1. Math Curriculum
1.1. Assessment
1.1.1. Knowledge and Understanding
1.1.1.1. knowledge/understand the content
1.1.2. Thinking
1.1.2.1. Use of planning skills
1.1.2.2. Processing skills
1.1.2.3. critical/creative thinking processes
1.1.3. Communication
1.1.3.1. Expression and organization of ideas and information
1.1.3.2. communicate to different audiences
1.1.3.3. use of vocabulary and terminology
1.1.4. Application
1.1.4.1. Apply/transfer skills and knowledge
1.1.4.2. making connections within various contexts
1.1.5. Math: The Achievement Chart (this website has a great explanation of breaking down the math achievement chart per strand)
1.2. Program Planning
1.2.1. High-Impact Practices
1.2.1.1. Importance of knowing the identities of all students and choosing appropriate approach for their student learning
1.2.1.2. Learning goals, Success criteria and descriptive feedback
1.2.1.3. Direct Instruction
1.2.1.4. Problem-solving tasks and experiences
1.2.1.5. Teaching about Problem solving
1.2.1.6. Tools and representations
1.2.1.7. Math Conversations
1.2.1.8. Small-group instruction
1.2.1.9. deliberate practice
1.2.1.10. flexible groupings
1.2.2. Role of ICT in Mathematics
1.2.2.1. technology can extend and enrich teachers' instructional strategies
1.2.2.2. understand the importance of tech and how it supports learning
1.2.3. Planning Math Programs for Spec Needs
1.2.3.1. Support all students in their learning, work collaboratively with special education teachers
1.2.3.2. Teacher plays a critical role
1.2.3.3. Needs of students is purposefully planned with the principles of universal design for Learning
1.2.3.4. Know the student's strengths, interests, motivations and needs in math to make accommodations and modifications
1.2.3.5. build student confidence
1.2.3.6. foster a positive attitude towards math
1.2.3.7. provide environmental, assessment and instructional accommodations that are specified in the IEP
1.2.4. Planning Math Programs for ELL
1.2.4.1. various linguistic identities are viewed as a critical resource
1.2.4.2. scaffolding their knowledge of social and cultural background
1.2.4.3. engage in open and parallel tasks
1.2.4.4. planned activities that use oral communication (eg. Think, pair, share")
1.2.4.5. In the video, Moises was confused about the wording of the question. As a teacher, we must learn to refrain from similar words with different meanings and accommodate to every student need.
1.2.5. Human Rights, Equity and Inclusive Education
1.2.5.1. students have access to enrichment support
1.2.5.2. develop practices that learn from and build on students' cultural competencies
1.2.5.3. Culturally relevant and responsive pedagogy (CRRP) -> teachers learn about their identities and how it affects their teaching
1.2.5.3.1. developing students' sense of self
1.2.5.3.2. Learn about others
1.3. Mathematical Processes
1.3.1. Apply these processes to work together along with Social-Emotional Learning
1.3.1.1. cannot be separated from knowledge, concepts and skills
1.3.2. Problem Solving
1.3.2.1. Connect mathematical ideas to develop conceptual understanding
1.3.2.1.1. Basis of effective math progress
1.3.2.2. strategies
1.3.2.2.1. methods to solve problems
1.3.2.2.2. engage students with solving various problems
1.3.2.2.3. students pose their own questions, flexible with strategies
1.3.2.3. Increase opportunity to use critical thinking skills
1.3.2.4. help develop positive math identity
1.3.2.5. use prior mathematical knowledge
1.3.2.6. make connections using mathematical knowledge, concepts and skill both outside and inside the classroom
