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.pdfProportionReason.pdfLNSAttentionFractions.pdfClementsSaramaLearning_trajectories_math.pdfNumber Worlds Learning Trajectories
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.
Alex Lawson describes working with a group of students over several years to help identify how a student's thinking demonstrates their mathematical understanding, where they fit into a developmental continuum and strategies for moving students forward.
Marion small helps to identify the most important math to assess; construct meaningful assessments—both formative and summative—to measure student understanding; and provide students with feedback that is clear, timely, and specific.
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.
Aligning Assessment to Brain Science.pdfPresentation by Jo Boaler on assessment and brain science.
Teacher_Moderation.pdfOntario's Capacity Building Series on teacher moderation and collaborative assessment of student work.
Use evidence of student learning to inform and guide planning for next steps with students
The Island Numeracy Network (INN) is a passionate group of K-12 educators from numerous districts and schools in the Vancouver Island region. This new assessment was developed to align numeracy assessment practices with current numeracy learning expectations of BC students.
Assess in a variety of different ways: product, observation, conversation
The Formative 5 Strategies
Everyday Assessment Techniques for Every Math Classroom
The Formative 5 Strategies.pdf