Learning The revised curriculum supports students learning mathematics with understanding and...

10
Learning The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior knowledge.

Transcript of Learning The revised curriculum supports students learning mathematics with understanding and...

Page 1: Learning The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior.

Learning

The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior knowledge.

Page 2: Learning The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior.

Conceptual Understanding

• Conceptual understanding refers to an integrated and functional grasp of mathematics.

• It is more than knowing isolated facts and procedures.

Eg. Multiplication the Algebraic Way

Page 3: Learning The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior.

Conceptual Understanding

• Conceptual understanding supports retention. When facts and procedures are learned in a connected way, they are easier to remember and use and can be reconstructed when forgotten.

Hiebert and Wearne 1996; Bruner 1960, Katona 1940

Page 4: Learning The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior.

Balancing Conceptual Understanding and Procedural Fluency

• Pitting procedural fluency against conceptual understanding creates a false dichotomy.

• Understanding makes learning skills easier, less susceptible to common errors and less prone to forgetting.

• Also, a certain level of skill is required to learn many mathematical concepts with understanding

Hiebert and Carpenter 1992

Page 5: Learning The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior.

Making Connections

1999 Curriculum-determine, from examination of patterns, the exponent rules for multiplying and dividing monomials and the exponent rule for the power of a power, and apply….

-determine the meaning of negative exponents and of zero as an exponent from activities involving graphing, using technology, and from activities involving patterning

COURSE: GRADE 9 Applied and Academic

Revision-describe the relationship between the algebraic and geometric representations of a single variable term up to degree three ( i.e., length, which is one dimensional, can be represented by x; area, which is two dimensional can be represented by x^2, and volume, which is three dimensional can be ….

Page 6: Learning The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior.

Continuum of Learning: Support Resource for Draft Revision Spring 2005

Number Sense and NumerationGRADE 1: read, represent, order, and compare whole numbers to 50, and investigate money amounts and fractions;

GRADE 5: read, represent, order, and compare whole numbers to 100 000, decimal numbers to hundredths, proper and improper fractions, and mixed numbers;

GRADE 2: read, represent, order, and compare whole numbers to 100, and represent money amounts and fractions using concrete materials

GRADE 6: read, represent, order, and compare whole numbers to 1 000 000, decimal numbers to thousandths, proper and improper fractions, and mixed numbers

GRADE 3: read, represent, order, and compare whole numbers to 1000, and demonstrate their understandings about money and fractions

GRADE 7: represent, order, and compare numbers, including integers

GRADE 4: read, represent, order, and compare whole numbers to 10 000, decimal numbers to tenths, and simple fractions, and expand their understandings about money

GRADE 8:represent, order, and compare equivalent representations of numbers including those involving exponents

Page 7: Learning The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior.

Developing Concepts Across the Grades

1997 Curriculum

Proportional Reasoning

Draft Revision Spring 2005

Proportional Reasoning

Grade 7: No Specific Reference Grade 7:

Number Sense and Numeration

Proportional Relationships

Grade 8: Under Applications Grade 8:

Number Sense and Numeration

Proportional Relationships

Grade 9 Applied:

Number Sense and Algebra

Solving Numerical Problems

Grade 9 Applied:

Number Sense and Algebra:

Proportional Reasoning

Grade 10 Applied:

Proportional Reasoning

Grade 10 Applied:

Measurement and Trigonometry:

Solving Problems Involving Similar Triangles

Page 8: Learning The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior.

Developing Concepts - Volume

Grade 4Measure Volume

Grade 5 Grade 6 Grade 7

Gr 8

Gr 9

Grade 9 Grade 9 Grade 10

Academic Applied AppliedSolve problems Develop formulas Solve problems

Involving optimal for the volumes of involving volumes

volume. Solve the pyramids, cones of prisms, pyramids

max and min vol and spheres. cylinders, cones,

pyramids, cones spheres, and a

and spheres. combination.

Page 9: Learning The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior.

Your turn to put the puzzle together

Gr 7 Gr 8 Gr 9 Gr 10

Your turn to investigate expectations from grade 7, 8, 9 and 10 that build on one another.

Page 10: Learning The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior.

On your tables you will find a green sheet that has an overall

expectation. Determine the prerequisite expectation(s) from Grade 10 to Grade 7 and remain in the same pathway. Use the

organizer and chart paper at your table. Post on the back wall

when completed.


