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Wednesday, August 30, 2017

How To Teach Math?

There are apparently so many good ways to teach math. I'm still thinking about the great conversation I had with a colleague last night about math education. As we spoke, I wondered how I would meld all the good math teaching techniques I've experienced over the years. Then when I woke up this morning, the ideas had solidified somewhat into this laundry list of math teaching techniques, techniques from multiple sources.

Introduce the Unit
My colleague noted that American math books are too thick, and our Middle School teachers make small booklets for each topic. The booklets provide students and their families a handy resource of the standards, essential questions, vocabulary, and practice exercises. It's a good go-to book for referral, practice, and study, yet it's not too big and overwhelming. I will use this approach for each unit.

Provide Context
Research I've read and my own experiences point to the need to provide context and meaning for each unit. Hence, the start of each unit will provide context led by the question, Where does this math concept, knowledge, and skill fit into the real world?

Break Apart the Standards
Years ago at a great professional learning event, a California curriculum leader showed us how to break apart the standards. Hence I'll create lessons based on each section of each standard with a focus on the important verbs, words, skills, and concepts.

Visual Models
We know that learning and understanding profit from visual models. We learn much more quickly through a visual model than a host of words. Hence I'll match a simple visual model with each concept we're learning. 

Less Talk
One area which may be obstructing our most challenged grade-level math learners, learners who often face issues of special education, English as a Second Language (ELL), socioeconomic issues, and more, may be the fact that there's too much language involved in each lesson. By lessening the language (teacher time) and increases the collaborative, practice, and student time, we may help those students grasp the topics better and succeed more.

Sufficient, Scaffolded, Varied Practice
Students need to have the opportunity to practice concepts in a variety of ways. I'm imagining a practice sheet that begins with the main concept with a visual model, simple explanation, and main vocabulary words. Then practice that scaffolds from simple to more sophisticated to enrichment. 

Practice with Peers
We know that students learn more when they are able to work with others, use language, and help one another. 

Online and Offline Practice
Using our hands to write is associated with good learning, so we want to make sure we have paper/pencil practice. Also the quick feedback of online math practice sites and the ability to quickly look up confusing concepts with what Friedman calls, "intelligent assistants," is very helpful. Thus a blend of online and offline practice will help.

Regular Simple Assessments
Simple assessments on a regular basis ask students to "show what they know" in an independent fashion, and then these assessments provide teachers a chance to evaluate student mastery related to concepts.

Mastery
Saul Khan encourages us to help students learn for mastery. So the goal for every unit and concept is to master each essential standard. We need to help students create and utilize positive learning paths to mastery, paths that include a good introduction, context, visual models, vocabulary, scaffolded online/offline practice, collaboration/share, assessments, reflection, revision, and enrichment.

Teaching All Students
Summer reading makes me question our efforts to separate students by ability. The reading about teaching all students and elevating students' progress suggests that we should make sure that we teach students about mindsets and behaviors that matter when it comes to teaching well. We should also present similar concepts to all students, and coach all students to mastery.

Positive Self Talk
SRSD, self regulation strategy development, or simply known as positive self talk works. Students need to understand this, teachers/parents need to model it, and then students have to utilize positive self talk to learn well.

Online Learning: Symphony Math, Khan Academy, Ten Marks, Flocabulary, and That Quiz
These sites are available to support student study, and we will immerse students into use of these sites to assist, develop, and forward their learning with grade-level standards, foundation skills, and enrichment.

Floor-to-Ceiling Explorations/Teach to Learn
Students will engage in floor-to-ceiling explorations, and then they'll teach the class what they learn from these standard-based explorations. We know that the best way to learn a concept is to teach it to others. 

Unit Assessment
There's a unit assessment for each unit, and we will teach students how to use the student packet to study for the unit. Unit tests will be evaluated by teachers, and those that don't achieve well will be coached more in an effort to reach mastery.