Fostering Mathematical Engagement and Love for Mathematics- Pt. 2 of 4
Learning That Sticks – From Concepts to Connections
"When students make connections between mathematical ideas, they are learning with depth. That’s what leads to flexible thinking and the ability to use mathematics in powerful ways."
-Jo Boaler in “Mathematical Mindsets”, Professor, Stanford Graduate School of Education
Hi, this is the GenWise team- we bring out this newsletter to help parents and educators to complement the work of formal schools and associated systems. We are also a founder-member of Gifted World- if you are interested in issues related to gifted education and talent development, and are looking for resources for students, do become a member of the Gifted World Community (membership is free).
Check out our upcoming courses for educators, parents and students in the ‘Upcoming Events’ section below.
This is the second of a 4-part series about the dreaded topic of math learning which will be published weekly. In this series, Sowmya Jatesan, Head of Teacher Development at GenWise, shares her insights from years of teaching math herself and mentoring math teachers. The 4 parts in this series are-
Learning That Sticks – From Concepts to Connections
Make it Real – Engagement Through Contexts, Games and Projects
The Math Teacher as a Guide – Mindset, Assessment and Level-Appropriate Challenge
Sowmya and her team are offering an online course for math teachers called ‘My Misconception Mentor’ starting June 7, 2025. The course is also open to interested parents. For details, check the Upcoming Courses section.
Learning That Sticks – From Concepts to Connections
In the last post, we looked at the importance of building foundations with the use of concrete materials and making sense of procedures. In this post, we look at what teachers need to understand and do to make Math learning across grades a coherent and connected experience.
A Spiralling curriculum
When the teacher views Math topics as part of an integrated whole rather than isolated topics, then the content is presented in such a way that core concepts are revisited repeatedly at increasing levels of complexity; this builds deeper understanding over time. Rather than treating topics as "done" after one unit, concepts reappear in new contexts and connect to new learning. For example, multiplication first appears with simple arrays, returns with fractions, then with decimals, and later in algebra.
The teacher’s view of the subject in this manner is foundational to help students internalize concepts and connections over a period of time. This is not an easy matter however and teachers need to be trained to have such a view of the subject.
What changes and what doesn’t? - Scaffolding during transitions
As students move to more generalized ideas in Math (e.g. from Whole numbers to Fractions or from Arithmetic to Algebra), they need deliberate scaffolding in the form of well-designed questions and teacher-led discussions to explicitly understand and make sense of what has changed and what has not; if this transition is not supported well, students proceed with misconceptions and partial understandings that erode confidence and clarity.
Through the Primary, students see several meanings of two symbols put together. e.g.
4 + 3 means Add 4 and 3 and similarly for the other operations
43 means 4 tens and 3 ones
4 / 3 means 4 thirds
But when Algebra is introduced, 4x now means 4 multiplied by x.
Helping students build Mathematical connections
Students who enjoy Math typically see it as a predictably connected network of concepts while students who are anxious about it see it as a complicated collection of different ideas that use arbitrary rules. This fragmented view comes in the way of building Number Sense, arguably the single most important Student learning outcome in the Primary years. In later years, fractions, percentages and decimals are often introduced as separate topics; linear equations are often taught separately from graphs. Students need to be able to see the connections between the different Mathematical ideas and be able to use them flexibly.
e.g. An 8-yr old student who uses the traditional vertical-aligned subtraction algorithm to solve 107-9 needs support to build his Number sense.
e.g. ⅕ + ¼ A student who has not understood the conversion between decimals and fractions is likely to do this using the “traditional fraction sum algorithm,” which can result in errors while the simplest way would be to add the decimal forms (0.2 + 0.25).
Using Visualizations & Technology tools
Visualisation & Representation are a key aspect of Mathematical thinking. This includes not only Tech tools such as Geogebra or Desmos but systematic representations beginning with a number line, tables, tree-structure etc.
Consider this popular problem: What is the sum of the first 2 consecutive odd numbers? How about the first 3? first 5? first 10? How about the first n?
While this problem can be solved algebraically, look at this visual representation from which the solution literally leaps to the eye. The sum of the first 2 odd numbers is 4= 22; the first 3 odd numbers is 9= 32; the first 10 odd numbers is 100= 102 and so on; The sum of the first n odd numbers is n2.
At each age level, students benefit from working on varied problems suited to different representations; they need well-crafted introductions to tech tools. The right kind of representation ignites Aha moments, helps to gain conceptual clarity, allows a Mathematical problem to be viewed conveniently to work towards a solution, and can often provide proof for the completeness of a solution.