1.3.2.7. Promote sharing ideas and strategies
1.3.2.8. use creative-thinking skills
1.3.2.9. Find enjoyment in math and lesson become more confident in their ability
1.3.3. Reasoning/Proving
1.3.3.1. Justify your thinking
1.3.3.2. Form math conjectures, to prove if it is true or not
1.3.3.3. justify and prove your solution with evidence
1.3.4. Reflecting
1.3.4.1. Reflect on what is working or not working
1.3.4.2. Ask "is there a better approach to this?"
1.3.4.3. Ask "what adjustments need to be made?"
1.3.4.4. Reflect on your new knowledge and apply them to past and future problems
1.3.5. Connecting
1.3.5.1. Connections help students grasp math concepts and principles
1.3.5.2. Use one area of math to understand another area
1.3.5.3. More connections that you make, the deeper your understanding developing your sense of identity
1.3.5.4. Students find math useful and relevant as it is in the world beyond the classroom
1.3.6. Communicating
1.3.6.1. Use oral, visual, written or gestural communication
1.3.6.2. active and respectful listening
1.3.6.3. support safe and respectful environment
1.3.6.4. students should feel comfortable and valued in your classroom
1.3.7. Representing
1.3.7.1. Use tools, pictures, diagrams, graphs, tables, numbers, words and symbols to communicate and represent
1.3.7.2. make connections among various representations
1.3.8. Selecting tools and strategies
1.3.8.1. Technology
1.3.8.1.1. technological/digital tools for students to interact and learn with
1.3.8.1.2. Examples: calculators, software to code, computer and tablets
1.3.8.1.3. Use with discretion, only when it makes sense and needed
1.3.8.1.4. use technology in their mathematics learning, they should apply mental computation, reasoning, and estimation skills to predict and check answers
1.3.8.2. Tools
1.3.8.2.1. students are encouraged to select and use tools to illustrate their mathematical ideas
1.3.8.2.2. see patterns/relationships
1.3.8.2.3. make connections
1.3.8.2.4. test, revise and confirm reasoning
1.3.8.2.5. communicate reasoning
1.3.8.3. Strategies
1.3.8.3.1. select appropriate strategy
1.3.8.3.2. judge when an exact answer is needed and when an estimate is all that is required
1.3.8.3.3. use of algorithms or the composition and decomposition of numbers using known facts
1.3.8.3.4. create computational representations of mathematical situations using code
1.4. Social-Emotional Learning skills and Mathematical Processes
1.4.1. Applying SEL skills and the mathematical processes is an explicit overall expectation in each grade
1.4.1.1. Skills support students in understanding mathematical concepts that are key to learning and doing mathematics
1.4.2. Identification and management of emotions
1.4.3. Stress Management and coping
1.4.4. Positive Motivation and Perseverance
1.4.5. Healthy Relationship skills
1.4.6. Self-awareness and sense of Identity
1.4.7. Critical and Creative thinking
1.5. Numbers
1.5.1. Students learn about different types of numbers and how those numbers behave when various operations are applied to them
1.5.2. Number sense- students develop the ability to relate numbers and relate computations
1.5.2.1. Use number relationships to make sense of calculations and assess the reasonableness of numbers used to describe situation
1.6. Algebra
1.6.1. Develop algebraic reasoning through patterns, variables, expressions, equations, inequalities, coding and process of mathematical modelling
1.6.2. Mathematical Modelling process connections to real-life situations
1.6.2.1. 1. Understand the Problem
1.6.2.1.1. What questions need answering?
1.6.2.1.2. What information is needed?
1.6.2.2. 2. Analyze the situation
1.6.2.2.1. What assumptions do I make about the situation?
1.6.2.2.2. What changes, remains the same?
1.6.2.3. 3. Create a mathematical model
1.6.2.3.1. What representations, tools, technologies, and strategies will help build the model?
1.6.2.3.2. What math concepts and skills might be involved?
1.6.2.4. 4. Analyze and assess the model
1.6.2.4.1. Can this model provide a solution to the problem?
1.6.2.4.2. What are alternative models?
1.7. Data
1.7.1. Support students in developing critical thinking skills throughout their development of data literacy to analyze, synthesize, understand, generate and use data
1.7.2. Develop an understanding of qualitative and quantitative data
1.8. Spatial Sense
1.8.1. Combines geometry and measurement to emphasize their relationship
1.8.2. provides students with the language and tools to analyze, compare, describe and navigate the world around them
1.8.3. Supports professions in STEM, builds foundational skills for construction, architecture, engineering, research and design
1.9. Financial Literacy
1.9.1. Students need the skills and knowledge to take responsibility for managing their personal financial well-being
1.9.2. Develop the ability to make informed decisions as consumers and citizens
1.9.3. Make connections to what they are learning in media literacy
1.9.4. Consider and respond to the range of equity issues related to diverse circumstances and lived experiences of students and their families