TRANSFORMING SCHOOLS INTO LEARNING ORGANIZATIONS: SUPPORTS ... · TRANSFORMING SCHOOLS INTO LEARNING ORGANIZATIONS: SUPPORTS AND BARRIERS TO EDUCATIONAL REFORM Raymond B. Williams,

TRANSFORMING SCHOOLS INTO LEARNING ORGANIZATIONS: SUPPORTS ... · TRANSFORMING SCHOOLS INTO LEARNING ORGANIZATIONS: SUPPORTS AND BARRIERS TO EDUCATIONAL REFORM Raymond B. Williams,

Mobile Learning in Museums: How Mobile Supports …i523/cahill.pdfMobile Learning in Museums: How Mobile Supports for Learning Influence Student Behavior Clara Cahill1, Alex Kuhn2,

Mobile Learning in Museums: How Mobile Supports …i523/cahill.pdfMobile Learning in Museums: How Mobile Supports for Learning Influence Student Behavior Clara Cahill1, Alex Kuhn2,

Copyright Clarity: How Fair Use Supports Digital Learning

Copyright Clarity: How Fair Use Supports Digital Learning

Technology Supports All Learning Theory Approaches

Technology Supports All Learning Theory Approaches

Learning Supports - Scholastic...The Case for a Learning Supports Approach Theory to Practice Barriers to Learning Scholastic’s Learning Supports Pathway is informed by the Learning

Learning Supports - Scholastic...The Case for a Learning Supports Approach Theory to Practice Barriers to Learning Scholastic’s Learning Supports Pathway is informed by the Learning

Perceptual information supports transfer of learning in ...

Perceptual information supports transfer of learning in ...

EXTENDED LEARNING AND INTEGRATED SUPPORTS (ELISS) …...Sep 13, 2017  · EXTENDED LEARNING AND INTEGRATED STUDENT SUPPORTS (ELISS) GRANT APPLICATION TECHNICAL ASSISTANCE WEBINAR Donna

EXTENDED LEARNING AND INTEGRATED SUPPORTS (ELISS) …...Sep 13, 2017  · EXTENDED LEARNING AND INTEGRATED STUDENT SUPPORTS (ELISS) GRANT APPLICATION TECHNICAL ASSISTANCE WEBINAR Donna

Schoolwires Supports Flipped Learning

Schoolwires Supports Flipped Learning

Instructional Practices and Supports: Creating a ... · SUPPORTS: CREATING A RESPECTFUL AND RESPONSIVE CLASSROOM LEARNING ENVIRONMENT LRE Training Module ... Describe how learning

Instructional Practices and Supports: Creating a ... · SUPPORTS: CREATING A RESPECTFUL AND RESPONSIVE CLASSROOM LEARNING ENVIRONMENT LRE Training Module ... Describe how learning

Office of Learning Supports Positive Behavioral Interventions and Supports: Universal Systems and Practices 2015-16.

Office of Learning Supports Positive Behavioral Interventions and Supports: Universal Systems and Practices 2015-16.

Arthur M. Freedman, MBA, Ph.D. 11/10/09 1 How Action Learning Supports Organization Development & Change How Action Learning Supports Organization Development.

Arthur M. Freedman, MBA, Ph.D. 11/10/09 1 How Action Learning Supports Organization Development & Change How Action Learning Supports Organization Development.

Unit 7 Community Language Learning - IAUNresearch.iaun.ac.ir/pd/shafiee-nahrkhalaji/pdfs/UploadFile_3455.pdf · learning security—non-threatening learning environment aggression—actively

Unit 7 Community Language Learning - IAUNresearch.iaun.ac.ir/pd/shafiee-nahrkhalaji/pdfs/UploadFile_3455.pdf · learning security—non-threatening learning environment aggression—actively

Actively Learning Mathematics RAC

Actively Learning Mathematics RAC

Actively Learning Ontology Matching via User Interaction

Actively Learning Ontology Matching via User Interaction

Learning Supports. Barriers to Learning Learning Supports Successful in School Core Instruction Range of Learners = Motivationally ready & able to learn.

Learning Supports. Barriers to Learning Learning Supports Successful in School Core Instruction Range of Learners = Motivationally ready & able to learn.

Blended Learning Supports

Blended Learning Supports

Learning Environments Preventative Behavior Supports for ... Webinars/ASD_project/3... · Learning Environments Preventative Behavior Supports for Students ... Sensory Integration.

Learning Environments Preventative Behavior Supports for ... Webinars/ASD_project/3... · Learning Environments Preventative Behavior Supports for Students ... Sensory Integration.

Learning Supports. Purpose Provide a brief overview of Learning Supports Demonstrate the relationship between RtI and Learning Supports No School.

Learning Supports. Purpose Provide a brief overview of Learning Supports Demonstrate the relationship between RtI and Learning Supports No School.

Chapter Learning to Listen Actively...Chapter Learning to Listen Actively. 1. Chapter. Learning to Listen 1 Actively. TAKE NOTE. Active listening is a framework for listening awareness

Chapter Learning to Listen Actively...Chapter Learning to Listen Actively. 1. Chapter. Learning to Listen 1 Actively. TAKE NOTE. Active listening is a framework for listening awareness

Learning How to Actively Learn: A Deep Imitation Learning ...Learning How to Actively Learn: A Deep Imitation Learning Approach Ming Liu Wray Buntine Faculty of Information Technology,

Learning How to Actively Learn: A Deep Imitation Learning ...Learning How to Actively Learn: A Deep Imitation Learning Approach Ming Liu Wray Buntine Faculty of Information Technology,