The philosophy of teaching mathematics at Grace Prep is embedded in our unique 20 points of effective mathematics teaching.
- Start class with a warm-up set of review or SAT problems. Give them opportunities for success right when they walk in the door.
- Introduce new content with real-life and realistic contexts whenever possible. Students need to be able connect the idea with their reality. Learning about linear equations is more connected to their reality when it involves cell phone bills than y = mx + b.
- Ask questions that make them think. These should be interspersed throughout your lesson. Never accept an answer without justification. If I say “15” you have no idea how I got there or what I am thinking. Ask them “Why?” “Can you explain?” “How do you know?”
- Never lecture on a new concept/skill for more than 15 minutes. Think about it! When was the last time you paid attention to someone talking for more than 15 minutes? That’s what I am talking about! Get them moving and change the pace especially in a block scheduling environment.
- Give them mini-quizzes to assess their understanding as you teach. You should be able to convince anyone who asks at the end of the period not what you taught that day, but what students learned. This should help inform you as to the quality of your instruction and what you need to re-teach.
- Write on tables when possible. Watch the interaction between students as they work on problems. You will be amazed.
- Learning is incremental. When you introduce a new skill limit the variations that you discuss on a particular day. Help them be successful early, review it, and then increase the variations at a later date. Space learning out over time.
- Don’t follow the book. Who thought of this order anyway? Skip around to topics that are not connected, but that students have the prerequisite information to be successful. Why? Many ideas in chapters are connected to other ideas in the same chapter if you haven’t mastered those ideas how are you going to have success on the next section that requires that you mastered the previous section? Not rocket science here!
- Have ice cream, make pancakes and order pizza once in a while. It tastes good and there are many mathematical ideas embedded in these things. Help your students discover them. Think of other ways to pull mathematical ideas from interesting, everyday stuff.
- If you present an idea that can be shown in multiple representations then show them the idea in those representations. The mind’s eye needs to be able to see those connections. Remember tables, graphs, charts, and equations. If it can be done in these representations do it.
- Don’t give chapter tests. Assess them when you think they are ready over a set of outcomes. Make it cumulative. Hold them accountable for learning, not cramming.
- The measure of good teaching is not only about the questions you ask, but how you respond to the questions they ask. Give them permission to ask the “What if” questions. Let them be inquisitive.
- Homework should be about reviewing skills and concepts and “doggy paddling” into the waters of new skills and concepts. It should not require them to swim the length of the pool. Save the harder questions for class time where they will have the time to get feedback and hints. Think of yourself as the “floatie”—you are there to prevent them from drowning!
- Ask hard questions that involve critical thinking. Make them take what they have learned and extend it or connect it with other ideas. Think hard about what this means.
- Use technology where it enhances learning. Does it allow you to generate numerous examples for conjecture? Does it allow you to see an idea across multiple representations? Does it allow to minimize focus on computation and maximize focus on the concepts you are trying to help them understand?
- Focus on the language. Just to get an idea. Videotape one lesson of yourself teaching. Now list all of the vocabulary that you used. Were you clear in the vocabulary that you used? Were there key terms that you assumed students knew? List out all these terms and the next day go back and review the vocabulary. You might be surprised.
- Collect data whenever you can. Make it fun and make it real. See how many jumping jacks your students can do in a minute. Wear them out and then teach them.
- Minimize what is not important. Cut the breadth down and dig deeper. Always ask, “So What” or “What does this buy the student?” Do I really need to know how to rationalize the denominator? Really! Are we still in the 20th century? Think hard about what matters.
- Build meaning of symbolic representations whenever possible. Focus on the operations and order when talking about algebraic rules. Hammer this home! There is no distributive property of exponentiation over addition (aka “the bonehead property”)
- Remember you are teaching mathematics because you were good at it and more than likely you have a dominant logico-mathematical intelligence. Most of your students, except for the ones who bring you apples, do not have this as their main mode of intelligence. Design instruction to embrace these other forms of intelligence. Look up Howard Gardner if you need a refresher.