This article shares how the approaches to learning can be integrated into mathematics through a shift in focus from pure concept teaching to the process of learning and integrating skill development. Regardless of level of proficiency in mathematics, every student enjoys and learns from the activity.
“I am a math teacher”. When I introduce myself this way, I always feel the words do not do justice to my role as an IB Primary Years Programme (PYP) mathematics specialist. I have three years of PYP teaching experience and I still feel as much of a student as I am a teacher–I am constantly learning how to teach–from my mentors, from my colleagues, from my experiences, and most of all–from my students themselves.
What makes teaching mathematics concepts different in a PYP environment? The PYP stresses that the development of skills and demonstration of a positive attitude towards learning is as important as the acquisition of knowledge. Concepts can be taught but attitude can only be role-modeled and experienced. I am aware that my students learn from me not only in my classes, but also by observing me–in class and outside; through my body language, my willingness to always be an open-minded learner, my sense of humour, the tone in which I speak to the “bhaiya” serving the snacks, and through my interactions with my colleagues.
To assimilate the PYP elements into my mathematics classes meant that I first had to make an adjustment in my thinking. I had to make a shift from a focus on conceptual content only to a focus on integrating development of skills and attitudes in my students. The core philosophy of the PYP is transdisciplinary learning integrated with the programme of inquiry. However, where it is not possible to integrate mathematics’ concepts within the programme of inquiry, the focus then is on inquiry-based learning and building the approaches to learning (ATL) skills. Students are encouraged to construct their own meaning rather than being “taught” in the conventional sense; they construct meaning when they build on their prior knowledge and make real life connections. A simple example can be the concept of calculating elapsed time. Students make real life connections by calculating the time taken for different activities during their daily routine in school such as their classes, time taken for lunch or time taken to travel to school. The learning is thus deeply rooted and enduring.
The most important message I wanted my students to imbibe is that “how we learn” is as important as “what we learn”. This would be a first step towards building of metacognition skills. If students can reflect on how they learn best, what works well for them, what difficulties they face, what skills they use; they are on their way to becoming independent learners. Translating this theory to awareness in the classroom is not easy; however, the first steps on this journey must be to enhance the student learning process.
A recent mathematics activity (a division relay) highlights how skills and attitudes can be developed through simple activities. This activity demonstrates how ATL skills can also be developed while teaching mathematics outside of the programme of inquiry.
Students were grouped randomly, based on single digit division quotients (eg 6 ÷2, 9 ÷ 3, 12 ÷ 4 grouped together). Division sums with 4 to 5-digit dividends and 1 or 2 digit divisors were written out on a sheet for them to solve. Instructions were given for each team member to do only one step of the division sum and then pass the baton to the next student. As in a relay, team members were not allowed to help one another. The next person would have to correct any error and then move on. The last step was rechecking their own answer using the (divisor x quotient + remainder) rule.
Many students were capable of doing the entire sum themselves, so it was difficult for them not to jump in to help their team, but they displayed respect and tolerance towards their group members. Students used their thinking skills (application of their knowledge of division) while participating in the activity with enthusiasm and confidence. Upon completion, students discussed what skills they applied during the activity. They observed the ATL chart which is displayed prominently in the classroom and listed the skills they felt they applied during the activity.
Students themselves were quick to point out that though this was a mathematics activity, social skills were more at play:
- They had to respect each other and cooperate while awaiting their turn at the division game.
- There were group decisions to be made. Students decided who would begin and who would complete the relay. They drew upon their experience from the recently concluded swimming relay held at school to decide what was more important for their group–to start strong versus a strong finish.
- Students had to accept responsibility–if their part of the division had an error, the entire team performance would fall behind.
Communication skills were involved while solving the sum; however, their body language played an equally important role. Was their body language encouraging their friends or disheartening them?
Students deployed self-management skills of time management and organization of work. I have been encouraging students to assign roles and divide responsibilities during group work: presenting the work, researching, keeping track of time, struggling and working out compromises in group work. Students reflected that the activity helped build collaborative skills as much as it enhanced their division skills.
It was important to help students understand that attitude is a more important factor in determining success than intelligence. As a teacher, it is my responsibility to shape student attitudes.
The highlight for me was that not only did all the students enjoy the engagement but each one learned something different: about division, skills needed to work in a group, collaboration and empathy. The student responses further reinforces my commitment to the PYP ethos. As a teacher, I also learn through the same cycle as students: conduct a learning engagement and then reflect how I can modify my methods and engagements and progress as a PYP teacher.
As Albert Einstein said “Education is what remains after one has forgotten what one has learned in school”–along with subject knowledge, teachers must aspire to build attitude and skills that will endure for a lifetime.
Sonia Trakroo is teaching mathematics at DPS International, Gurgaon, which is an IB continuum school in India. She has 3 years experience as a form tutor and mathematics specialist. Sonia enjoys planning strategies to empower students with learning skills. She is passionate about student engagement in the learning process and wants to develop a love for the subject in every student within the framework of the PYP. You can follow her on twitter @soniatrakroo.