Concept Based Mathematics by Paige Goren-Levithan

Strategy 1: Create a Social Learning Environment

pgorenle — 2025-02-14 00:07:16 UTC

Social interactions are an integral part of each day. In a collaborative environment, students participate more in discussions and are given opportunities to give more reasoned explanations. They use mistakes to improve understanding. They learn to listen and reflect on the ideas of others and dialogue in the language of the discipline. They develop mathematics fluency.

Strategy 2: Provide an Open, Secure Environment to Allow for Mistakes as Part of the Learning Process

pgorenle — 2025-02-14 00:10:10 UTC

Efforts and mistakes are important stages of learning. Our brain grows and develops when a mistake is made and corrected. It is important to encourage mistakes in a safe, secure environment. Fight stereotype threats that only certain people can do math, as everybody can do math with hard work, practice, and good facilitation.

Strategy 3: Use Appropriate Levels of Inquiry and Employ Inductive Approaches to Develop Conceptual Understanding

pgorenle — 2025-02-14 00:13:24 UTC

Concept-based math lessons provide a clear path from the facts and processes to conceptual understandings. Lessons should accommodate opportunities for learners to take different lines of inquiry. Provide opportunities for students to discover generalizations—statements of conceptual understanding—by utilizing the inquiry continuum and inductive approaches.

Strategy 4: Reduce Whole Class Teacher Talk Time

pgorenle — 2025-02-14 00:16:52 UTC

Students should be able to engage in the lesson from start to finish. Lessons are best in 15-20 minute increments or segments because it is the optimal time for working memory to be able to focus and retain learning in adolescence. Therefore, 60-minute lessons should be broken into three parts.

Strategy 5: Cater to Everyone in Your Class; use Differentiation Strategies

pgorenle — 2025-02-14 00:19:00 UTC

1. Content: In mathematics, differentiating content involves giving tiered tasks of varying levels of difficulty and allowing students to choose entry levels.

2. Process: Differentiating the process implies that the learning outcomes are the same, but students are given a choice of process during the learning experience.

3. Product: The product is what a student essentially produces at the end of a unit to demonstrate mastery of the content.

4. Affect: Affect refers to the ability to move emotionally or touch your students' feelings.

Strategy 6: Assessment Strategies

pgorenle — 2025-02-14 00:21:24 UTC

Diagnostic (pre-assessment) and formative assessment strategies can be used before, during, and at the end of the lesson or even at the end of the topic or unit. Assessing constantly the level of mastery though many different methods will give the best results as to where the students are in levels of mastery.

Strategy 7: Be Purposeful When Asking Students to Answer Questions; There Is Safety in Numbers

pgorenle — 2025-02-14 00:25:10 UTC

"hands up" can let quieter kids take a step back and not participate, letting more outspoken students carry the lesson. Random calling also runs the risk of calling on a student who does not know the answer and embarrassing them publicly.

"thumbs to chest" or "think, pair, share" are two options where the students have time to think and complete things individually but also communicate with their teachers discreetly.

Strategy 8: Flexible Fronts: Arranging Your Classroom

pgorenle — 2025-02-14 00:27:21 UTC

Structuring the classroom so there is no front and back is a great way to integrate the teacher throughout the class and foster a room full of collaboration. Flexible fronts! Structure your classroom so the teacher is integrated in the learning and acting more as a “guide on the side” and a “meddler in the middle” rather than a “sage on the stage.”

Social Beings

pgorenle — 2025-02-14 00:35:01 UTC

Employers value people who collaborate well with others because solving problems and creating new ideas is enhanced when multiple minds and perspectives interact. Creating a learning environment that engages group and individual intellect and promotes learning from different angles.

Michael Swan of the University of Nottingham

pgorenle — 2025-02-14 00:39:55 UTC

Swan has developed many strategies to encourage collaboration in the mathematics classroom. In his research paper Collaborative Learning in Mathematics (2006a), Swan says, “Traditional, ‘transmission’ methods in which explanations, examples, and exercises dominate do not promote robust, transferable learning that endures over time or that may be used in non-routine situations. They also demotivate students and undermine confidence. In contrast, the model of teaching we have adopted emphasizes the interconnected nature of the subject, and it confronts common conceptual difficulties through discussion.”

Tuned out?

pgorenle — 2025-02-14 00:41:37 UTC

After 15-20 minutes, students usually tune out, zone out, or completely shut down. Thomas Warren-Price (2003) concluded that less TTT resulted in more student autonomy. Reducing TTT will encourage student-centered learning and engagement and reduce the risk of students’ inattention.

Sternberg’s and Grigorenko (2000) tri-mind strategy

pgorenle — 2025-02-14 00:45:21 UTC

Students are given the same learning outcomes but three different ways to approach them: analytically, practically, or creatively. This tool supports differentiation of different thinking styles in your classroom.

Giving Students Choice

pgorenle — 2025-02-14 00:47:56 UTC

-Allow students to practice the understanding of concepts through different mediums, such as practicing problems through computer games, using manipulatives to complete a task, or working in small groups

-Give students a choice whether they would like to attend a mini workshop with you to clarify conceptual understandings

-Allow students to choose from a variety of different tasks offered

-Allow students to choose whether they need to watch a video to support learning

"Layered Curriculum"

pgorenle — 2025-02-14 00:53:03 UTC

Nunley (2004,2006,2011)

1) Students should be offered a choice to provide differentiation

2) Students should be held accountable. Grade points should be awarded for the actual learning of an objective or the acquisition of a particular skill rather than for completing an assignment or for practicing a skill.

3) Students should be encouraged to do more complex learning by dividing the instructional unit into three layers. Basic route, application and manipulations, and critical analysis.