What is Scaffolding?

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Karen Wootton, Director of Curriculum & Assessment, karenwootton@cpm.org

Last year, a tweet came to my attention when it made the rounds in the Twittersphere:

It made me wonder what most teachers think scaffolding is. Would most agree with the tweeted definition? Or would some define scaffolding with something more specific and concrete?

So I posed the question on social media: What is scaffolding? Before you read some of the responses, answer this question yourself.

Here are some of the answers:

“Structuring problems to build on one another.”
“Providing supports a student needs to do the task.”
“Unfortunately, it can be and often is a way to help struggling students pass without understanding what’s going on.”
“It is an attempt to structure and sequence the learning; the attempt is to make the learning easier for the students. It is the exact opposite of [Jo Boaler’s] rich problem and group based math learning techniques. It is an attempt to do the student’s thinking for them.”
“I think that is how we usually see scaffolding implemented, but ideally supports (i.e. clarifying, probing, or extension questions) should strive to avoid taking over student thinking.”
“Enable students to access higher concepts, like allowing student who struggle with times tables to use calculators so they can interact with proportion/percent/probability ideas.”

Each of these responses helped me think further about scaffolding, and I have tried to come up with a way to describe it so that scaffolding makes sense and is easier for everyone to understand. Because scaffolding is a building term, it makes sense to continue with that analogy.

Imagine that a student is seen as the builder of his or her own knowledge. The student builds this knowledge structure in a number of different ways: through play, conversations, actions, practice, etc. Everything the student does helps to build the structure.

Sometimes the building process becomes difficult, and the student might struggle to continue with the building. At that point, it might be helpful to the student to have support, without taking over and finishing the building for them. Maybe the student just needs another hand to hold something in place. Another time the student might need a platform to allow them to reach higher. Maybe the student will help someone else build their structure and learn from that experience. No matter what the reason for the support, we should understand that the goal is for the support to be temporary. Once the support has done its job, the student can continue to build upon what they learned while the support was in place. It is also important to note that just as scaffolding does not take the place of the building under construction, scaffolding should not take the place of the student knowledge under construction. The student still needs to work, and the cognitive demand should not be lessened because of scaffolding.

In working on CPM’s intervention course, Inspirations & Ideas, numerous times the writing team struggled with the amount of scaffolding the materials should provide. A guiding principle for the team is this notion: You can always provide further support, but once given you cannot always remove what was given. The writing team made the decision that most of the student support would not be in written form in the student text, but rather, the teacher materials would provide suggestions on how to support students in order to encourage productive struggle. The teacher materials offer pocket questions, suggested Study Team and Teacher Strategies, manipulative use, plus more, to scaffold (that is, support) student learning. The use of all of these supports are at the discretion of the teacher, who can add more if needed. Scaffolding does not need to be written, but can occur through questioning, explaining to others, or by using manipulatives.

Every teacher should have an arsenal of ways to support student learning at their disposal. These scaffolds can take many forms, but with any form you choose, start with the minimal amount of support necessary. Remember, you can add, but you cannot subtract.

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Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

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Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.