The NeusLab Approach: Learning How to Learn

Robotics Makes Abstract Ideas Accessible for Exploration

Educational robotics is a practical tool for us. It allows us to connect a number, formula or algorithm to an object that can be built, measured and programmed.

A fraction becomes half a turn of a wheel. A gear ratio explains why a mechanism moves more slowly but can deliver greater torque. A condition in a program determines whether a robot stops in front of an obstacle. Changing one parameter produces an observable result that can be compared with the original hypothesis.

We gradually move from working with an object to a drawing or diagram, then to a formula and the independent application of the principle to a new problem. For example, after working with a gear train, a pupil returns to ratios and fractions, now expressed numerically. This is how we check what connection they have made between practical work and mathematics.

How Mathematics Becomes Motion

Take a simple task: a robot needs to travel a given distance. To calculate its motion, the pupil works out how the rotations of the motor and wheel are related, measures the wheel's diameter and finds its circumference:

If we define the gear ratio as $i=n_{\text{двигателя}}/n_{\text{колеса}}$, the calculated distance is:

Here, $n$ is the number of rotations, $D$ is the wheel's diameter and $s$ is the distance. Diameter and distance are expressed in the same units.

For example, with a wheel diameter of 6 cm and gearing in which three motor rotations produce one wheel rotation, the robot is calculated to travel approximately 62.8 cm over ten motor rotations.

The pupil then runs the robot and measures the actual distance travelled. The calculation assumes rolling without slipping; in a real mechanism, grip on the surface, measurement accuracy and the operation of the drive affect the result. Any discrepancy is an opportunity to check the model and the experimental conditions.

One task brings together geometry, proportions, fractions, units of measurement, programming and error analysis. With practice, this calculation becomes a familiar tool: the pupil can explain where the numbers came from and what needs to change when a different wheel is fitted. The relationship between rotations, circumference and distance is also used in LEGO Education learning activities.

The Ideas We Explore Through Robotics

The content depends on the pupil's prior knowledge and skills. We begin with measurements and simple relationships, then move on to more complex models of motion and control.

In the turning formula, $s_R$ and $s_L$ are the displacements of the right and left wheels, taking direction into account, and $b$ is the distance between their rolling lines. The angle $\theta$ is obtained in radians; to convert it to degrees, multiply it by $180/\pi$. The model assumes no slipping. In the torque formula, $\ell$ denotes the perpendicular moment arm of the force. $I$ is the moment of inertia and $\alpha$ is angular acceleration.

The technical basis of these examples is described in LEGO Education's materials on gears, WPILib's documentation on kinematics, and the OpenStax sections on torque and rotational dynamics.

At an advanced stage, control can be expressed using successive sensor measurements:

Here, $A_k=A_{k-1}+e_k\Delta t$, $u_k$ is the control output, and $K_p$, $K_i$, $K_d$ are adjustable coefficients. This formulation uses a constant interval $\Delta t>0$. Implementation also takes into account motor limits, sensor noise and a limit on the accumulated error. The meaning of the components is explained in WPILib's PID documentation.

We introduce pupils to these models through an understandable task: for example, stopping at a given point or maintaining a heading. Complexity is introduced when they are ready. A practical project may lead to a topic before it appears in the school curriculum, while the depth of study is determined by the pupil's ability to explain and apply the principle.

An Individual Approach Begins with How a Pupil Solves a Problem

Our groups have no more than six pupils. This format allows the teacher to observe each pupil's work, notice difficulties and adjust the task's complexity, the pace or the amount of support.

Strengths and gaps in knowledge can combine in different ways. A child may propose an interesting design and a logical algorithm but struggle with fractions. We then work out exactly which step is causing difficulty: the meaning of a fraction, the relationship between quantities, units of measurement or the order of calculations.

The pupil may have memorised a rule but not yet be able to explain why it works. We revisit that point through an object they know: half a rotation, a ratio of sizes or a change in the speed of a gear train. We then offer a different task to check whether they can apply the principle they have discovered independently.

We use strengths as a starting point for explanation and gradually add other ways of working: reasoning, diagrams, calculation and experiment. Individual pieces of knowledge begin to form a connected system.

