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In recent years, the debate surrounding homework has been recurring. As a faculty, the question is twofold: Should we assign homework? And, if we do, how do we ensure it is truly effective for learning?
At Innovamat, our primary focus has always been to develop a curriculum meant for the classroom. After all, that is where mathematical thinking is planted and cultivated.
However, through our collaboration with different schools and families, we have identified a demand that extends beyond the work we do in the classroom: the need for homework that not only provides additional practice but also creates a structured opportunity for families and allows them to better understand how children learn mathematics.
The structure of the new Extra Practice
The Extra Practice proposal consists of one resource per session, included in both Number Talks and Adventures.
This practice is available for all sessions from 3rd to 6th grade, the elementary grades that focus more directly on the institutionalization and automaticity of certain content and strategies, and where there is a greater demand for resources to generate a habit of practice outside of school.
The philosophy behind this new resource
It is essential to understand that this extra practice never intends to replace the vital classroom moments: the active construction of knowledge and the institutionalization of concepts. The classroom is the space where, through dialogue and guided exploration, mathematical meaning is discovered. Conversely, practice at home should not be the place for planting new ideas, but the constant watering that allows students to gain fluency and develop automaticity through greater exposure to practice situations.
But, how do we ensure that this “watering” is truly rich and effective?
The key lies in coherence. Just as teaching guides and classroom resources should promote learning through activities and tasks that invite students to observe, reason, connect, and reflect, practice at home should be designed with the same approach.
The goal is not to provide students with a sheet full of mechanical calculations or repetitive exercises. It is about providing a complementary opportunity to consolidate content, while activating and applying different mathematical processes.
Notice the difference between these two cases. Instead of asking students to solve a list of additive operations, we encourage them to complete number cascades where they have to reason where to start, the type of operation they need to perform (addition or subtraction), and the strategy they want to use to solve it.
Let’s also look at this other example. Instead of classifying given shapes, we present them with the search for triangles on a geoboard, inviting them to reflect on the relationship between the number of equal sides and the number of lines of symmetry. The objective is not only to practice geometric vocabulary and the representation of triangles that meet specific conditions, but also for students to notice a pattern that characterizes these polygons: if they have two equal sides and one different, they always have a single line of symmetry. On the other hand, if all their sides are unequal, they never have lines of symmetry.
Promoting autonomy
The extra practice proposal has been designed to be accessible and autonomous for students.
Therefore, each page includes support elements that guide them in their individual work:
- Introductory texts: They appeal directly to the student and specify what they can expect from this extra practice. Additionally, in some cases (such as in estimation practice sessions), they highlight the need to practice and better understand the content they will be working on.
- Clear instructions: They are short and understandable, and sometimes include worked examples that help the child better understand what they need to do.
- Direct help: Help or references are offered directly to the content worked on in class. For instance, in the initial practices of conversions between units of measurement, references are included that help solve the activities more easily.
- Guide for self-validation: Finally, self-validation questions are also included that guide the student to detect possible errors independently. For example:
How to use Additional Practice
The purpose of practice is for students to have more opportunities than those given in the classroom to consolidate their learning. However, it is crucial that this objective be perceived by students.
If practice is seen as a formality or a control tool, there is a risk that the student will resort to methods that harm their learning, such as copying or the automatic application of procedures.
To avoid this, consider these key points:
- Be selective: Having a practice proposal for each session does not mean it always has to be sent. Send the practice you consider necessary in each situation.
- Consider the context: take into account the number of hours the student already spends in school, the need for balance between different subjects, and the individual conditions of each student to be able to complete the task outside of school hours.
- Dedication is what counts: The interest dedicated to each practice is a more important factor for learning than the number of practices they complete.
- Conscious follow-up: Conscious follow-up makes the student show more interest. This way, they will be able to use this resource to improve their learning, seeing the value of the work done, and not just the possible grade or penalty for not doing it.
- Encourage discussion: Use some activities sent home for class discussions or conversations in class, but without setting aside the sessions that allow building knowledge and institutionalizing it. Collective reflection helps practice take on real significance within classroom dynamics.
A new window for interested families
To facilitate communication with families and ensure they have tools to better understand what is expected of children, we have designed two main resources to accompany the practice proposals:
Commented answer key
All practice proposals have an answer key accessible through a QR code. This not only offers the answer to the proposed tasks, but often includes explanations that clarify:
- The purpose of the tasks.
- The possible strategies and reasoning we expect to emerge.
Strategy explanation pages
We have designed explanatory pages that accompany some specific proposals and describe key strategies (such as known facts-derived facts, the jumping strategy, etc.) as well as important factors that, given their own school experience, may generate doubts (such as, for example, the order in which multiplication tables are built). This resource is particularly beneficial for families who:
- Are not familiar with the different strategies.
- Want to understand in greater depth how we work and why we do it.
Example of explanatory page for the jumping strategy.
If you want to know more…
If you want to know more about the role of homework and how we can maximize its effectiveness, we recommend reading the article What is the role of homework? How to design it to be effective in consolidating knowledge by Cecilia Calvo, PhD in Mathematics Education.
