“Broad Strokes” Analysis of SIM1 Math Stickies – Informed by Anthony & Walshaw Best Evidence Synthesis
1. A Non-Threatening Classroom Atmosphere
Anthony & Walshaw describe a non-threatening classroom atmosphere as one in which there is an
acknowledgement that all students, irrespective of age, have the capacity to become powerful mathematics
learners. They write about the development of a trusting climate yet also a culture of academic press in which
“teachers who truly care about their students have high yet realistic expectations about enhancing students’
capacity to think, reason, communicate and reflect upon their own and others’ understanding.” Supported by school
leadership and fostered by strong home/school/community partnerships and communities of practice, teachers
work at developing interrelationships that create spaces for learners to develop their mathematical identities and
cultural identities.
Representative SIM1 Math Stickies quotes:
 “A positive encouraging safe attitude and space to allow for risk taking
 “Safe environment to explore”
 “Teacher has a growth mindset that is communicated to students”
 “Respect and trust”
 “Co-learning approach is a norm in classroom”
 “Responsive classroom where educator is co-learning with students, using inquiry methods exploring
concepts of a mathematical premise”
 “Differentiated instruction within respectful interactions”
 “Mistakes valued”
 “Accommodations for identified students”
 “Student engagement”
2. Instructional Tasks
Anthony & Walshaw describe Instructional Tasks as focused on the solution of genuine mathematical problems.
The most productive tasks and activities are those that allow students to access important mathematical
concepts and relationships, to investigate mathematical structure and to use techniques and notations
appropriately. Tasks need to provide the appropriate challenge, provide opportunities for cognitive engagement
and have press for understanding. In order to make mathematics more meaningful and accessible for all
learners, mathematics curricula frequently advocate the use of contexts – a real or imaginary setting for a
mathematical problem, which illustrates the way the mathematics is used.
Representative SIM1 Math Stickies Quotes:
 “Critical Thinking Challenges with Rich Tasks”
 “Problem-Solving Activities:
 “Inquiry-Based”
 “Real-life applications”
 “Students begin with a realistic, relevant problem to solve and apply”
 “Focus on learning goals and expectations”
 “Provocative questioning”
 “Student collaboration in small groups – Bouncing ideas around”
 “Think time and curriculum content”
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3. Tools and Representations
Anthony & Walshaw describe Tools as thinking spaces that help to organize mathematical thinking. Symbolic
artefacts or inscriptions/representations characteristic of mathematics include the number system, algebraic
symbolism, graphs, diagrams, models, equations, notations for fractions, functions, calculus, pictorial imageries,
analogies, metaphors, models (such as pizzas, chocolate bars and ten frames), examples, stories, illustrations,
textbooks, rulers, clocks, calendars, technology such as computers, calculators, digital, and problem contexts.
Anthony & Walshaw look at how teachers use tools to support students’ learning, and how students use tools to
reorganize their activity.
Representative SIM1 Math Stickies Quotes:
 “Manipulatives”
 “Co-constructed anchor charts”
 “Technology used to enhance learning and engage students”
 “Use of models”
 “Multi-resources, e.g. manipulatives, technology, e-learning”
 “Multiple representations of student thinking”
 “Multiple tools for problem solving”
4. Classroom Discourse
Effective teachers engage in classroom discourse by valuing students’ ideas, exploring students’ answers,
incorporating students’ background knowledge, and encouraging student explicit communication about
mathematical learnings. Anthony & Walshaw describe Classroom Discourse as more than developing a
respectful, trusting and nonthreatening climate for discussion and problem solving – it also includes socialising
students into a larger mathematical world that honours standards of reasoning and rules of practice. Articulating
comprehensible explanations about mathematical concepts is a learned strategy – and the art of communicating
about mathematics has to be modelled through explicit instruction. Mathematical language involves more than
vocabulary and technical usage; it encompasses the ways that expert and novice mathematicians use language
to explain and justify concepts. Competency in mathematics allows the student to understand discussions about
mathematics and comprehend the mathematical way of speaking. Effective classroom discourse involves
supporting students in developing the skills of explanation, argumentation and justification.
Representative SIM1 Math Stickies Quotes:
 “Math talk – focused, use of the language of math, puzzling and discussing”
 “Kids explaining/talking about their solutions/answers”
 “Students able to talk about problem solving steps they followed and computational strategies”
 “Thoughtful feedback”
 “Student input leads to instructional talk”
 “Kids thinking aloud”
 “Students discussing, free to disagree and test using a variety of methods”
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