Creating A Mathematical School-Wide Culture

How to Apply OUR Knowledge of Mathematics for

Teaching to Improve Student Learning

A consistent, school-wide & grade-by-grade approach to mathematics will lead to improved student learning.  The information presented here comes from Asking Effective Questions & Maximizing Student Mathematical Learning in the Early Years.  

“Deepening of Teacher Understanding + Shifts in Instructional Practice = Impact on Student Learning” 

2010–2011 Early Primary Collaborative Inquiry

A Starting Point ...

Immerse yourself in the curriculum and supporting documents. Attain a better understanding of the expectations and the seven mathematical processes by reading about the explanations and rationale in the front matter of the Full-Day Early Learning Kindergarten Program and Grades 1 to 8 Mathematics curriculum. Look before and beyond the grade you are teaching to see how concepts build upon each other. There is a wealth of resources that can offer extra insight into the mathematics itself and can help to identify and connect the key mathematical concepts. Some of these include the Guides to Effective Instruction in Mathematics and the works of Dr. Marian Small, Catherine Twomey Fosnot and John A. Van de Walle. Our professional learning journey will be most effective when we delve into mathematical ideas with colleagues and together inquire about how our understanding impacts our related teaching.

As a school, we need to develop a collective understanding around the following concepts:

1. IDENTIFY AND USE EVERYDAY MATHEMATICS KNOWLEDGE TO PLAN INSTRUCTION
2. ENCOURAGE AND FOSTER “MATH TALK.”
3. FACILITATE EXPERIENCES THAT ALLOW FOR MATHEMATIZATION OF EVERYDAY KNOWLEDGE
4. MODEL AND NURTURE POSITIVE ATTITUDES, SELF-EFFICACY AND ENGAGEMENT...

Some Practical Tips for Creating a Mathematics-Rich Environment

Researchers have identified five common core characteristics of early learning environments that support effective mathematical pedagogy and foster positive attitudes and beliefs about mathematics 

(Clements & Sarama, 2009, p. 259).

Asking Effective Questions

    Provoking student thinking & deepening conceptual understanding in the mathematics classroom

Researchers support a problem-solving approach in the mathematics classroom because it engages students in inquiry, prompting them to build on and improve their current knowledge as they “construct” explanations that help them solve the task at hand. “In a constructivist classroom,” Marian Small writes, “students are recognized as the ones who are actively creating their own knowledge” (2008, p. 3).

The classroom becomes a workshop ...

“ ... as learners investigate together. It becomes a mini- society – a community of learners engaged in mathematical activity, discourse and reflection. Learners must be given the opportunity to act as mathematicians by allowing, supporting and challenging their ‘mathematizing’ of particular situations. The community provides an environment in which individual mathematical ideas can be expressed and tested against others’ ideas. ... This enables learners to become clearer and more confident about what they know and understand.”

(Fosnot, 2005. p. 10)

James Hiebert (2003) suggests three situations in which teachers might consider conveying information to students:

1. Students need conventional written notations. For example, how to represent a fraction, how to show that a quantity is greater than another and terms related to solving problems that require them. For example, “You’re saying this triangle has no equal sides. You’re describing a scalene triangle.” Students don’t always have the language to respond to open questions such as, “How do you know?” Modelling this language is important in building students’ sense of self-efficacy.

2. During consolidation, teachers may present alternative methods that have not been suggested by students. Teachers may choose to do this if a particular strategy would help students better understand the big idea underlying the problem. The strategy should be presented as just another alternative, and not as the preferred strategy.

3. Again during consolidation, teachers may highlight the mathematical ideas embedded in the students’ solutions. These can be made explicit by posing questions that focus the students’ attention on these ideas. The teacher may annotate the solutions to make these ideas visible, and add them to the chart of summary and highlights constructed by the class. For example, the teacher may record right on a student solution that the authors have used the strategy of making friendly numbers in order to solve the problem. Another teacher might highlight the way the students have shown how multiplication and division are related.

Questioning is a powerful instructional strategy. Open questions that are related to the big ideas embedded in the curriculum expectations and learning goals will excite student curiosity, provoke critical thinking, elicit reflection and help students construct their own meaning for the mathematics they are studying. Their responses will help the teacher assess what students know and what next instructional steps might be. Developing skills in questioning for understanding and content knowledge evolves over time and like anything else, requires practice. The payoff is significant in terms of students’ conceptual understanding.