| As a teacher for 11 years and middle-school math | | | | what you thinking including confusion, emotions, |
| teaching consultant, I've seen a wide array of | | | | skills, strategies and more. |
| different math programs and classes. I'm sharing | | | | When you do this, also let your students know |
| here the 10 best teaching tips I've compiled over | | | | how mathematicians think. One piece of research |
| the years. | | | | that is helpful to know is that mathematicians |
| 1. Provide compelling content to study. | | | | spend a long time thinking about how to set up a |
| Years ago, a colleague I was working with said, | | | | problem, a little bit of time doing the problem, and |
| "Maybe class can be fun, but I can't make class | | | | a long time "looking back" by asking the question, |
| compelling. I have to teach math!" It's an | | | | "Does this make sense?' Model that for your |
| assumption worth exploring. | | | | students, by putting up a complex problem on the |
| Take Ron Berger's middle-school math project to | | | | board and spending time not just jumping into a |
| study levels radon in their own homes. Studying | | | | solution, but just talking about what strategies |
| radon is boring. But Berger's class project has got | | | | you might use to solve the problem. |
| to be one of the most compelling projects in | | | | 6. Provide feedback that is immediate, relevant to |
| math class history. What if his students | | | | the task, non-comparative, and leads the way to |
| discovered dangerous levels of radon in the | | | | next steps. |
| homes of one geographic area and published the | | | | Many teachers believe that grading is a form of |
| results as they had intended? What would happen | | | | feedback. It isn't. Grading, when done well, can be |
| to real estate values in that area? What he found | | | | a form of assessment of learning, but the |
| is that students were highly engaged in mapping, | | | | distinction should be clear. Grades are not an |
| taking averages, looking at standard deviations- | | | | effective tool as assessment for learning. Grades |
| students that heretofore didn't care one bit about | | | | are the end of the road, when you assess what |
| radon or the other concepts. | | | | has been learned, but they should not be intended |
| So what's the trick? The trick is that there isn't | | | | to inform a student where to go next. |
| one. You can't trick students into finding | | | | Take, for example, three groups of students who |
| something compelling if it isn't. Take a little bit of | | | | received different kinds of "feedback" on math |
| time to develop a few topics of study throughout | | | | papers they had "turned in." The first group |
| the year that you find compelling- the Economy, | | | | received only narrative feedback (no score) |
| the Presidential Campaigns, the Human Body, etc. | | | | informing them where and how they made |
| Find an authentic way to present your result- the | | | | mistakes. The second group received a grade (or |
| paper, the web, a magazine. Keep the project | | | | score) and narrative feedback. The third group |
| small, authentic and do-able. | | | | received just a grade. Not surprisingly, the |
| Students of teachers that do take this kind of | | | | students who received narrative feedback |
| time have better outcomes on state tests than | | | | improved when re-tested. Those who had |
| students of teachers who only stick to the text. | | | | received only a grade did not have the |
| Almost any social studies context provides a | | | | information to improve, and performed the same |
| backdrop for learning that adds depth. | | | | when re-tested. But here is the surprising part. |
| Even teachers who hold a math "topics" class only | | | | There was no difference between "grade-only" |
| once a month see real benefits, so you don't | | | | group and the group that received the grade and |
| have to abandon your regular class. And, you'll find | | | | narrative feedback. Why? The students who |
| that students are more engaged when regular | | | | received both a grade and narrative feedback |
| class is held. | | | | completely ignored the written suggestions and |
| If you want to go really deep and have solid | | | | only looked at the score. "I got a blah, blah, blah... |
| administrator support, look into the school reform | | | | what did you get?" |
| movement of Expeditionary Learning Schools who | | | | Because we live in a world where grades and |
| have an excellent approach to thematic teaching. | | | | formalized assessments are so important, work |
| 2. Don't use extraneous rewards such as candy, | | | | with the system by differentiating assessment |
| purchase points, stickers, etc. | | | | for learning and assessment of learning. |
| There is nothing more certain than seeing the | | | | When you are grading, one guide is to reference |
| culture of a math class decline over a period of | | | | Rick Stiggins strategies of assessment for |
| years when a teacher bribes them. The intent of | | | | learning. That way, when you are conducting an |
| the teacher, of course, is good. A teacher cares | | | | assessment of learning (i.e. grading), you'll notice |
| about his or her students and wants the very | | | | that you are momentarily stepping out of the role |
| best for them. "I don't care how they learn | | | | of improving a student's learning and won't have |
| math," one teacher said to me. "I just want them | | | | the conflict of trying to do two things at once. |
| to learn it so that they are prepared." The | | | | 7. Change mimeographed sheets to problems you |
| teacher cared enough to purchase candy out of | | | | and your students personally develop. |
| her own pocket, but the real message to | | | | A pervasive aspect of our culture is to give out |
| students is this: the "positive reinforcement" of | | | | page after page of information. In faculty |
| candy means "math isn't worth doing on its own." | | | | meetings, business meetings and conferences, |
| The research is clear on the matter too, and | | | | hundreds of pages of documents are handed out. |
| shows us that extrinsic, non-relevant rewards | | | | It makes us look organized and prepared. It's also |
| hurt learning. | | | | a way to "cover" content. But for a middle-school |
| Even if the effects aren't immediate, over time | | | | math student, it also makes it hard to determine |
| so called "positive reinforcements" like these | | | | what is important. Was it the fractions part? Was |
| mentioned above erode an otherwise high-quality | | | | it the decimals section? Was it the number line? |
| math program. As a teacher, you are much | | | | Was it the triangle puzzle problem? Was it the |
| better off trying to create inherently compelling | | | | cartoon? |
| curriculum than buying candy. | | | | Instead of another mimeographed page, have |
| 3. Build a culture where students teach each | | | | your student write their own story problems. Tell |
