The following is an approach to use to gain an understanding of the prior knowledge and mathematical understanding that students bring to our classes.
Record observations about students' interests, readiness to work collaboratively, mindsets towards mistakes and struggle, etc.
Have all students complete 2-3 diagnostic problems (in one day) and do not return these to students.
Organize diagnostic data into "piles" to identify the background students DO enter with.
Record observations about students' interests, readiness to work collaboratively, mindsets towards mistakes and struggle, etc.
Have all students complete 2-3 diagnostic problems (in one day) and do not return these to students.
Record notes about where students fall along the developmental continuum.
Record observations about students' interests, readiness to work collaboratively, mindsets towards mistakes and struggle, etc.
Have all students complete 2-3 diagnostic problems (in one day) and do not return these to students.
Record notes about where students fall along the developmental continuum.
Plan targeted interventions to move students along the developmental continuum.
Using diagnostic tools can be helpful to determine where students might need additional support and interventions to address unfinished learning and help them develop a more solid understanding of mathematical concepts and relationships.
Taking inspiration from resources developed in intermediate classes (Grade 7 Long Range Plans and Grade 8 Long Range Plans), we have created resources to help us learn about the thinking and understanding that students enter our classes with, related to key areas in the MTH1W course:
Proportional Reasoning
Integers
Fractions
Algebra
Linear and Non-Linear Relations
The diagnostic "thinking tasks" are designed to be fairly open to various approaches so that they are accessible to all students and where students can use different ways of communicating or justifying their thinking.
This tool allows teachers to track where a student starts in relation to expectations from previous courses and determine what needs to be done next to move the student along the continuum for that topic.
Embedded in each set of diagnostic thinking tasks are links to resources, strategies, and tools that can be helpful when planning follow-up interventions and learning opportunities for the whole class, small groups or individual students.
focusing on what students DO understand
learning about how students think
determining what knowledge and understanding students enter our class with
identifying where unfinished learning might exist
making plans for interventions to address unfinished learning or extend current understanding
focusing on what students DO NOT understand
sorting students into categories
justifying why students need to take a different course or pathway
During the first few weeks of the course or before a unit or chunk of lessons on a topic, choose 2-3 problems (slides) from the relevant diagnostic thinking task to print or provide digital copies of for students.
Give ALL students the problems.
Encourage students to show their thinking because you are curious about what they remember. This is NOT a test, and instead a tool that will help you figure out what to do next!
Provide opportunities for students to use concrete materials and/or to explain their thinking verbally.
Gather the student work and do not return it to students or provide any feedback on it.
Carefully look at students' thinking on sets of problems.
Organize them according to
the strategies students use
the models they feel comfortable with
any misconceptions that exist
similarities in thinking or approaches
Keep these diagnostics as "benchmark" indicators of where students started at the beginning of the semester.
Use your observations to aid in planning for how to address the needs of specific students.
Carefully look at students' thinking on sets of problems.
Make notes on the developmental continuum based on what students are demonstrating.
Keep these diagnostics as "benchmark" indicators of where students started at the beginning of the semester.
Use your observations and notes to aid in planning for how to address the needs of specific students.
As you address students' needs, keep track of how students are moving along the continuum.
At the end of each diagnostic thinking task slidedeck, there is a collection of resources listed:
Follow-Up Teaching Strategies
Materials / Manipulatives / Models
Additional Resources
These supports will aid in planning for whole class, small group or individual opportunities to address unfinished learning revealed in students' thinking.
Connect with an Itinerant Coach and/or work with your course team to develop responsive approaches to supporting students' development along the continuum for each area.
This document offers potential resources to help address areas of concern observed early in the course.
They can be used to design whole class learning, small group instruction or one-on-one support.
You may want to connect with an Itinerant Coach to design and explore ways to support students together.
Assessment from a CRRP stance, by its nature, encompasses a wide variety of assessment approaches. It is designed to reflect, affirm, and enhance the multiple ways of knowing and being that students bring to the classroom while maintaining appropriate and high academic expectations for all students. The primary purpose of assessment is to improve student learning.
incorporate a variety of ways that students can demonstrate their understanding
gather information using all of observations, conversations and products
design tasks to be low floor, high ceiling so that all students have an opportunity to show what they know and can do
interview students with IEPs to find out from them what has been helpful to accommodate them in the past
adopt an asset-based focus for your students with IEPs
Take time to know them and build relationship
Encourage the use of primary languages for translanguaging
Connect tasks to their background experience/activate their prior knowledge
Provide thinking time before speaking, speaking time before writing
Amplify the most important learning through visuals, exemplars, modelling, think alouds, audio/video, tech, etc.