Share your thoughts in the comments section of this post or write to sowmya@genwise.in. Next week, we will look at ways of spurring engagement and developing higher level mathematical thinking through the use of rea-life contexts, games and projects.
Upcoming Courses
My Misconception Mentor (Math Series- Primary and Middle)- for educators and parents
Early Bird Registration ends by May 20, 2025; Course starts June 7 and ends in Sep 2025
Online on Saturdays- 1 to 3 PM IST (Primary); 330 to 530 PM IST (Middle School)
‘My Misconception Mentor’ is an 8-session online course based on the data of top misconceptions identified by Ei ASSET, the leading diagnostic assessment in India and the UAE. ASSET data have been bringing student misconceptions and common errors to light for over 2 decades. By understanding the roots of these misconceptions, we prioritize the most pressing learning gaps. Focusing on addressing well-documented misconceptions, we prevent cascading learning gaps, build stronger foundations for later concepts, and improve learning outcomes. There are 2 series of Math courses- one covering grades 1-5 (primary) and another covering grades 6-8 (middle).
While the course is targeted at teachers, parents are welcome to participate. Parents who participated in our ‘Mathtastic Teaching’ and ‘GenAI for Educators’ courses found great value.
The course is composed of 2 parts
Misconception Decoder- The first two sessions directly focus on misconceptions and the most common errors as seen in national data from the ASSET assessment.
Deep Dive: Content & Connections- The remaining 6 sessions focus on Subject Knowledge, Pedagogical Content knowledge and teaching strategies in the context of specific topics.
More details about the courses are available in this document and the links therein.
Participants also have an option to register only for the Misconception Decoder part of the course.
Register for My Misconception Mentor (Early Bird Fee of INR 16,000- GST included)
Register for Misconception Decoder (Early Bird Fee of INR 4,900- GST included)
An example of a student misconception from ASSET data and how the course would help teachers address such learning issues is discussed below.
This grade 8 question was administered to 6710 students nationally.
Only 30% of students estimated the answer correctly (slightly less than 16). 27% said it would be slightly more than 4!
Symptomatic approaches to fixing this misconception would involve teaching tricks like "move the decimal point to make it a whole number" or giving rules like "when dividing by a decimal less than 1, the answer will be bigger than the number you started with".
Such symptomatic approaches are insufficient because
They don't address the fundamental misunderstanding (division and decimals here)
Students can't explain why their answers make sense
The learning doesn't transfer to new situations
Students struggle when numbers or contexts change
The misconception often resurfaces in more complex problems
Our approach helps the teacher go deep below the surface; sometimes she may even have to work with teachers in other grades to tackle the roots of such learning problems. It is a slower and more painstaking process that takes time as the teacher builds on her subject and pedagogical content knowledge and also how students think. However, it is also motivating and rewarding when you start seeing students make sense of their learning and come up with their own innovative methods. Most importantly, this approach results in a sustained change in the teacher’s mindset, knowledge and skills.
Misconceptions are just the tip of the iceberg- we don’t want to address just the tip but the root causes that form the huge underwater mass of the iceberg.
Thus, for the decimal division example shared above, teachers would, over a period of time, focus on building number sense beyond whole numbers, connecting division and fraction concepts etc.
Gifted Online Summer Program- July 2025- for students
Early Bird Registration ends by May 31, 2025
This program provides young school students a front-row seat to mind-expanding courses, brilliant mentors, and a tribe of gifted thinkers. Courses range from Astrophysics, Storytelling, Physics of Ancient Arms, Algebraic Patterns to GenAI and Scientific Inquiry (please visit this page for more details including the eligibility criteria for the program).
✅ 2 - 4 weeks of fun learning
✅ Each Learning Quest is 12+ hours of live, small-group sessions with world class mentors.
✅ Resources and assignments from each session help expand and consolidate your learning.
✅ Saturday Circles with inspiring guest speakers and alumni
✅ Quizzes, challenges, and chances to win recognition
✅ A fun and supportive online community where the child finds ‘their tribe’
✅ Certificate and written feedback at the end of the course
Dates: July 7 – Aug 2, 2025
Location: 100% Online | Serving Gifted Students in India & the UAE
Grades: 5–9 (2025–26 Academic Year)
Eligibility: Ei ATS top performers for advanced courses; Other courses open to all Gifted World members. Check details here.