| other. | | | | them to add artwork for comprehension. Give |
| For many teachers, one student helping another is | | | | them the latitude to make them fun. Celebrate |
| called cheating. But I actually found that the better | | | | them by posting them in class. Give them 5 |
| middle-school math programs all encouraged | | | | home-made story problems they create for |
| students to team together at certain times | | | | homework instead of a mimeographed sheet with |
| throughout the week. The activities were usually | | | | 30 problems, and really dive into improving them |
| graded as complete or not-complete, and when | | | | through revision. |
| tied to meaningful tasks, such as building a survey | | | | 8. Use story to teach math. |
| together and collecting original data, student | | | | Write a story, a real story with characters and |
| comprehension was greater than on individual | | | | plot, and add the math problem set. Write about |
| tasks. | | | | wizards that need to use angles for their sorcery. |
| Building the kind of culture that works for student | | | | Write about spice trading ships on the deep seas. |
| pairs or groups takes years and lots of practice. | | | | Write a story that lasts a whole page before |
| But before you give up and decide it doesn't | | | | even getting to the math portion. You've engaged |
| work, determine if you are following tips #1 and | | | | the right-side, or less analytical, part of the brain |
| #2 first. | | | | and you'll see a powerful effect of enhanced |
| 4. Give less, but more meaningful work, including | | | | engagement. |
| homework. | | | | 9. Get math tutor volunteers once a week for |
| The Trends in International Mathematics and | | | | two-months before state testing. |
| Science Study labels the curriculum in the United | | | | As a teacher or administrator, spend time during |
| States as "a mile wide and an inch deep." Their | | | | the fall months by planning for and scheduling a |
| review of math texts in middle-school found that | | | | single day each week during the months of |
| some were almost 700 pages long. With heavy | | | | February and March (right before testing) to have |
| pressure to teach to the standards, as a teacher | | | | volunteers come in to teach math in small groups. |
| you might be tempted to skip and jump to many | | | | But what's nice is that if developed correctly, |
| topics throughout the text. Don't. It achieves little | | | | these volunteers don't need to have any special |
| learning. | | | | training in math. |
| Choose the most important pieces before the | | | | Start with a simple plan. Each student has 10 skills |
| beginning of the year, and keep it simple. Teach | | | | they have chosen to work on during the whole |
| the concepts you do teach with depth. | | | | class tutoring session and have written down their |
| The national advisory counsel formed from the | | | | practice problems in class. The phone calls are |
| study recommended "put first things first" and | | | | made, the specific planning with an administrator is |
| suggested that indeed, less is more. Take the | | | | done, and volunteers come in and help the |
| time to cull the curriculum to a manageable size | | | | students answer the 10 questions during class |
| for your students, and present them with only | | | | with support. Schedule tutoring once every week |
| that. If you have to "cover" standards, find out | | | | for two months before testing and see your |
| what standards and document when you indeed | | | | scores greatly improve. |
| teach them in class. You'll find that teaching with | | | | 10. Work with the emotions your students have |
| depth often reaches to a broad array of | | | | for math. |
| standards. | | | | 10a. Ask your students how they feel about |
| It's helpful to know what's driving the breadth. As | | | | math. Use a bit of class time periodically to gain a |
| the national study panel concurs, publishers are | | | | better sense of where they are. And, just let |
| trying to meet demands of hundreds of different | | | | them feel how they feel. If they like math, they |
| districts by including everything that any school | | | | like it. If they are bored, empathize. If your |
| might want. And while publishers have been | | | | students can't stand math, you will gain far more |
| attempting custom publishing, it is just as difficult | | | | ground by seeing their perspective than trying to |
| to create a math curriculum for a small district as | | | | prove they are wrong. As a teacher this is hard |
| a large one. Thus, the challenges of book | | | | because we are so accustomed to trying to "fix" |
| publishing lead to a single, uniformly created | | | | the situation, and of course, our ego is tied to |
| overarching textbook. Often this is a very large | | | | student emotion. If our students are bored, we |
| text or an entire series. | | | | feel like we aren't doing the right thing. But the |
| In the classroom, teachers and students become | | | | larger truth is that there is an ebb and flow in all |
| overwhelmed and unable to handle the scope or | | | | of us for the topics we are learning. When the |
| breadth of learning in this form. As teachers, we | | | | boredom, frustration and negativity does emerge, |
| have to recognize that predominantly negative | | | | try understanding it. Perhaps class does feel a little |
| emotions surround math in middle-school, and that | | | | boring. That's o.k. Sometimes it will. And then |
| anything we can reduce those emotions will go a | | | | slowly, over a period of years, build those |
| long way toward gains in learning learning. Placing a | | | | compelling pieces into your classes so that you |
| 500 page text in front of a 7th grade student is | | | | punctuate boring times with excitement and joy. |
| unlikely to help, so use it sparingly and build little, | | | | 10b. Go slowly. Changing the direction of your |
| home-made notebooks for daily use. | | | | math class is like trying to change the direction of |
| 5. Model thinking, not solutions or answers. | | | | a large ship, especially when dealing with emotions. |
| Don't show a student how to solve something. | | | | Even once everything is place for the changes to |
| Instead "think aloud". For example, you might | | | | occur, you will notice the "ship's" momentum going |
| have a whiteboard with a problem up, and start | | | | in the same old direction before you sense any |
| by saying, "o.k., I notice that the 4 numbers I am | | | | real shifts. This is part of the process. It took me |
| to sum are all in the thousands category, and that | | | | three years to develop a coherent math program |
| the first is near 3,000, the second near 5,000, and | | | | at my middle-school and even then, we |
| the third... I am confused about..." Model exactly | | | | occasionally slipped in to old patterns. Good luck! |