1.10. Integrated Learning
1.10.1. Apply learning to relevant real-life contexts
1.10.2. Make connections between mathematics and other subject areas
1.10.3. Improve the ability to provide multiple responses to a problem
1.10.4. Debate and test whether responses are effective and efficient
1.10.5. Apply a range of knowledge and skills to solve problems in mathematics and in their daily experiences and lives
1.10.6. Literacy in Mathematics
1.10.6.1. Reading a mathematics text requires specific literacy strategies, unique to mathematics.
1.10.6.1.1. Support all students in developing an understanding of mathematical texts
1.11. Transferable Skills in Mathematics
1.11.1. Critical Thinking and Problem Solving
1.11.1.1. Learn and apply strategies to understand and solve problems
1.11.2. Innovation, creativity and entrepreneurship
1.11.2.1. Pose questions, make and test conjectures and consider problems from different perspectives to generate new learning
1.11.3. Self-directed learning
1.11.3.1. Initiate new learning, monitor their thinking and their emotions when solving problems and apply apply strategies to overcome challenges
1.11.4. Collaboration
1.11.4.1. Students and educators engage with others productively to better understand ideas and problems
1.11.5. Communication
1.11.5.1. Use tools and language of mathematics to describe their thinking and to understand the world
1.11.6. Global citizenship and sustainability
1.11.6.1. Recognize and appreciate multiple ways of knowing, doing and value different perspective
1.11.7. Digital Literacy
1.11.7.1. When and how to use appropriate tools to understand and model real-life situations
2. Assessment for a Growth Mindset
2.1. Students and teachers define success in math in terms of letters and numbers
2.1.1. Doing so fails to describe children's knowledge and misrepresent it
2.2. good testing asses what is important
2.3. teachers in Finland use rich understanding of students' knowledge gained through teaching to report to parents
2.4. Students work through open-ended projects attempted hard and difficult questions
2.5. Growth mindset
2.5.1. Positive beliefs about their own ability and problem solving, mathematical tools that they are prepared to use in any math situation
2.5.2. Grades/test scores demotivate students, results in lower classroom management
2.5.3. Grading reduces achievement
2.5.3.1. Move from grades to diagnostic comments allows teachers to give students the gift of knowledge/insights on how to improve
2.5.4. Turn the classroom into an open learning space, students work harder and achieve higher levels
2.6. Assessment for Learning (A4L)
2.6.1. 1. Formative
2.6.1.1. informs learning
2.6.1.2. Find where students are in their learning
2.6.2. 2. Summative
2.6.2.1. Summarize student learning
2.6.3. Clearly communicating to students what they've learned
2.6.4. Help students become aware where they are in their learning journey and where they need to reach
2.6.5. Giving information on ways to close the gap between where they are now to where they need to be
2.7. Developing student self-awareness/Responsibility
2.7.1. powerful learners who are reflective engage in metacognition
2.7.2. 1. Self-assessment
2.7.2.1. Student thinks about what they have learned and what to work on
2.7.2.2. Give time to reflect upon their learning
2.7.2.3. Younger students can use smiley faces or weather to indicate students understand concepts
2.7.3. 2. Peer assessment
2.7.3.1. Assess each other's work rather than their own
2.7.3.2. Students open to hearing criticism/suggestion from another student
2.7.3.3. Eg. 2 stars and a wish
2.7.4. 3. Reflection Time
2.7.4.1. Provide class time to reflect
2.7.5. 4. Traffic Lighting
2.7.5.1. using red, yellow and green to see if students understand the concept or if the teacher needs to slow down and reiterate
2.7.6. 5. Jigsaw groups
2.7.6.1. Student group works together and master the problem given to them. Divide students up to form new groups and share their expertise.
