P rovoking 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 teacher’s skilful questioning plays a vital role in this context, helping students to identify thinking processes, to see the connections between ideas and to build new understanding as they work their way to a solution that makes sense to them. In order to know what questions to ask to move the mathematical ideas forward, it is critical that teachers continually work to develop their knowledge of mathematics for teaching as they connect this understanding to the curriculum. By listening attentively to students’ ideas and keeping the learning goal and the big mathematical ideas in mind, we are able to identify and develop the important ideas in the students’ discourse. In addition to making decisions about what questions to ask during student discussions, teachers can plan effective questions to ask as they prepare lessons. Knowing the development of big ideas across the curriculum, reading material in teacher resources and solving problems themselves are examples of activities that may support teachers as they determine which questions to ask during lessons. VISIT ASCD.CA FOR INFORMATION ON UPCOMING CONFERENCES AND MORE! IN THIS ISSUE Dr. Marion Small Conference Paying attention to Mathematics Education K to 12 pg 2 16th Annual Northeast Affiliates Conference Learning and Leading: Transformation Matters pg 3 TRILLIUM A Resource for the Ontario Association for Supervision and Curriculum Development The Ontario ASCD, a diverse community that promotes excellence in education, is dedicated to supporting the growth and success of each learner. Winter 2012/13 Asking Effective Questions From the Capacity Building Series www.edu.gov.on.ca/eng/literacynumeracy/inspire INSTEAD OF TELLING STUDENTS WHAT TO DO . . . “Never say anything a kid can say! This one goal keeps me focused. Although I do not think that I have ever met this goal completely in any one day or even in a given class period, it has forced me to develop and improve my questioning skills. It also sends a message to students that their participation is essential. Every time I am tempted to tell students something, I try to ask a question instead.” (Reinhart, 2000, p. 480) PAYING ATTENTION TO MATHEMATICS
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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 teacher’s
skilful questioning plays a vital role in this context,
helping students to identify thinking processes, to
see the connections between ideas and to build new
understanding as they work their way to a solution that
makes sense to them.
In order to know what questions to ask to move
the mathematical ideas forward, it is critical that
teachers continually work to develop their knowledge
of mathematics for teaching as they connect this
understanding to the curriculum. By listening
attentively to students’ ideas and keeping the learning
goal and the big mathematical ideas in mind, we are
able to identify and develop the important ideas in the
students’ discourse.
In addition to making decisions about what
questions to ask during student discussions, teachers
can plan effective questions to ask as they prepare
lessons. Knowing the development of big ideas across
the curriculum, reading material in teacher resources
and solving problems themselves are examples of
activities that may support teachers as they determine
which questions to ask during lessons.
VISIT ASCD.CA
FOR INFORMATION ON UPCOMING CONFERENCES
AND MORE!
In ThIS ISSueDr. Marion Small ConferencePaying attention to Mathematics Education K to 12 pg 2
enjoy free PArking, A conTinenTAl breAkfAsT, Morning And AfTernoon
heAlTh breAks, A hoT buffeT lunch, And A free coPy of MAriAn’s
greAT WAys To differenTiATe MATheMATics . . . With so much at stake for students who do not do well in mathematics, the Ontario Ministry of Education assembled
a Mathematics Teaching and Learning Working Group in September 2010 to identify what it would take to bring
greater depth and coherence to the K–12 mathematics program. Representing experts in mathematics pedagogy,
curriculum and research, and including members from the ministry, district school boards, federations, professional
associations and universities, the group adopted a highly collaborative approach in order to surface current,
research-based knowledge in mathematics teaching and learning, K–12. Following this research and consultation,
this group developed 7 foundational principles to serve as a guide for planning and implementing future
improvements in mathematics teaching and learning. Refine your own school's mathematics teaching and learning
by fully incorporating these newly-developed Ministry best practices.
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dr. MAriAn sMAllDean and Professor Emerita at the University of New Brunswick,
has been instrumental in coaching Ontario school boards to
implement differentiated mathematics instruction. Marian’s work
is expressly referenced in our own new Ministry Guideline:
ANNOUNCING ThE 16Th ANNUAl NORThEAST ASCD AFFIlIATE CONFERENCE
Learning and Leading: TransformaTion maTTers
November 30 –December 1, 2012 with Pre-conference Workshops on november 29boston Park Plaza hotel, boston, Massachusetts
This year's Conference features internationally renowned presenters to help you explore when and how "Transformation Matters" in education practice while learning
new ways to be more effective in your schools, districts, and organizations.
rick WorMeli // cArol Ann ToMlinson // ToM dAccord // kiM MArshAll // beA McgArvey // jonAThAn cosTA // chris lehMAn // The righT QuesTion insTiTuTe
If you wish to comment or write an article or notice, based on one of the themes, for consideration in an upcoming Trillium, contact Dave Bird at: [email protected]
view this and archived issues of The Trillium online at www.ascd.ca/ascd/on
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