In Early Years, we view assessment as a cyclical process in which we focus on data collection, its analysis and subsequent reflection, in order to improve educational practice and learning opportunities for all students (Landa et al., 2021).
And how can we collect data? Observation of what happens in the classroom is probably one of the most common tools, but we cannot forget about conversation and documentation, including students’ visual or graphic representations. In this way, we do not need to create specific moments to carry out this evaluation process, the well-rounded activities that we suggest for the day-to-day at Innovamat, and real life moments, are a perfect framework for this data collection.
Let’s look at some real examples, we will analyze representations on the Workshop worksheets, and also observations of students’ actions and conversations during the Spaces.
Evaluating content and processes on a day-to-day basis: examples of well-rounded tasks
In this case, we will analyze evidence on paper (blank pages), from the Kindergarten’s Workshop 6. The students have discovered, in an experience-based way, different ways of breaking down 6 into two addends; and, in the last part of the workshop, after a discussion with the whole class, they are asked to represent what they have done during the workshop. In the comments on each worksheet we can see how to assess, at the same time, the decomposition of 6 content and the processes of Communication and Representation and Problem-Solving.
In this case, the student has represented some of the pairs of numbers that add up to 6 (2 and 4, 3 and 3, 1 and 5), but we also see a wrong solution (1 and 4). We also detect that the notation of 5 is rotated, and, although we could help them find a model of the number to revise it, at this point we must focus on the decomposition of 6 and the mathematical argumentation that has led to this solution.
This student has combined the drawing with the digit, since they have drawn a hand (the quantity 5) and a 1: they have represented that 5 + 1 is a possible decomposition of 6. We can see, then, that as far as communication and representation are concerned, they are transitioning between the pictorial and the abstract. As for Problem Solving, we note that they have found only one solution.
In contrast to the previous case, this student has represented all numbers abstractly. Specifically, they have used the numbers 6, 4, and 2 to represent a pair that adds up to 6. Although they have not yet used signs or constructed the complete mathematical sentence, as in the previous case, they have found a solution.
In this case, we can see a change with respect to the previous example in the process of communication and representation. The student has found a correct solution and, in addition, has added the + and = signs to construct a complete mathematical sentence.
This student has shown different decompositions of 6 in two addends and has tried to be thorough. In this case, not being systematic (i.e., they have not ordered the solutions) has caused them to skip a solution (1 + 5 = 6).
This last part of the workshop, the blank page, gives students the opportunity to reflect on what has been done in the classroom and to express what they have learned. Their representations give us valuable information to understand the individual learning process of each student, and also to have a global vision of the group so we can adapt our educational practice.
Let us now take a look at observations in moments of play. In the teaching guides for the Spaces, we provide a table with suggestions in the ‘what can I observe?’ section while students are on a particular challenge. Anticipating what can happen in these moments and what mathematical content and processes can emerge helps us to make a better observation and documentation.
For example, in ‘Table of mathematical material’, in which the symbol-amount relationship is explored, we can see Numbers and Operations content, and mathematical processes related to Problem-Solving and Communication and Representation.
Let’s look at examples where students use this content and processes during their game.
Students build towers taking the relationship between the symbol and the amount into account. We can extend the information by asking questions such as “how many cubes did you use?”, “how did you know to use them?”. In this case, the student answers, “I looked at what’s here [indicating each card] and made towers 1 at a time.”
They order the cards and towers in ascending and/or descending order. In this case, not only have they built towers for each symbol, but they have ordered them. It is interesting to observe, or ask if they count each one of the cubes in the towers or if, on the contrary, they take advantage of the fact that in a tower there are 5 cubes, for example, so to build a tower of 6, one more is needed. This would be a good indicator of the Problem-Solving process, since they would have used an efficient strategy.
As we read in How to assess in math class?, we must distinguish between formative assessment and graded assessment. In Early Years, it makes little sense to set a grade that students will find difficult to interpret. We must focus on a formative assessment that allows us to analyze the individual learning of each student and adjust the teaching processes to their needs (Sanmartí, 2020), to support them and help them progress in their knowledge and competency.