Get Started. It's Free
or sign up with your email address
Mathematics by Mind Map: Mathematics

1. from noticing to describing to creating to problem solving to algebraic reasoning

2. Assessment

2.1. Collection

2.1.1. evidence

2.1.1.1. of competencies/proficiency/learning

2.1.2. feedback

2.1.2.1. toughtful/intentional/specific

2.1.3. informs

2.1.3.1. understanding/misconceptions/ways of thinking

2.1.3.1.1. ways to adapt teaching

2.2. summative

2.2.1. assessment of learning - at the end

2.2.1.1. tests/assessments

2.3. formative

2.3.1. assessment for learning - to inform practice - during

2.3.1.1. show me/interviews/observation/hinge questions/exit tasks/questions

2.4. Fluency

2.4.1. Efficiency

2.4.1.1. speed

2.4.2. Accuracy

2.4.2.1. correct

2.4.3. Flexibility

2.4.3.1. cross connections and adaptability

2.4.4. Appropriateness

2.4.4.1. fit

3. Program of Studies

3.1. Outcomes

3.1.1. General Outcomes

3.1.1.1. overarching statements of expected learning in each strand/sub-strand

3.1.1.1.1. l

3.1.1.2. GOs the same throughout the grades

3.1.2. Specific Outcomes

3.1.2.1. statments that id the specific skills/understandings/knowledgestudents are expected to achieve in a given grade

3.1.2.2. SOs different throughout the grades

3.1.2.2.1. follow the verbs in the SOs. Ex: Demonstrate Understanding used frequently accross grades.

3.2. Nature of Math

3.2.1. Change

3.2.2. Constancy

3.2.3. number sense

3.2.4. patterns

3.2.5. relationships

3.2.6. spatial sense

3.2.7. uncertainty

3.3. Mathematical Processes

3.3.1. critical components that students must encounter in a mathematics program in order to achieve the goals of mathematics education and embrace lifelong learning in mathematics.

3.3.1.1. Communication [C]

3.3.1.1.1. communicae in order to learn and exress their understanding

3.3.1.2. Connections [CN]

3.3.1.2.1. connect mathematical ideas to other concepts in math, everyday experiences and other diciplines

3.3.1.3. Mental Mathematics & Estimation [ME]

3.3.1.3.1. demo fluency with mental math and estimation

3.3.1.4. Problem Solving [PS]

3.3.1.4.1. develop/apply new math knowledge through PS

3.3.1.5. Reasoning [R]

3.3.1.5.1. develop math reasoning

3.3.1.6. Technology [T]

3.3.1.6.1. select/use tech as tools for learning & PS

3.3.1.7. Visualization [V]

3.3.1.7.1. develop visualization skills to assist in processing info, making connections & PS.

3.4. Strands

3.4.1. how the learning outcomes are organized

3.4.1.1. Number

3.4.1.1.1. GO: develop number sense

3.4.1.2. Patterns & Relations

3.4.1.2.1. Patterns

3.4.1.2.2. Variables and Equations

3.4.1.3. Shape & Space

3.4.1.3.1. Measurement

3.4.1.3.2. 3D objects/ 2D shapes

3.4.1.3.3. Transformations

3.4.1.4. Statistics and Probability

3.4.1.4.1. Data analysis

3.4.1.4.2. Chance and uncertainty

4. Achievement Indicators

4.1. sampels of how students may demonstrate their achievement of the goals of a specific outcome. The range of samples provided (in the doc) are intended to reflect the scope of the specific outcome.

4.1.1. EX: Recite number names from a given number to a stated number (forward – one to ten, backward – ten to one), using visual aids.

4.2. Derived from the PoS

4.3. AI doc provides specific indicators to each of the general and specific learning outcomes in the curriculum doc.

4.4. Can be used as evidence that learning objectives (outcomes) have been achieved

4.5. provide examples of the scope of the specific outcomes

5. FNMI Foundational Knowledges

5.1. FNMI

5.1.1. TRC - Calls to Action

5.1.2. Seven Sacred Teachings

5.1.3. Indigenous perspectives

5.1.4. Holistiv view

5.1.4.1. Connections when learning

5.1.4.2. Contextualized learning

5.1.4.3. Learning through active participation

5.1.4.4. Oral over wrtitten

6. Teaching Content

6.1. Patterns and algebraic thinking

6.1.1. 3 Key Points

6.1.1.1. A wide variety helps build recognition and skills

6.1.1.1.1. repeating/ computational/ increasing/ decreasing

6.1.1.2. growing/shrinking patterns involve changes in features and attributes

6.1.1.2.1. repetition/core/elements/complexity

6.1.1.3. Understanding patterns contributes to algebraic reasoning

6.1.1.3.1. identifying/ reading/ describing/ extending/ rules/ translating/ parity

6.2. Sorting and Classifying

6.3. Number Sense

6.3.1. heirarchical inclusion/ decomposition, cardinality/ conservation/ subitizing/ skip counting/ unitizing

6.3.1.1. rekenrek, ten frame, cuisenaire rods, number lines

6.3.2. operations (number)

6.3.2.1. addition

6.3.2.1.1. counting all/counting on/adding chunks/doubles/friendly numbers/partial sums/compensation/decompose/algorithms/

6.3.2.2. Subtraction

6.3.2.2.1. adding up/counting back/chunks/doubles/adjusting one number/partial differences/compensation/decompose/place value/algorithm

