Instead of going over the classroom rules and policies on the first day of each year, I took the time to always do two things. First, I started with a fun problem that showed the beauty, intrigue, and fun of the math I would be teaching that year. Second, I would teach the students how to read a textbook. Yes, I did this at the high school level and in both my Algebra 1 and Pre-Calculus classes.
Some might say I was wasting my time doing this, especially at the pre-calculus level. After all these were almost all Juniors and Seniors who had been reading textbooks for years. Surprisingly enough I had more of my Pre-Calculus students thank me and tell me they had never been shown or taught how to read a math textbook. I realized how many times we as teachers assume that students know how to do the little peripheral skills. Sadly, many times they do not.
Note Taking Skills
Those things that teachers all think, and hope students already know from previous classes are not always there. Some of these items are extremely important and if you do not take the time to address these skills you will continue to be frustrated. For instance. Students taking notes is a good example. If you look at many of your students notes they are more of a transcript of what was said in class rather than notes. No one has ever shown them how to take notes. They assume students already have been shown this before and do not want to take the time to repeat the lesson on taking notes.
I would argue that you can’t afford not to take the time. It is time well spent and will save you more time down the road. There is no one right way to take notes but there are researched methods that will help students improve their skills. A some good examples would be either the “Three Column Method” or the “Cornell Method”. If you take no more than a class period to walk students through either of these methods, while you teach a lesson, not only will the students skills improve, but you will also save time in the long run.
Estimation
An often-overlooked important skill for students to practice and use is estimation. Students do not take the time to make a reasonable guess and have an idea what an answer must be before they start solving the problem. We must show and train students to do this in our classes. You can easily do this by asking a few questions BEFORE you ever ask for or accept an answer from students. Ask questions like: Is the solution going to be larger or smaller? Is the answer going to be positive or negative? Is the answer going to be an integer or fraction/decimal? What would a reasonable answer be between?
By regularly asking your students these questions or questions like these questions before you solicit a solution students will begin to understand the need for and importance of making a good estimate for the problems before you ever start to work the problem. Good estimation skills are invaluable for students. Students need to understand that by estimating solutions before they start the problem may solve the problems without ever working it. This is very true on many of the standardized multiple-choice assessments like the PSAT, SAT, ACT, and many placement tests.
Mental Math
A skill we can all use that will make us better is mental math. I am amazed at how so many people try to use brute force to bludgeon through a make problem. If you use simple skills that can help you do mental math the problems can be so much easier. For instance, if I ask you to add 37 + 45 + 68 + 23 + 55 + 91 + 12 + 89 + 84 many people would start by adding 37 + 45 get an answer then add 68, get and answer and so on and so on. Others would quickly search for and grab a calculator to work this problem.
The reality is it can be easily done using mental math and groups of 10. Look at the one’s digits. Add the 7 in the 37 + the 3 in the 13 = 10 do this and continue to make groups of 10. 5 + 5, 8 + 2, and 9 + 1 so there are 4 groups of ten and a four left over. So, the one’s digit is 4. Then add the ten’s digits similarly in groups of 10. Be sure to remember you have a 4 to carry over from the 4 groups of 10 in the one’s place. 3 + 2 + 5, 4 + 6, 9 + 1, and 8 + 8 + 4 would make two groups of 10. The final answer would be 504. This may look complicated but if you practice, it becomes easier and easier. Try it yourself for 14 + 54 + 83 + 66 + 97 + 26 + 47 + 51 =?
Mental math not only works for addition, but you can use similar methods and do place value multiplication for problems like 57 x 32. Break 57 into (50 + 7) and 32 into (30 + 2) then multiply 50 x 30 is 1500 50 x 2 is 100 7 x 30 is 210 and 7 x 2 is 14 so the answer is 1824. If you know and remember your Algebra 1 and the special cases, you can do some mental math even easier.
Examples of this would be 46 x 54 which would be 2500 – 16 = 2484 or is you or problems like 482 which would be 1600 + 640 + 64 = 2304. I will let you figure out how those both work like that. I will give you a hint: “Perfect Square Trinomials” and “Difference of two Squares”.
Test Taking Skills
I just mentioned “Perfect Square Trinomials” and “Difference of two Squares” which are always on the PSAT and SAT Assessments in some form or another. Test like the PSAT and SAT bring up another topic that has many key skills students should know and use.
