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What is the first thing that comes to mind when you prepare for your next session? Planning a good math class requires much more mental effort than many people realize, especially when math is just one of the many subjects we manage daily.
However, this anticipation phase (Smith and Stein, 2016), often invisible from the outside, is crucial. Preparation serves as the foundation and has a direct impact on the quality of the learning opportunities created later in the classroom. So before we explore what happens in class, let’s take a moment to understand how to prepare effectively to maximize our teaching.
Contents
Our roadmap: the teacher guide
When planning an activity for class, it’s important to anticipate outcomes, clarify objectives, and consider potential solutions, strategies, and interactions that may arise. Various proposals grounded in scientific evidence and developed by expert educators can assist us through teacher guides.
However, caution is necessary! Just as with any written material, reading and understanding are not the same and require different levels of engagement. We will have to read them consciously. It is not the same to know what the activity is about as to understand the learning objective, the mathematical concept involved, anticipating difficulties, managing time effectively, fostering potential mathematical conversations, and connecting with students’ prior knowledge. This understanding significantly influences the session’s quality and enhances students’ chances to benefit from the learning opportunities offered.
That’s why session preparation is key: it requires going beyond the teacher guide and drawing upon a foundation of mathematical, didactic, and pedagogical knowledge (including classroom management). Achieving this requires dedicated spaces and resources for teacher training that can transform “what is stated” in the guide into effective teaching practices.
How to meaningfully prepare a session
To illustrate this, let’s imagine we have a session tomorrow with the learning objective of exploring length using non-standard units of measure.
Activity summary
In this session, students measure objects in their environment with their bodies and note the differences in the units used.
- As a whole class, they will measure the length of the board using their bodies.
- In small groups, they will measure the length of tables with different parts of their bodies.
- Individually, they will measure the length of different objects in their logbook.
Here are some points to help transition from a simple reading of the guide to a deeper understanding:
1. Contextualize:
Where are we coming from? Before diving into today’s activity, let’s look back: Have they previously worked on measurement concepts? Have they compared objects directly? Understanding their prior knowledge allows for a connection to the new challenge, providing both security and meaning. A rich learning experience often arises when new knowledge connects to what students already know.
2. Define the teacher’s “glasses”:
While the learning objectives are clearly outlined, it is essential to understand them thoroughly. This means staying two steps ahead of what students need to learn and mastering the teaching strategies that will aid their comprehension.
During this measurement session, what am I really looking for? As a teacher, I must be clear that before measuring with standard units and instruments, students approach the idea of measuring from direct and indirect comparison and, later, from the use of non-standard units, such as hand spans or feet. In this phase, the need arises to agree on the use of units and instruments. If I lose sight of this learning trajectory, my preparation may devolve into a series of isolated decisions.
And let’s not forget about mathematical processes. If, as a teacher, I don’t understand what it means to solve problems or reason, I probably won’t promote it in the classroom and won’t formulate questions to make these processes emerge (why?, how did you think about it?, what do you think will happen if…?, why does this happen?…).
3. Anticipation:
This is a crucial point: anticipating what might happen in the classroom. By understanding the activities outlined in the student logbook, we can prepare relevant questions and foresee potential situations. This proactive approach keeps the future in focus.
To put it into practice, I propose some actions:
Solve the activities beforehand: for example, if when I try to measure the pen in the logbook with clothespins I realize that the clothespin can be placed in different ways, this will determine the unit of measure and can generate a rich conversation in the classroom.
Plan how you will use the space to carry out the activity: does the guide suggest taking students to the board? Sitting on the floor to work in a circle?…
- Be very clear about the essential moments of the session, including the key questions you are going to ask or when you will pay special attention to student interventions (it’s impossible to be alert during the entire session!).
- Visualize how the class will be distributed and what the guide tells us about it: How do we distribute time? Do we start as a whole class and then move to small groups? At what exact moment do we distribute the material so that it is not a distraction element? Clearly outlining how we are going to guide this exploration is vital for maximizing learning opportunities.
