Because the acquisition of mathematical thinking, skills, competencies, and understandings is not linear, the gradual release model should only be used for learners struggling with a specific process.
Modeled and Shared Math:
The teacher purposefully plans, introduces, models and explicitly demonstrates the concept. Connections are made to prior learning. The teacher may start with an “explore” activity that allows students to reason, conjecture, solve problems, and interact with the concept.
The teacher elicits and shares student thinking and reasoning, recording and discussing strategies. The teacher may model mathematical thinking using a think-aloud.
The teacher models procedures to be used and explicitly explains vocabulary, symbols and models. The teacher may demonstrate with a think-aloud. Connections are made between symbols, procedures, manipulatives, models, and where the math content is found in the learner’s social or physical world.
There is a gradual release of responsibility, where students observe modeling, try independently, discuss and practice collaboratively, share strategies and solutions, examine errors and misconceptions, and receive immediate and specific feedback.
Opportunities are provided for students to consolidate thinking through meaningful dialog, discussion or debate. Students share thinking and reasoning.
- Modelling and Sharing:
- Connects mathematical ideas into a continuum of understanding
- Builds lesson logically and sequentially
- Directs students to efficient strategies
- Models thinking, representing, and reasoning
- Makes sense of mathematical phenomena
- Demonstrates correct use of symbols and algorithms
- Reveals vocabulary and symbols relevant to the material
- Connects mathematics to real world and helps students identify with the concepts
- Uncovers a variety of entry points, strategies, and ways of reasoning
- Helps clear up misconceptions
|Modeled/Shared Math Is….||Modeled/Shared Math is Not….|
|Explicitly planned, well organized, and logically presented in keeping with learners’ maturity and personal experiences. Difficulties and misconceptions anticipated; a variety of strategies planned to differentiate.||Haphazard, unorganized, improvised, and sporadic.|
|Interactive: (a) requiring learners to think, conjecture, dialog, and experiment; and (b) requiring teachers to deviate from the strategy plan in response to learners’ thinking, conjectures, dialogs, and experiments. Learners contribute to the lesson.||Lecture (“Chalk and Talk”) Teacher Centred.|
|Connects new ideas to prior learnings, and connects procedures to models. Helps students make sense of strategies and procedures and where the math content is found in the learner’s social or physical world.||Teaches math as “piecemeal”—a series of discrete and disconnected ideas. Teaches procedures as steps in an algorithm to be memorized and duplicated.|
|Effective when used prior to learners being asked to practice the skill or strategy.||Told, but not followed up with practice, or activities are presented without giving students a firm understanding of themathematics involved.|
|Integrates a variety of instructional strategies.||Teaches concepts one way.|
|Responsive: Uses ongoing formative assessments and check-ins to determine learner readiness for more difficult problems or to work more independently.||Scripted.|
|Brief, engaging, and purposeful.||Teacher talk dominates class time.|
|Demonstrates the strategy, allowing more repetition to students who need it, and allowing alternative challenges to learners who need easier entry points or enrichment. Differentiated.||“One size fits all”, with limited examples, or too much repetition for students who are ready to try on their own, or not enough explanation or support for students who require more.Offers only one level or type of examples.|
Guided math (small group instruction, stations, or PODS or side by side conferencing) is a way of either discovering what needs to be taught, or practicing and reinforcing what has already been taught well. Practicing in a small group allows for a variety of experiences and opportunities for differentiation. Small group instruction may include a “teacher table”, where the teacher can work intensively with a small group of s to differentiate, reinforce, and assess. Guided math may also take the form of conferring with students and providing strategic support or nudging a learner to move to the next level of understanding.
- Whatever stations or activities you choose need to reinforce the math concept being taught in a meaningful way.
- UbD helps us align activities not only with specific outcomes, but specific skills or concepts within the outcome.
- It is not enough for the activity to be engaging—it must also be purposeful and support learning.
- Groups should be flexible.
- Often we create groups based on performance on a pre-assessment.
- It can be convenient to have groups of “like” learners together at times, so that we can target instruction to those learners; however, it is important that our groups change. If learners label themselves they have done more damage to their mindset toward learning than we may be able to effectively recover, even with excellent instruction or intervention.
|Guided Math is Not….||Guided Math is Not….|
|Continually changing flexible groupings to meet the learning needs of learners.||Establishing static groups that remain unchanged.|
|Varying instructional time and content based on learner need.||Each learner receives the same amount of instruction and same task.|
|Culturally responsive teaching based on observation.||One size fits all work and activities.|
|Using a variety of activities and modes of learning to reinforce understanding of math.||Overuse of technology or paper pencil tasks.|
|Rigorous, accountable engaging learning activities.||Fun games that are chosen because learners like them, not because they provide meaningful practice.|
|Learners learning independently, interdependently and collaboratively.||Learners wondering what to do with their time.|
|Learners are clear about expectations. They look for help from peers and have alternative tasks if they are unable to complete tasks at stations.||Learners interrupt the teacher who is at a table with a group, or students sit and wait until their time at a station is over.|
|Learner work samples, notes on conversations, and observations of ability are collected to create a diverseportfolio of learners’ accomplishments.||Learners are not accountable for the learning they do at stations.|
During independent practice a student demonstrates their understanding of the concept by using it independently. During this time, students can be challenging their own thinking and teachers can be nudging them or “What if-ing?” them to delve deeper into concepts of which they have a basic understanding.
Guided instruction and independent practice are interwoven as teachers use this opportunity to gather formative assessment data around the needs of every student at each end of the understanding spectrum. Independent practice allows the teacher to work with small groups for strategic intervention, guided math support, or conferencing with individual learners.
Learners may be at any point in the model depending on their level of understanding and need for support. Learners who are still struggling and needing more support may require more modeled or shared instruction. Learners who are needed occasional nudging or reminders of learned content or procedures may need more shared and guided instruction. Learners who appear to be independent may still need guided support to nudge them and extend their learning to deeper application of their mathematical thinking. A learner who may have been independent in one area, may require more modeled instruction in another. Understanding this model as a gradual release will help teachers to choose the instructional practice that best meets the needs of the learners collectively and individually.