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Learning Progressions

An Introduction

The following documents have been created as a resource for classroom teachers, math interventionists, and special educators who are creating learning opportunities for their students to achieve the concepts targeted by the HLCs. These learning progressions are specific to the grade level All Learners Network HLCs.  They do not attempt to include all of the concepts that students are introduced to and practice at individual grade levels. We would encourage teachers to investigate the Common Core State Standards for Mathematics, Achieve the Core’s Coherence maps, among many other available resources to find learning progressions for all the grade level standards.

The HLC Learning Progressions identify developing stages along a continuum of concepts, models and skills that lead toward student understanding and application of the HLC. Teachers can intentionally plan lessons based on where a student or students can be placed on the learning progression to help him or her move forward in their learning. These learning progressions are not meant to be used as a checklist.  They should be used as reference points to highlight students’ progress toward conceptual understanding of grade level mathematics.

The learning progression documents are formatted to show increasing complexity from top to bottom and from left to right. The concepts in each row are sequential and provide a progression of how we believe students develop the high leverage concepts at each grade level.  It is important to note that the format does not represent the amount of time necessary for each student to build understanding of the concept. Students will make progress through the learning progression at his or her own pace through the support of targeted learning opportunities provided by the classroom teacher, math interventionist or special educator.

We encourage teachers to read  HLC Learning Progressions from previous grades to highlight some of the prerequisite concepts.  Knowing the previous grade concepts and helping students make connections from prior knowledge to learning a new concept is critical.

The High Leverage Assessments can help identify areas of strength and areas of need and therefore support the design of instructional strategies.

Finally, there is a common thread throughout all of the Learning Progressions - the use of models.  Students should have access to and use of models daily and in all activities which support learning the high leverage concepts, in fact all mathematical concepts. Models support students when building conceptual understanding of important mathematical ideas. Please take the time to review the suggested Models for Intervention and Models for Instruction detailed in the HLC Maps.