arnav feels quite confident. He used to ace the 1-minute practice worksheets for multiplication they got each week in class.
She has also taught them shortcuts that Arnav loves. For example, Arnav is very quick with multiplication by 10 and powers of 10. He “knows’ the rule - ‘Just add the same number of zeroes!”
Now in grade 4, Arnav is learning multiplication of decimal numbers by 10 and 100 and he finds that he has gotten most of the questions wrong. Here are three of his responses:
0.73 x 100 = 0.7300
0.040 x 10 = 0.0400
1.5 x 100 = 1.500
Case 2:
Akhil on the other hand has had a teacher who has helped them learn multiplication a little differently. She has also made it very important for them to check if their answer seems to be correct.
He is very confident of multiplication tables up to 5 and he knows those of 9 and 10. The rest, he “builds”.
To multiply by 7, he usually multiplies by 5 and 2 and then adds. He finds it fun to multiply two-digit numbers mentally.
For example, 23 x 8. His thinking goes like this:
I know 10 x 8 = 80; so 20 x 8=160.
I know 3 x 8 = 24, so 23 x 8 = 160 + 24 = 184
He then checks for what his teacher calls “reasonableness.”
He knows 23 x 10 = 230, and he knows 3 x 8 = 24, so the product must end in 4.
So, it seems to him that 184 is “reasonable”.
When he is introduced to decimal multiplication by 10, he sees the problem differently.
For example, when he sees this question
0.73 x 100
He thinks of making the 0.73 larger by 100 times. He remembers that there is some rule about moving the decimal point and first writes
0.73 x 100 = 0.0073
Then he checks his answer and realizes that he has made his number much smaller, so something is not correct.
He writes
0.73 x 100 = 73
And this seems to him to be “reasonable” since, 0.73, a number close to 1 on the number line has now become 73, a number near 100 on the number line.
Upcoming Online Course- Mathtastic Teaching
Details of the course are available here and those interested can register here. There is one batch targeting grades 3-5 and another batch targeting grades 6-8. A summary of the course highlights is shared below. If you have any queries, you can contact Sowmya on sowmya@genwise.in or +91-9606810163.
Course duration, content, interaction hours and dates:
6 months; starting 17 Aug 2024 and ending Jan 2025
12 sessions in total- 2-hour online sessions, twice a month, on Saturdays
Asynchronous Assignments:
Assignments to be completed offline and submitted (2 hours expected to complete assignments of each session)
Weekly Office Hours with Course Instructor:
The course instructor will be available online from 6 PM to 7 PM, every Tuesday to meet any teachers who have doubts or want to discuss any topic. Participation in these sessions is optional.
Expected time commitment:
An average of 8 hours of work per month- 4 hours in the live online sessions and 4 hours of ‘offline’ work on assignments (including classroom instruction with students), which can be done flexibly as per individual schedules.
Nature of Assignments
1. Materials related to the topic covered along with a set of structured reflection questions.
Participants will read/watch the materials offline and share their reflections. As they do this, teachers will be encouraged to share their questions/comments to initiate discussions on an online platform (probably a WhatsApp group).
2. Specific assignments such as designing/adapting a task/assessment or using a technology tool like Desmos/ chatGPT to teach a topic more effectively
3. One specific activity to be tried out in class/ with students, and a structured reflection on the observations
About the Course Designers and Facilitators
Jayasree Subramanian has a master’s in mathematics from IIT Madras, and a PhD in Mathematics Education from Homi Bhabha Centre for Science Education, TIFR, Mumbai. She is a senior mentor at GenWise and is also part of the IIT Palakkad outreach team- in these roles, she has conducted multiple courses and sessions for school students. She has also conducted multiple teacher training workshops. Earlier, Jayasree was Maths assessments lead at Educational Initiatives and prior to that she taught Maths at a leading school in West Gujarat.
Sowmya Arunajatesan has a bachelor’s from IIT Madras and a Master’s from Penn State. Sowmya heads the teacher development practice of GenWise. She is trained in the Montessori method (for students up to age 12) and has worked for over 15 years with both (elementary and middle school) students and teachers in several alternative schools. For the last 3 years, she has been the Project Director for a Maths and Science teacher development project for a leading international school in Bangalore. As part of this project, she and her team work closely with nearly 60 teachers. This work helps teachers build both their content knowledge and knowledge of the teaching/learning process and build a reflective teaching practice.
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