Once we have a clear mental outline, defined objectives, and anticipated possible challenges, we are ready to enter the classroom!
We enter the classrooms
And the big question appears: does what we imagine before starting resemble what actually ends up happening? Well, let’s look at this session that I carried out:
The session begins with a challenge: how many children do we need to measure the length of the board? What we are looking for here is not only for them to conjecture, but for them to justify the why: how they thought about it. Then, we will check their ideas.
But what happens when the situation changes? For example, if instead of standing together, the children sit apart. Before checking it, I ask them: “What do you think will happen now?” And here conjectures appear again. The children think and justify their answers before checking them. While they discuss, I offer precise mathematical vocabulary and help them associate each idea with a word. This step is important, because it’s difficult to use the correct term if no one gives you the words to do it.
After this first dialogue with the whole class, I propose activities to continue experimenting, but this time in small groups. An important point: I limit the experimentation time to 5 minutes. This way, I encourage children to look for the most efficient strategies to solve the situation.
And after a good while of conversation, conjecturing, arguing, checking conjectures and connecting ideas, the time comes for individual work in the logbooks. I choose to provide them with the logbook only at this moment to control the materials students use during each phase. Once they have recorded their individual findings, the session concludes.
And once the session ends, what?
In teaching practice, the habit of reflecting is key: asking why students exhibit specific errors or difficulties, asking if these are related to the didactic models we use, knowing other models that help avoid those errors or difficulties… We know that time doesn’t help develop this habit and that doing it individually isn’t simple either, but that doesn’t mean we should stop doing it.
That’s why, to close the article, I want to show you my reflection with two graphs that summarize what happened in the classroom. I don’t expect you to have to make them every time you finish sessions. Not at all. But now they help me reflect the questions and reflections we should ask ourselves when finishing a class.
In this first graph, we can make a clear comparison between the duration of each activity that the teacher guide proposed, the one we planned, and the one that actually happened. As we can see, the conversation time after measuring the board extended longer than expected, because the challenge ended up generating a very rich dialogue and I decided not to cut it short. That made me have to reduce the time to 5 minutes at the end to contrast strategies for how they had measured the table.
I would have liked to make a final closure of the complete session, the one where we share final strategies and institutionalize which ones have been the most effective. Even so, the learning objectives have been met, and I know it’s content they will revisit in the future.
This second graph reinforces several ideas. On one hand, at the level of content, although the focus was measurement, many connections between number and operations concepts appeared naturally.
As for the processes, opportunities arose to work on three of them (Reasoning and proof, Problem Solving, Links). On the other hand, if we look at the type of interactions, we observe the play of groupings, which allowed me to create different levels of mathematical communication (individual reflection, dialogue between peers and whole class discussions guided by the teacher).
And that leaves us with a simple but important conclusion: planning and anticipating is key, but even more so is knowing how to adapt. Understanding your group, recognizing what needs to be addressed, preparing the pathway, and setting clear learning objectives provide the confidence to be flexible with time without losing focus.
Questions to reflect on your session
To conclude, I end with a few questions you can ask yourself to look at your session with greater intention and to prepare for future ones:
- How much have the students talked? How much have I talked as a teacher?
- What type of contributions have the students made? Were they mostly asking what they needed to do, or were they sharing their reasoning and strategies?
- How did I intervene as a teacher? Did I spend a large portion of the time explaining concepts, or did I focus more on asking questions?
- Did the group achieve the learning objectives? What percentage of students did not achieve them? Was it 20%? 50%?
- What is the impact of not “having understood it”? Was it the first session in which they worked on the content? Or had they already worked on it in several sessions and students continue to show difficulties? How far have I moved away from or approached the session preparation? Have I made decisions with criteria?
If you want to explore this further, I recommend watching the webinar where we analyze a complete session and identify areas for improvement.
