Cultivating Early Learners through Mathematics
"Mathematics." "Mathematical." "Mathematizing." "Mathematical literacy." "Numeracy." "Numerical." "Quantitative thinking." These are a few of the many terms and phrases employed in ministerial reports, monographs, memoranda, and curricular documents. It speaks to the importance of how number operates in our everyday world and of the pressures educators face in their roles accordingly.
Children also enter into the Early Learning environment with a broad range of experiences working with and being in relation to number (Capacity Building Series, 2011). Ventures in measurement through travel or transportation, playing with number in found, acquired, and repurposed objects at home, organizing, developing, and reinterpreting principles or rules of various games, and testing out theories through predictions, experiments, and other probabilistic methods showcase some of the diversity with which mathematical thinking becomes an intuitive practice in children's daily lives.
How might educators extend and enrich children's everyday mathematical practice at school while at the same time make sense of and honour the regulatory demands of mathematics curricula evident today in the teaching profession?
Some guidance on this question can be sought through a close reading of key texts, and such effort has eventually crystalized into some pedagogical tips for carrying forward an effective mathematical program embedded within an interdisciplinary, holistic, and emergent teaching and learning environment.
Observe and document student's expressions of mathematical behaviours: At loose parts centres, during risky and rough play, and throughout the play-based learning environment, educators are wise to assume an interpretive orientation with respect to observing and listening. This means considering what is seen and heard in ways that are open to more than one viewpoint or perspective. Questions are elicited in this mindset instead of judgements or evaluations, so it involves collecting data from various stakeholders, proceeding to do so over a timespan, and done in different assessment contexts. Recording of data along with anecdotal comments, checklists, or other means of capturing initial thoughts on the topic can be a resourceful tool to commence planning and assessment guidelines for future mathematics practices, tasks, and play activities.
Co-build a Math Talk Community: In the act of observing students working on problems, educators are positioned to detect how to effecively intervene in that situation. Should students be perceived as "stalled," that is, when cognition fixates or centres around an unresolved issue but no further developments take place, educators can share a series of probes or prompting questions that helps to redirect energies into more productive or fruitful endeavours. "I see that your working really hard to figure out this [problem] ... What are some other ways you might be able to work this out? I see that you have used [ manipulative or tool] in this way. What other ways could you use this tool to work this out?" If the student is proceeding to work out a problem, or is developing the ability to problem-solve, the educator can encourage further development by exercising patience and waiting to intervene when appropriate. This silent gesture communicates trust in the student and confidence in her/his abilities to figure out a solution. Making visible student thinking and making latent students efforts at rich mathematical tasks can be brought into comprehension through these informal math talks (Surrtamm, Quigley, & Lazarus, 2015), and in the process positions students to become sources of their own mathematical ideas, strategies, and theories.
Extend and enrich mathematical endeavours: As students participate in inquiries, provocations, and play-based activities, time to explore and further wrestle with problems is inextricably embedded within these spaces. Educators can facilitate further relationships with materials, situations, and problems inherent in such contexts through extensions to emergent accomplishments. For example, "Wow! I see you have made a blanket with eight buttons, where the pattern is one red button for every two yellow buttons. I wonder if you continued with this pattern how many yellow buttons you'd have after 20 button in total?" If the student is not able to comprehend the newfound challenge, reword it or paraphrase it in a way that is accessible but do not reduce the complexity of the challenge. "Let's see if you can add more buttons in the pattern you used - I see one red button, then two yellow buttons - until you reach 20 in total. How many yellow buttons would you have when you have 20 buttons in all?" Students who are on the precipice of deeper and more complex mathematical behaviours should be challenged further but in ways that lead to new inquiries, new pursuits, and with deeper passions for learning.
Celebrate accomplishments through passion, confidence, and curiosity for learning: Educators who exude confidence in their craft model a very powerful message about learning - that education is a life-long process, can be very fun and rewarding, and that no one stands above others in the quest for new knowledge. Gaining insight through inquiry, playing with peers, responding effectively to challenges, and asking open, adventurous, and collaborative questions are all ways to undertake learning, regardless of age, socioeconomic background, ethnicity, ability, gender, or any other social construct. When children observe and reflect on these teacher behaviours, they are positioned to acquire greater resiliency and success in their own mathematical undertakings.