How do I know what my students know, can do, and understand?

"The most important single factor influencing learning is what the learner already knows. Ascertain this and teach … accordingly." (Ausubel et al, 1978)

Considerations:

  • develop my professional knowledge of mathematical concepts in order to support student learning through examining learning continua, trajectories, and progressions
  • give students opportunities to make their mathematical thinking visible through multiple communication formats:
    • constructing with materials and building models
    • dialogue and discussion
    • drawing diagrams, pictures, charts
    • using symbols
    • photos and descriptive captions
    • creating narratives
    • writing
    • use technology tools to capture student learning
  • recognize and embrace "mistakes" as part of deep learning and productive struggle
  • use evidence of student learning to inform and guide planning for next steps with students
  • assess in a variety of ways: product, observation, conversation

Resources:

Develop profession knowledge of mathematical concepts in order to support student learning through examining learning continua, trajectories, and progressions

These resources are very helpful for working on our understanding of the mathematical concepts we are teaching.

PayingAttentiontoAlgebra.pdf
ProportionReason.pdf
LNSAttentionFractions.pdf
ClementsSaramaLearning_trajectories_math.pdf

Number Worlds Learning Trajectories

Developmental Continuum Grade k-9.docx

Developmental Math Continuum Summary developed by SD71

Numeracy Continuum K-10 developed by the New South Wales Department of Education

First Steps Mathematics is a series of teacher resource books will help teachers to diagnose, plan, implement and judge the effectiveness of the learning experiences they provide for students.

PRIME is a program for math educators that many districts have access to - check with your district if you are interested.

This book identifies the critical learning phases children go through as they develop their mathematical understanding that is essential to building a solid foundation of numerical reasoning.

Give students opportunities to make their mathematical thinking visible through multiple communication formats

This book provides strategies for maximizing student's comprehension by integrating visual thinking into the classroom.

Hull, Ted 2011

This resource helps teachers direct student thinking and structure classroom discussion. Good for all grade levels.

Ritchart, Ron 2011

To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like to get there.

Hattie, John 2016

The authors offer an alternative assessment method by examining a wide variety of assessment tools and match the student evidence with a description of achievement.

Videos:

What is Visible Learning for Mathematics with John Hattie.

App-Mazing Math Through Visible Learning

Aligning Assessment to Brain Science.pdf



Teacher_Moderation.pdf



Use evidence of student learning to inform and guide planning for next steps with students

School District #22 teachers have created 'screeners' to identify what students know, can do, and understand in mathematics Grades 1, 3 and 5.

Assess in a variety of different ways: product, observation, conversation