Algebra is an eminently useful endeavor and a fun (I know I’m a nerd) way to spend time. However, few pursuits offer the variety of potential mistakes that algebra does. I am far from mistake proof in my algebra doings, but I am much better than I used to be. Here are some tips I’ve gathered along the way to reduce stupid mistakes:
- Algebra typically involves doing a lot of calculations. Therefore, the probability of making a mistake is higher. Train yourself to pay attention to every detail–both in the given problem and when solving it. I cannot tell you how often I’ve pulled my hair out because my solution didn’t check, only to eventually figure out that for some reason my brain insisted that 3 + 4 is 12. I mean I could tell you. Never once did I actually pull my hair out. I feel that I may be losing my point here…
- If a problem seems unreasonably difficult, or if it gives some long-winded decimal expansion when you were expecting an integer, check to make sure you’re working on the given problem and not some transcription error (i.e. you copied the problem incorrectly when transferring it to your notebook). If the problem on the test has a minus sign, but the one you’ve been working on the last ten minutes has a plus sign, then you should feel silly.
- For problems with a lot of computation (e.g. factoring large polynomials), it is important to have a clean and organized solution system. That way you can quickly and clearly see how each step progresses, and you can check your work at each step since checking the final solution might take too much time.
- Draw a box or circle around your solution as soon as you write it down. That way, if you check your solution by writing calculations underneath your solution, you’re not as likely to accidentally write the wrong thing onto the test paper.
- When checking your solution, always check against the one given on the test (not the one you wrote on scratch paper) just in case you transcribed the problem incorrectly when transferring it to your scratch paper.
- Always check your solutions! You may think you know what you’re doing, but sometimes you don’t. Trust me!
- Every time you make a mistake, get to the bottom of it. Were you careless? Were you not paying attention? Do you not understand the material? Vow never again to make that mistake.
- …and of course, always check to see if your answer can be simplified or factored further.
Do you have any tips on avoiding mistakes that I haven’t covered? Please let us know!