Do you talk to your students about test taking skills? It is amazing how many students are counter-productive with their approaches to test taking. They stay up all night and cram for the test. We all know they will do better and be far more productive if they would study for shorter times over a few days before the test and get a good night sleep the night before a test.
Have you mentioned that and talked to students about these facts? For multiple-choice tests do students know to rule out possibilities and narrow the choices down? Are students aware they can plug in answer choices and see which answers make the problem true? Do you talk to students that when they get stuck on a problem skip it move on and come back to it later? How about guessing? Students should attempt and at least guess on every problem.
Who knows if they did get a good night sleep the night before the test their subconscious may help them choose the correct answer. Did they eat a good healthy breakfast or lunch before the test? Did then use good time management skills to help them complete the entire test in the given amount of time? These are all test taking skills we all need to be discussing with our students. They need to hear these important facts over and over again until they internalize them and use them regularly.
Basic Organization and Planning Skills
Another key skill we could all use is basic organization and planning skills. Teaching students to use an electronic calendar or even just a manual assignment log could be a game changer for so many students. When you are young and feel like you are invincible it is easy to get lulled into the idea that you don’t need to write things down because you will remember everything. I wish that were true.
Writing things down not only helps you remember things, but it will also help you organize and prioritize things. Keeping an electronic calendar where you enter the assignment and when it is due will let you easily refer to and determine if the assignment needs to be done immediately or can wait a while. The electronic calendar will even give you a notification when something is due.
Since most students have phone, iPads, smart-watches, laptops, and computers electronic calendars are easily synced between devices and can be accessed from the various devices. I know my electronic calendar has saved me more times than I can count from missing important items I needed to make sure I had completed and ready to go.
How to Stay Organized
Finally, keeping an organized folder either an actual folder or an electronic folder does not matter. Having it organized does matter! A folder is a great place to keep supplies like paper and something to write with, notes, assignments, and the assignment log we just wrote about. Having it organized and grouped together is also very important. I have seen both actual folders and electronic that are in such a state of disorganization they are practically useless.
How you organize them is a personal preference. Organizing them is an absolute must for them to be useful. There have been many studies that show people who are organized are far more productive and far more successful than someone who’s organization is in a constant state of disarray. Having requirements for students to have an organized folder either actual or electronic I feel is a good way to facilitate the student’s success.
If you leave it up to chance and if the students wants to keep an organized folder then you are leaving a possible opportunity for the student to succeed up to chance. I never wanted to take that risk that a student might have been more successful if I had only talked about and required the students to have some sort of folder either actual or electronic.
How to Teach Students to Read a Math Textbook
Oh yeah by the way, I started this blog off by saying I teach students how to read a math textbook. I have been asked by teachers that have wondered how I did that. Here is what I did. I shared with students that we read novels word or word starting at the upper left on the first page and read right to left to the bottom right of the page line by line.
We DO NOT read a math textbook that way. If you are reading a math textbook like a novel for enjoyment, you need to seek professional help and do it quickly! You read a math textbook by just skimming it in the following way:
Look at the Title of the lesson.
Look for any goals and objectives stated
Skim the lesson for all Bold Face, Underlined, and Highlighted words.
Make sure you know what those words mean. If not define them by looking them up in the back of the book or online.
Look at the examples in order. Make sure you understand the steps and processes being shown.
Try some problems (usually odd numbered problems as those answers are most often in the back of the book) and see if you can work the problems correctly.
If you get the problems correct when you checked them in the back of the book you are good to go. You never actually need to read the book word for word like you do a novel. If you are not getting the problems correct when you checked them in the back of the book, then and only then you might want to actually read the entire lesson word for word like you would read a novel.
For most students this means the only look for the Bold Face, Underlined, and Highlighted words. This along with looking at the examples gives the students all they need to know for the lesson. “Reading” a math textbook is more skimming than reading.
Finally, I would demonstrate what I had just showed the students by taking them through the first lesson in the math textbook and following the steps outlined above. That solidified what I had just shown them most of the time and saved many students a great deal of time and effort.
Conclusion
I hope you realize that these little skills and lessons need to be taught at all levels and repeatedly. We cannot assume that students know or use these skills. If a student has already seen and uses these skills, then it will be an easy lesson for them. If a students has not seen these skills or had a lesson teaching these skills, it could make a significant difference to that student and help them succeed. I strongly feel it is not worth the risk of having a student not know and use these skills even if it means a few minutes of math instruction is lost by teaching these skills. I feel the gains far outweigh the losses.