6.3.2.3. Multiplication

6.3.2.3.1. repeated addition/skip count/doubling/halving/friendly numbers/partial products/constant proportion/decomposing one or more number/algorithms

6.3.2.4. Division

6.3.2.4.1. Repeated subtraction/multiply up/partial quotients/constant proportion/decomposing one or more/algorithms

6.4. Fractions

6.4.1. parts of wholes

6.4.1.1. partitioning

6.4.1.1.1. fraction splat game

6.4.1.2. iteration

6.5. Geometry (Space and Shapes)

6.5.1. sorting, comparing

6.5.2. congruency/ similarity/ symmetry/ asymmetry/ transformations/ reflections/ rotations/ cartesian plane

6.5.2.1. quick draw, pattern block quick image

6.5.3. spatial reasoning; representations of things

6.6. Measurement

6.6.1. Linear

6.6.1.1. three stages

6.6.1.1.1. definition/comparison,

6.6.1.1.2. non-standard units

6.6.1.1.3. standard untis

6.6.2. Area

6.6.3. Volume

6.6.3.1. the amount of 3D space an object takes up

6.6.4. Capacity

6.6.4.1. a measure of the maximum amount that something can contain

6.7. Descriptions - language to describe

6.7.1. Attributes

6.7.1.1. Shape

6.7.1.2. Size

6.7.1.3. Thickness

6.7.1.4. Colour

6.7.2. Properties/Features

6.7.2.1. Round/Square

6.7.2.2. large/small

6.7.2.3. Thick/thin

6.7.2.4. Black/Red

7. Teaching Practice

7.1. Eight Effective Teaching Practices

7.1.1. explicitly, intelligently, intentionally:

7.1.1.1. establish goals to focus the learning

7.1.1.1.1. broad goals/unit goals/actual lesson - what is being learning

7.1.1.2. implement tasks that romote reasoning and problem solving

7.1.1.3. use and connect math representations and strategies

7.1.1.4. facilitate meaningful mathematical discourse

7.1.1.5. Pose purposeful questions

7.1.1.6. build procedural fluency alongside conceptual understanding

7.1.1.7. support productive struggle in learning math

7.1.1.8. elicit and use evidence of student thining

7.1.1.8.1. assessment -what are we looking for?

7.1.2. contribute to learning success and achievement

7.2. Zager

7.2.1. Doing math

7.2.1.1. the math processes

7.2.2. Safe Classroom

7.2.3. Risks and Challenge

7.2.4. Productive Struggle

7.3. FSDUMath

7.3.1. Tasks

7.3.1.1. Entry

7.3.1.1.1. gather info about what they know

7.3.1.2. Apprentice

7.3.1.2.1. gather info about what they can n express and justify and what they're learning

7.3.1.3. Expert

7.3.1.3.1. information about how they transfer what they know to real tasks

7.3.1.4. Milestone

7.3.1.4.1. assess student thinking and ability to justify

7.3.2. Practices

7.3.2.1. Multiple entry/exit points

7.3.2.2. Productive struggle

7.4. 5 Practices for Orchestrating Productive Mathematical Discussions - Stein/Engle

7.4.1. Anticipating

7.4.2. Monitoring

7.4.3. Selecting

7.4.4. Sequencing

7.4.5. Connections

7.5. Building Thinking Classrooms - Peter Liljedahl

7.5.1. A framework of methods/tools/practices that engage students and are easy for teachers to apply

7.5.1.1. vertical non permanent surfaces

7.5.1.2. visibly random groups

7.6. Teaching Tools

7.6.1. Properties and Attributes

7.6.2. WODB

7.6.2.1. See new things - see in your own ways - see in others ways

7.6.3. WYR

7.6.3.1. Make a choice and justify your response

7.6.4. Notice and Wonder

7.6.4.1. Noticing stuff is the first important element in learning mathematics and connects to everything that a mathematician does

7.6.5. Spiralling

7.6.6. Concretedness Fading

7.6.6.1. Concrete ( enactive)

7.6.6.1.1. manipulatives

7.6.6.2. Representational (iconic/visual/pictoral)

7.6.6.2.1. pictoral modelspictures, charts, graphs

7.6.6.3. Abstract (symbolic)

7.6.6.3.1. formulas/symbolic notation

7.6.7. scaffolding

7.6.8. Learning Trajectories

7.6.8.1. learning goal

7.6.8.2. developmental path

7.6.8.2.1. conjectured route through instructional tasks to move students through developmental levels of thinking and support SOs in particular domains

7.6.8.3. matched activities

7.6.9. Cross curricular connections

7.6.10. Growth Mindsed, Carol Dweck

7.6.11. Critical Features

7.6.11.1. Depending on the features our attention attends to, we will see and learn things differently. To teach something, you must first know that you're looking at the same features of it.

7.6.11.1.1. arise in lessons

7.6.11.1.2. teachers job is to create opportunity to see critical features

7.6.11.1.3. must me discerned to see and learn in a specific way

7.6.12. Success Criteria

7.6.12.1. specific, concrete, measurable statements that describe what success looks like when a learning goal is achieved.

7.6.13. Learning goals

7.6.13.1. what we intend for students to learn

7.6.13.1.1. goals first, then tasks

7.6.14. Questions

7.6.14.1. open ended

7.6.14.2. high; elicit and build

7.6.15. Lesson [Plan]

7.6.15.1. 3 part

7.6.15.2. whole/part/whole/class/guided/instruction/groups/consolidation/3part problem solving/effortful tasks

7.6.16. 5 Strands for Proficiency

7.6.17. Talk Moves