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“Numerous research studies (Silver, 1994) have shown that when students are given opportunities to pose mathematics problems, to consider a situation and think of a mathematics question to ask of it—which is the essence of real mathematics—they become more deeply engaged and perform at higher levels.”
(Boaler, Mathematical Mindsets, 2015, p. 27)
Considerations:
Considerations:
develop mathematical habits of mind
model and nurture a growth mindset with your students
encourage risk-taking in problem-solving
value mistakes as learning opportunities
notice, name and nurture core and curricular competencies
build a community of thinkers
provide time and space for student reflection on learning, growth, and next steps
Resources:
Resources:
Develop mathematical habits of mind
Develop mathematical habits of mind
Assessing Early Numeracy.pdfHabits of Mind
Habits of Mind
Extensive research indicates that for students to develop mathematical habits of mind they must encounter and interact in intentional learning settings. Classroom design combined with active participation strategies will enhance student learning, increase achievement, and factor in the development of the well-educated citizen.
Students who have developed mathematics habits of mind exhibit expertise in:
persevering and using mathematics to solve problems in everyday life
recognizing there are multiple ways to solve a problem
demonstrating respect for diversity in approaches to solving problems
choosing and using appropriate strategies and tools
pursuing accuracy in problem solving
Model and nurture a growth mindset with your students
Model and nurture a growth mindset with your students
Growth Mindset: Carol Dweck
Growth Mindset: Carol Dweck
Growth Mindset: Jo Boaler
Growth Mindset: Jo Boaler
Ability and Mathematics: the mindset revolution that is reshaping education
Encourage risk-taking in problem-solving and value mistakes as learning opportunities
Encourage risk-taking in problem-solving and value mistakes as learning opportunities
Tracy Johnston Zager's book, Becoming the Math Teacher You Wish You'd Had, discusses mathematical habits of mind and how to encourage mathematical thinking in students.
Tracy suggests introducing students to the question about what is math through mathematical scavenger hunts, picture books, and online videos. She also emphasizes the importance of connecting what is happening in our classrooms with what mathematicians do :
"I can't emphasize this point enough: this mini-unit [What do Mathematicians Do?, Becoming the Math Teacher You Wish You'd Had page 17] has to connect to the rest of math class. It makes no sense to spend a few days developing a definition of doing mathematics that includes powerful words, such as notice, wonder, imagine, ask, investigate, figure, reason, connect, and prove, and then switch back to downloading procedures through "I do, we do, you do" demonstratations, guided practice and drills. Students won't buy it either. They're smart, and they learn more from our actions than our words. If we want students to build this complex, authentic understanding of the discipline of mathematics, they need to engage in these wonderful verbs as they learn new mathematical content throughout the year."
Tracy Johnston Zager, Becoming the Math Teacher You Wish You'd Had, page 28
From Jo Boaler's You Cubed is a resource that explores the science behind making mistakes and why they are so important to learning.
This video goes into more detail into how mistakes and working through difficult problems are vital to our learning in mathematics. From the "How to Learn Math" video series.
Notice, name and nurture core and curricular competencies
Notice, name and nurture core and curricular competencies
notice_wonder_one_pager.pdfnotice_wonder_intro.pdfNotice Wonder
Notice Wonder
The educators at the Math Forum, Annie Fetter and Max Ray have shared the power of using Notice Wonder as a routine to tap into children's curiosity and show them the importance of asking questions - "What do you notice? What do you wonder?" Check out the one-pager to the right to learn more about what this could look like in your classroom and the learning involved.
Annie Fetter's IGNITE talk "Every Wonder What They'd Notice"
Suggestions for Notice Wonder and Recording Template
Build a community of thinkers
Build a community of thinkers
Hands Down, Speak Out
Hands Down, Speak Out
A powerful way to engage students in purposeful dialogue. This blog describes and explores this technique and its' applications for the mathematics class.
Hands-Down Conversations (HDCs) are a structure for dialogue that is designed with the intention of deepening the level of classroom discourse by creating conditions in which students take greater ownership of and have more decision-making power in conversations. The primary goal of HDCs are to build students’ agency as readers, writers, mathematicians and world-changers who are prepared to use their words to take on the world!
This resource guides readers through 5 practices (anticipating, monitoring, selecting, sequencing, and connecting) to develop productive mathematical discussions.
(2nd Edition)
The next application of the 5 practices to create productive mathematical discussions is explored through a middle years focus.
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