Building Capacity To Foster Mathematical Habits of Mind

How can educators who are committed to a classroom culture that is centered on mathematical thinking (the heart of the CCSSM) improve their instructional practice?  We believe that supporting teachers to scaffold and facilitate, without enabling, is empowering for both the students and the teacher.

Despite the contentions surrounding accountability and standardized testing, putting student learning first, raising the bar, and providing access to best teaching practices are not controversial. Furthermore we need to prepare students. We're reading how "PARCC testing begins December 2014" and "SBAC will be implemented 2014-2015"

Considering these quotes from a recent Hechinger Report post:

"Many in the world of math contend changing how teachers organize their lessons and lead their classrooms is essential to making a difference."
“We don’t have an achievement gap in this country,” said Leinwand [Steven Leinwand, principal researcher at the American Institutes for Research’s Education Program]. “We have an instructional gap.”
“I, we, you sometimes makes sense,” said Leinwand. “But sometimes teachers need to turn it on its head with some version of you, we, I. That requires students to struggle, explore, share, justify, compare and debrief.”

How do we make math problem solving, critical thinking, and student learning self-directed, not necessarily adaptive? How can we genuinely encourage students’ engagement in the mathematical practice standards?

Thinking this way, we thought it would be interesting to view elements of Achieve’s EQuIP math rubric, I. Alignment, II. Key Shifts, III. Instructional Supports and IV. Assessment, through the lens of our app. We believe CueThink allows teachers to turn traditional instructional models “on their head”. 

I. Alignment to the Depth of the CCSS

"The lesson/unit aligns with the letter and spirit of the CCSS: Standards for Mathematical Practice that are central to the lesson are identified, handled in a grade - appropriate way, and well connected to the content being addressed."

CueThink’s platform provides students with opportunities to make sense of problems and persevere (Math Practices 1 and 3).  Once student work is submitted, teachers and peers can review and critique (Math Practice 3).  

II. Key Shifts in the CCSS  

"The lesson/unit reflects evidence of key shifts that are reflected in the CCSS: Focus, Coherence, and Rigor...Rigor: Requires students to engage with and demonstrate challenging mathematics with appropriate balance among: Application, Conceptual Understanding and Procedural Skill and Fluency."

Rigor doesn’t mean harder! Our model problems are rich, relevant, and engaging.  They provide the opportunity for deep discussion and learning; in many instances the actual “question” could be open ended and allow for multiple solutions.  We also suggest extensions or modifications for accessibility without compromising the mathematical learning objective.


III. Instructional Supports

Engages students in productive struggle through relevant, thought-provoking questions, problems and tasks that stimulate interest and elicit mathematical thinking.
Provides appropriate level and type of scaffolding, differentiation, intervention  and support for a broad range of learners.
Recommends and facilitates a mix of instructional approaches for a variety of learners such as using multiple representations (e.g., including models, using a range of questions, checking for understanding, flexible grouping, pair-share).

CueThink’s platform fosters productive struggle and perseverance with appropriate scaffolds, allowing opportunities for all levels of learners.  The four phases of problem solving establish a common structure and language. Our platform brings problems “off the page” with rich prompts, entry points, and flexible transitions. The gallery is a collection of student work showcasing multiple strategies solutions and representations.


IV. Assessment

"The lesson/unit regularly assesses whether students are mastering standards-based content and skills:  Is designed to elicit direct, observable evidence of the degree to which a student can independently demonstrate the targeted CCSS."

CueThink’s platform captures all aspects of the student’s problem solving process, including omissions, and provides opportunities for metacognition.  By making student thinking visible, teachers gain valuable formative insights and students are able to reflect metacognitively.

Taking this one step further, we looked at some EngageNY resources which are aligned with the EQuIP rubric. We feel that that CueThink would be an asset for implementation, most specifically in supporting classroom strategies (section III of the rubric). For example:

Facilitating productive struggle, fostering mathematical discourse, [and] creating climate and culture for multiple strategies and solutions.
Capturing student work to assess student growth and reflect on best practices.

What implementation challenges are you facing in your classroom?  What are you looking for to support problem solving and critical thinking? Our mission is to empower learners to see problem solving challenges as opportunities, and we want to hear from you!