The First Lessons: Getting to Know the Pupil and Choosing a Starting Point

Over years of practice, we have developed a sequence of observations and tasks that helps us choose a group and learning programme.

The first lesson is about getting to know the pupil: what interests them, what they have already worked with, how they understand a problem statement and where they begin their solution. Short tasks involving numbers, patterns, structures and algorithms help reveal their current ways of working.

We pay attention to whether the pupil can explain their thinking, suggest a way to check it, use a hint and continue after an unsuccessful attempt. These observations are refined in subsequent lessons: a new environment, unfamiliar equipment or unclear wording can affect the initial result.

When choosing a group, we consider age, prior knowledge and skills, working pace and independence. Within a shared topic, pupils may have different tasks and forms of support: one needs a diagram, another an additional calculation stage, and a third a more challenging constraint.

The Learning Programme as a Decision Tree

The programme has shared goals and a sequence of skills. We choose the next step based on how the pupil handles the current task and what help they need. Below are examples of how these pathways can be developed.

The pupil confidently follows an example but struggles to start independently. We gradually reduce the amount of ready-made instruction: we ask them to complete part of an algorithm, choose between two approaches and then make their own plan. A sign of progress is that the pupil proposes a first step and explains how they will check its result.

The pupil has little experience of independent experiments so far. We begin with a small investigation: change one parameter, predict what will happen and compare the result with the prediction. If the child is afraid of making a mistake, we discuss acceptable and safe changes in advance. Gradually, they begin to choose for themselves what is worth testing.

The pupil comes up with solutions but struggles with calculations. We connect the mathematical step to their own design. We work through the specific gap and return to the project. Then we change the numbers or conditions: recalculating independently shows that the explanation has become usable knowledge.

The pupil experiments actively but changes everything at once. We add an experimental plan and a short record: what we change, what we keep constant and what we measure. The pupil learns to distinguish a chance successful run from a result that can be repeated and explained.

The pupil knows the formulas but struggles to apply them to a mechanism. We start with a drawing, label the quantities and estimate the expected result. The pupil connects the symbols to parts of the design, chooses a model and checks the units. The next step is to independently choose the appropriate calculation for a similar mechanism.

The pupil independently explains solutions and transfers knowledge. We offer problems with several possible approaches and competing requirements: increase speed while maintaining accuracy; lift a load with a limited set of parts; compare two algorithms using test results. At an appropriate level, we add problems with contradictory conditions, where the pupil needs to justify why a solution is impossible under the given constraints.

One pupil may need several kinds of support at the same time. We adjust the pathway as they progress and check the results through new tasks.

Experiments That Help Build Understanding

In our lessons, we help pupils develop the habit of following a sequence: formulate a question, propose an explanation, choose a test, gather data and draw a conclusion.

For example, a robot stops beyond the intended point. The pupil checks the calculation, the actual rotation of the wheels, the initial speed and the braking conditions. Each subsequent attempt should answer a specific question. If speed, the program and the design are all changed at once, it will be difficult to understand what caused the result.

The teacher helps organise the investigation: bringing attention back to the problem statement, asking clarifying questions and, when needed, demonstrating a particular technique. As the pupil gains a grasp of the task, the amount of help decreases and they make more and more decisions themselves.

How We Recognise Learning Outcomes

A working model makes it possible to check the result. We also ask the pupil to explain why it works, what they changed after testing and how they will proceed under new conditions.

Progress is visible when the pupil becomes more confident in identifying what is known and unknown, planning a test, finding the cause of an error and using a learned principle in another task. This helps us assess independence separately from the speed of assembly or the number of exercises solved.

We continually revisit our tasks, learn to use new tools and try teaching techniques. Changes are grounded in what happens during a lesson: where understanding breaks down, which hint helps a pupil continue and which explanation enables them to act independently.

At NeusLab, we create a learning environment in which children gain experience of their own investigations: from a first question and an uncertain attempt to a solution they can explain and test.

Programme Selection Diagram

The diagram shows examples of teaching decisions. Pathways can be combined and are revised based on the pupil's work.