Learning & Teaching Tips
It’s a good idea for students to write out Math/Arithmetic problems in ink rather than in pencil. If students make a mistake, they can cross through the line and move on. But this way, the student (and anyone helping them--parent, teacher etc) can go back and look to see where a mistake was made. Seeing what was done wrong is a very big help to teachers in grasping how the student is thinking and where their logic is wrong, so it can be corrected. Without a doubt, students' mistakes are their best learning tools!
It’s good to space out lessons so there is constant review, rather than covering using a full block of time to cover only one topic. In classes, students often cover one topic one day, and go on to another the next day—-or week. Retention and understanding are both vastly improved when teachers move back and forth between different ideas, giving the material time to "sink in.” This requires some organization on the teacher’s part, and it can be challenging for students as they are forced to integrate all the different mathematical processes. But the payoff in greater understanding and retention makes it more than worthwhile.
Research in Education backs this up but it’s still an approach that isn’t used as much as would be helpful, probably because it’s somewhat less convenient. Even the simple act of making every test or quiz include a few “old” problems from previous chapters/units, would go a long way toward helping students. And that is something easy for teachers to implement. It would at least push students to review previous topics of study before each exam.
Whenever possible, using humor and/or the arts can help make classroom lessons more memorable and fun. There are well-known rhymes and chants that have helped children memorize things, and make learning fun, such as learning the alphabet song. Or think of this one: “Thirty days has September, April, June, and November; All the rest have thirty-one” (though February is an exception). Or this one: “ i before e except after c or when sounding like a as in neighbor or way.”
Here is a funny story: My last name is also an exception to this rule. Bernstein is spelled with the e before i. Years ago, I discovered one of my children was spelling his own name incorrectly, and it hit me that he might be thinking of the “i before e rule!” :)
Students have to learn a lot of facts in school, from their multiplication tables to the laws of physics, etc. But thinking up a way to put them into verse can be a lot of fun. Once that is done, the facts/formulas etc are easily and pleasantly committed to memory.
In addition, "Arts Integration" programs that use music, dance, or other arts in the curriculum are great for incentivizing students. There are some very unique Arts Integration programs for Math that can be run as a fun exercise in applying Math principles. Readers are encouraged to ask me about these programs—which I’m happy to run
When students do math problems, they often apply formulas they have learned. There are formulas for areas and volumes, finding x in a quadratic equation such as the one shown below, etc. Here is a tip for taking exams when a student has a variety of equations to apply to a problem set. Before looking at the exam questions, turn over the back of the exam paper and write down all the equations that had to be memorized. This tends to make students feel relaxed, as they know they won’t forget or block on a formula. Then as they work through the test questions, they can turn over the exam paper and choose the equation that applies to each problem.
Thinking of what formula applies to a problem is much harder and can cause considerably more stress without such a list to look at. This is because without a list, the details of the problem tend to “crowd” the student’s thinking and make it harder to remember all the formulas.
