THE second term of the 2024-2025 academic year has commenced. The progress and the interest shown in improving critical thinking and problem-solving skills in mathematics students at the secondary level, so as to have a greater number of our children passing this subject, must continue with the same or more verve as the previous term.

We implemented simple but proven strategies in term one, and it is imperative that we build on these strategies to further the gains that were made in the teaching, learning, and modelling of mathematics at the secondary level.

To conclude the first term of the academic year, most students were given formative assessments in mathematics. Analysis of these results will inform us as to how effective the strategies deployed in term one really were. Our maxim “no child left behind” is a solemn commitment to our children, especially important in schools that consistently experience a pass rate of under 50 per cent in the subject, that has to be supported by data driven actions. Understanding the gaps evidenced by the results of the formative assessments given at the end of the first term will guide students, teachers, and principals as to how to proceed over the next few weeks.

Bubble children

There is a unique group of students that we refer to as “bubble children”. We use the examination results to determine the students in this bubble. If for example, the mathematics pass mark at a particular school is 50 per cent, so-called bubble children will be the ones who scored 10 -15 per cent below the pass mark. These “bubble children” are so named because with intentional intervention, they can “burst” forth (like bubbles) and join the students that are already at and above the passing grade (please note that individual schools and/or teachers can determine the actual threshold that is used to define this specific group of students). Bubble children are the ones who we know can achieve at least a grade three in Caribbean Secondary Education Certificate (CSEC) mathematics if specific strategies, which will be outlined here, are followed.

Step 1: Determine from your class lists the students who fall into the category of bubble children. This must be done precisely, and for the students who were absent from assessments or who were low-end outliers, simply use previous course work to determine where exactly they fall.

Step 2: Apply “a-name-to-the-face-to-the-grade” to each bubble child identified in Step 1. This “a-name-to-the-face-to-the-grade” is a specific strategy I have evolved for dealing with bubble children. Way too often, we overlook the rich information available to us from the data, by simply reporting on broad performance metrics, akin to general statements like “30 per cent of the class passed” which do nothing to define and inform actionable steps. Leverage the data to provide insights as to the opportunities to level up performance! Who are the children that could have passed but missed the grade because of a misunderstanding of a single topic, or a gap in their understanding of fundamental concepts?

Address our bubble children by their names. Especially for teachers with multiple classes, unless a child is doing well or extremely poorly, their face does not readily come to the teachers’ minds. Bubble children tend to be in an amorphous group in the minds of many teachers, one anonymous face blending into another anonymous face. These bubble children represent the best avenue to lift the performance of the entire cohort in the shortest possible time. Learn the faces of these children, how they look – their unique features – so that the intervention process can be specific and meaningful. Once their names are known and they become easily identifiable by the mathematics teacher, then quantify the gap between their actual grade and the pass mark. The results of the formative tests will also indicate the specific knowledge and skills gaps that exist for each bubble child. Armed with this information, the teacher is now able to address and close these gaps with precision.

Step 3: We now really know each bubble child by face and by name, and what is needed to improve their performance. This is a very purposeful way of creating deep academic relationships with the students we teach. Once the bubble children and their needs are known, the actual mathematics targeted interventions should commence immediately. Be sure to create records that serve as a checklist of students’ errors that need to be addressed. Ensure that the fundamental concepts that undergirds these misunderstood mathematical principles are documented for review with the students. For example, if a student could not correctly factorise a quadratic expression, the teacher should determine if the student has a multiplication problem, or a directed number problem. When this task is completed, then all the errors could be grouped into broader categories and intervention by the teacher done according to the errors that were presented. This task does not have to be tedious as students can be grouped and various interventions deployed. Remember that intervention does not mean reteaching the entire topic, as research shows that broad reteaching (after proper teaching was done) yields the lowest level of improvement. Note, however, when all the students in the class are analysed, if the entire class found the topic problematic, reteaching in parts, even by a different mathematics teacher at the institution, is a very viable course of action.

The interventions could be as direct as asking students to explain their thoughts on the topic or question, with any misconceptions coming out of their responses clarified, and/or the use of technology to reinforce specific points, especially more abstract areas, the use of peer teaching, and the use of modelling where the topic allows.

A practical approach to deploying targeted interventions

Teachers may understandably balk at the thought of implementing these recommendations. The reality is that they have other students who need to continue their own mathematical journey. The answer, whilst simple, requires proper planning, good class control, and flawless execution by the teacher. One way of achieving multiple objectives is by creating groups within the class. These are best created with a mixture of both bubble and non-bubble children based on the gaps identified. This will facilitate mathematical discussions that are student-centred, pointed, and maybe more readily and easily understood by the students. Here, the teacher will act as the facilitator and must resist the urge to do chalk-and-talk for these sessions. These different groups should be working on different problematic topics. The teacher can create flash cards of questions that are designed to target the errors. When each group successfully completes their initial set of cards, they are given a different set from another group or from the facilitator. If this is done once a week, this configuration and approach can correct misconceptions and redound to the benefit of all students, especially the bubble children.

The call to action

There are many researched, targeted approaches that when utilised, will see our bubble children moving into a path of success. This article outlined only a few options available to teachers. It is hoped that the ideas shared will serve as starting points for the teachers of mathematics, sparking ideas that they can build upon, and/or modify, customising interventions appropriate for their particular context. It is imperative that within the next four to six weeks, errors and misconceptions in their students’ mathematics knowledge and competence are clarified, as intentional noticing of students and their mathematical work continue. Interventions in these specific areas will significantly help to improve students’ foundational understanding, and in turn, these bubble children who would likely have received a grade four in CSEC mathematics, could improve to at least a grade three.

Judicia Nembhard is a math educator.