2.7.7. 6. Exit tickets
2.7.7.1. Students reflect, help their learning and give teacher valuable information on student's learning/ideas
2.7.8. 7. Online forms
2.7.8.1. Non-verbal students will most likely share feedback online
2.7.9. 8. Doodling
2.7.9.1. Show understanding in a sketch, cartoon or doodle
2.7.10. 9. Students write Questions and test
2.7.10.1. Students design an assessment for other students
2.7.10.2. Think creatively
2.7.11. Diagnostic comments
2.7.11.1. given when most helpful to students, doesn't have to be everyday
2.8. Advice on grading
2.8.1. 1. Allow students to resubmit work/test for a higher grade
2.8.2. 2. Share grades with administrators, but not with students
2.8.3. 3. Use multidimensional grading
2.8.4. 4. Do not use 100-point scale
2.8.5. 5. Do not include early assignments from math class in the end of class grade
2.8.6. 6. Do not include homework, if given, as a part of grading
2.9. The students from the problem-solving school did so well in the standardized national exam because they had been taught to believe in their own capabilities
2.9.1. they had been given helpful, diagnostic information on their learning
2.9.1.1. solve any question, as they were mathematical problems solvers
3. Using Humour to Gain mathematical Insight
3.1. Think creatively to experience the pleasure of mathematical insight
3.1.1. Creative means using comics, poems and interviews
3.2. gain attention
3.2.1. improve comprehension and cognitive retention
3.3. rewarding to see students listen with enjoyment
3.4. Create positive learning environment
4. Classroom Data Analysis with The Five Strands of Mathematical Proficiency
4.1. Teachers can give special attention to areas of need identified by assessment
4.1.1. Quantitative assessments have limitations
4.2. Five strands are tandems and represents the idea that learners must connect knowledge to be proficient
4.2.1. 1. Conceptual Understanding
4.2.1.1. - Represent mathematical situations in different ways
4.2.1.2. - How different representations are useful for different purposes
4.2.1.3. -Uses picture or concrete materials to show various ways to the solution (different solution methods)
4.2.1.4. -Able to explain a concept
4.2.2. 2. Procedural Fluency
4.2.2.1. -Carries out procedures flexibly, accurately, efficiently and appropriately
4.2.2.2. -Support conceptual understanding
4.2.2.3. -Estimate the result of a procedure
4.2.2.4. -Select appropriate tool for a given situation
4.2.3. 3. Strategic Competence
4.2.3.1. -Represent mathematically (eg. numerical, symbolic, verbal and graphical)
4.2.3.2. -Generate mathematical representation of the problem captures core mathematical element (eg. draw/write equations, tangible representation)
4.2.4. 4. Adaptive Reasoning
4.2.4.1. -Knowledge to justify and explain the conclusion and one's work
4.2.4.2. -Capacity to think logically among concepts and situations
4.2.5. 5. Productive Disposition
4.2.5.1. -Make sense of math as useful and worthwhile
4.2.5.2. -View ability as expandable in response to experience
4.2.5.3. -Positive outlook in math
4.3. Gather Qualitative data from students
4.3.1. Following the steps is helpful, but there's a lot of work to put into it so it's not feasible for every lesson
4.3.2. Analyze Data
4.3.2.1. Design a lesson
4.3.2.1.1. Get feedback from peers and mentors
4.4. Student thinking process is at different speeds, differentiated instruction
5. From Tracking to Growth Mindset Grouping
5.1. -Tracking "sething" is separate classes with high or low level content
5.1.1. Opportunity to Learn (OTL)
5.1.1.1. Students spend time in class with high level content and achieve higher levels
5.1.2. Heterogeneous groups > tracking system
5.1.3. 1. Provide open-ended tasks
5.1.3.1. Growth mindset
5.1.3.1.1. -Teacher decides to challenge, supports students
5.1.3.2. Students more interested, challenged and supported
5.1.3.3. Students are helping each other
5.1.4. 2. Offer Choice of tasks
5.1.4.1. Offer choice or challenge in tasks
5.1.5. 3. Individualized Pathways
5.1.5.1. SMILE cards
5.1.5.2. Allows student to choose their own content
5.2. Multidimensionality
5.2.1. Teacher thinks of all the ways to be mathematical
5.2.2. Math is social and interpretive
5.2.3. Work in groups
5.2.4. Students encouraged to represent ideas in different ways (eg. words, graphs, tables and symbols)
5.2.5. Use multiple methods and show work
5.2.6. Students start through encouragement from peers/rereading/asking questions
5.2.7. Deal with real-world situations
5.3. Roles given to each student
5.3.1. Facilitator
5.3.2. Recorder/Reporter
5.3.3. Resource manager
5.3.4. Team Captain
5.4. Assigning Competence
5.4.1. Publicly praising student
5.5. Students are responsible for each other's learning
5.5.1. Talk about the do's and don'ts for working in groups
5.5.2. What the student themselves value (eg. don't speed )
5.6. "Group tests"
5.6.1. work individually but only mark one student's test
6. Teaching Through Mistakes
6.1. Mistakes grow your brain
6.2. Talk about where mistakes come from
6.2.1. If one person makes a mistake, others are as well
6.2.1.1. Students contribute to solve problems together