Clear, accessible objectives support purposeful engagement and progress toward mastery.
Goals are posted, shared and reflected on during the lesson and throughout the course.
Learning outcomes guide support the development of challenging goals that increase rigor and depth of learning for students.
UDL Learning Goals separate the goals and the means to focus on construct relevance to minimize barriers to learning.
Connections to prior knowledge support comprehension, deepen understanding, and increase engagement.
7 Steps for a CGI (Cognitively Guided Instruction)-Inspired Approach to College Mathematics
Introduce concepts through meaningful problems.
Start each new topic with a real-world or discipline-relevant problem that engages students and reveals their prior knowledge and thinking.
Anticipate student difficulties.
Identify potential misconceptions or challenges students may encounter as they tackle the problem, so you can prepare targeted support.
Design guiding questions.
Develop questions that help students reason through obstacles without giving away solutions, promoting deeper understanding.
Observe and probe student thinking.
As students work, listen and ask questions to uncover their reasoning, strategies, and conceptual understanding.
Document understanding and misconceptions.
Record observations to inform follow-up instruction, formative feedback, and curricular adjustments.
Have students share and compare strategies.
Encourage students to present their approaches, starting with simpler methods and progressing to more sophisticated reasoning.
Facilitate reflective discussion.
Lead a discussion analyzing the strategies used, highlighting connections, and emphasizing the mathematical ideas and reasoning that emerged.
Structured discussion helps students articulate and refine reasoning while building understanding and collaboration.
Peer collaboration with random groups (Flippity Random Name Generator)
Peer discourse with short frequent opportunities for think-turn-talk
Talk moves Simple moves for discourse, "Math talk", Five talk moves
Building community norms: Shifting mathematical authority, Classroom norms, RUME classroom authority
Productive struggle fosters persistence, deep understanding, and problem-solving skills.
What is productive struggle? Teacher shares experiences; NCTM Talk
Scaffolding questions guide reasoning while supporting engagement, persistence, and independent problem solving.
Starting with inquiry allows the professor to understand the students' thinking, diagnose misconceptions and offer the next piece of feedback to support mathematical learning. Honing your practice around these 100 Mathematical Questions that Promote Discourse can support students' path to understanding.
Timely feedback supports reflection, reasoning, and sustained understanding.
Digital collaboration platforms that allow instructor to monitor progress and/or provide immediate feedback (e.g., Amplify Classroom [formerly Desmos Classroom], online homework systems)
Provide access to problems with worked solutions for students to check their work.
Allow students to submit requests for problems to be modeled during classes or seminars prior to the class so they can receive feedback and guidance by design.
Support prompting with AI as a math coach.
Peer support fosters collaboration, understanding, and confidence through guidance and modeling.
Make opportunities for office hours, peer tutors, and campus support clear and accessible in the syllabus and revisit throughout the course.