Series: Supporting Dyscalculic Learners in Secondary Physics: (Part 2 of 6) | Read time: 3 minutes
The Problem: Jumping Straight to Algebra
Physics instruction often jumps into multiplicative equations like F=ma or V=IR too early. For dyscalculic students, who frequently struggle with number and ratio relationships, this introduces high cognitive load before they have grasped basic quantity conservation.
This post introduced the bar model: a pictorial representation of quantities and the relationship between them. This post describes the use of bar models to show additive relationships: specifically energy, current at junctions and resultant forces.
1. Currents at a Junction (Kirchhoff’s First Law)
Understanding and calculating currents splitting at a parallel junction is challenging for students, especially those with dyscalculia or mathematical learning needs.
A simple additive bar model visually shows that the total current entering a junction equals the sum of the currents leaving it:
- Total Current In = 6 A (Top whole bar)
- Branch 1 = 4 A + Branch 2 = 2 A (Bottom split bars)
Why it helps: The lengths of the bars make it easier to visualise the quantities and the relationship between them. This reduces the cognitive load for all students and is especially helpful for students with mathematical learning difficulties.
2. Energy Transfers
Bar models are helpful when tracking energy shifting between stores.
When a rolls down a slope, the energy in the Gravitational Potential Energy Store decreases while its Kinetic Energy Store increases. Some energy is transferred to the Thermal Store.
- Total Initial Energy = 100J (Top whole bar)
- Kinetic Store = 60J + Thermal Store = 40J (Bottom bars)
Why this works: It clearly shows that energy is conserved and makes the maths visual..
Even better if: Use cubes to represent the energy. For example, if 1 cube represents 10J, 10 cubes represents the energy when it is all in the Gravitational Potential Store. If 6 cubes are moved to the Kinetic Store, it is clear that the remaining energy cubes are in the Thermal Store.
3. Balanced Forces and Resultant Force
Calculating resultant forces often causes sign and direction confusion for dyscalculic learners. Additive bar models compare opposing forces visually by treating the larger force as the whole bar:
- Forward Thrust = 500 N (Top whole bar)
- Air Resistance = 300 N + Resultant Force = 200 N (Bottom split bars)
The thrust is the top bar (500 N). If air resistance takes up 300 N of that bar, the remaining portion represents the resultant acceleration force (200 N).
Note: there is potential confusion in choosing which bar represents which quantity.
Which Value is The Top Bar?
Students can find it tricky to identify which value should be in the top bar and which ones make up the bottom. Modelling the process with a think-aloud, an I do-we do-you do or a class discussion can help students understand how the situation is mapped onto the bar model.
| Key Takeaway: Additive bar models build a sense of quantity without algebra. Once dyscalculic students trust that bars represent conserved physical quantities, transitioning to multiplicative bars (F=ma) becomes simpler. |
Next Post
In Part 3, we build on this foundation by introducing Multiplicative Bar Models for F=ma, V=IR, and W=mg.
