Welcome! My name is André and I help students succeed in math, from pre-algebra to calculus. If you're in the Coachella Valley, we can meet in person. Here are some of my best ideas to help students improve their confidence and grades. You can reach me at:
Success in math comes from three main factors: knowledge, habits, and mindset. When we get stuck solving a problem, a lack of knowledge is often the cause. In this article I’ll explain how we can get ourselves unstuck so we can get back to solving problems again. And of course, the more problems a student solves, the better their confidence and grades.
When a student gets stuck solving a problem, they have a math gap.
So, what exactly are math gaps? They are the missing parts of a student's knowledge preventing them from finishing a problem. If you've ever gotten stuck or felt lost, you know the feeling. Momentum comes to a halt, which frustrates most everybody. Instead of giving up or skipping the problem, we can figure out what we are missing.
Here's one way to repairing math gaps: I start by finding out what missing concepts are needed. Asking an educator or knowledgeable classmate what you are missing can often point you in the right direction.
Once you identify the missing concept, you can begin the repair process. I recommend solving a handful of problems to get students back up to speed. I find it a good idea to set aside a half hour or more to relearn the missing concepts.
Here's the big take-away:
1) Acknowledge when you get stuck that you likely have a math gap.
2) Set aside some time to find and relearn the missing concept.
a) Solving atleast 3 to 5 problems tends to be a good start.
Yes, you will find small and large math gaps along the way. Please be patient with yourself. It takes time and effort to relearn topics, practice the necessary problems, and integrate it back into your current math skills. Just know that when you tackle your math gaps as soon as you find them, homework and tests get easier.
Whether we get our homework from a textbook, worksheets, or an online site, the most common approach is to dive right in. But this often backfires when the assignment gets difficult faster than we can keep up. My approach reduces this struggle by solving a handful of warm-up problems first. Students can then complete their homework with less frustration and earn higher test grades.
If you get stuck with your homework, I recommend this:
Try solving some example problems on paper.
It may be tempting to skip them and plow through the assignment. However walking through the examples can give us crucial insight with tougher homework problems. Here's why. Examples tend to be simpler versions of homework problems. This allows us to more easily learn the new concepts. They also contain step-by-step solutions along with explanations. By comparing your approach to theirs, you can correct any misunderstandings much quicker. Then it becomes easier to earn right answers on the rest of your homework. If your assignment has no example problems available, try looking online for similar ones to solve.
Re-solving example problems on paper.
For more difficult topics I will also solve the beginning problems for any new sub-section of exercises, such as 1, 3, and 5. Since they are usually the easiest, I can establish early wins and boost my confidence for the rest of the homework. Also, most textbooks provide answers to the odd-numbered exercises in the back. Solving these allows me to compare my answers with theirs to see if I'm still understanding the lesson. And when I get a wrong answer, I can use this feedback to untangle any incorrect thinking. For those who don't have access to answers, I recommend answer-checking any questionable results.
Yes, this pre-homework protocol can take anywhere from 10 to 20 extra minutes. However it will skyrocket your ability to complete the rest of the homework. So when it comes time to take a test on the material, all those easy wins will contribute to better test results too. And from what I've seen, students who get into the habit of turning in finished homework tend to get the grades they want.
To recap:
1) Try solving the textbook's example problems on paper.
2) Aim to solve the first few problems of any assigned sub-section.
3) Correct any mistakes after comparing your results with the published answers.
Few students find anything as stressful as taking a math test. Solving problems against the clock can frustrate even the most prepared test-takers. I have found the following strategies reduce stress and raise scores:
Complete the practice test with a timer.
If your teacher usually gives a 50 minute test, then set that for the timer. The closer you treat it to an actual test, with no breaks or interruptions, the more relaxed you will feel during the real one.
When time is up, I recommend grading all answers using the attached answer key. This self-graded score gives a rough idea on how you'll do for the upcoming test. To do this, let's tally up all the points scored and divide by the total worth of the test. If I score 62 out of 80 possible points, then 62 / 80=.775 or 77.5%. Consider putting aside any feelings of discouragement if you scored lower than expected. The rest of this article provides tips to help raise your score, no matter how you performed.
Now it's time to improve our score. We do this by creating a personalized study guide. Circle all problems that took too long to complete, got skipped, or answered incorrectly. These will be the center of your re-studying efforts. If some of them felt too difficult to solve, then find 1 to 2 easier textbook or worksheet versions to help ramp up your skills. For example, let's say a student couldn't solve 4 problems from the practice test. I suggest they aim to solve 4 to 8 slightly-easier practice problems. If you still feel stumped, then it's worth asking for help from an educator or knowledgeable classmate.
Do you want to skyrocket your test results even more? Then it's worth retaking the practice test again the next day, to see how you've improved. Why again? Because chances are, you have forgotten exactly how to solve those problems. So the practice test can still challenge you enough to improve your skills one last time. Following this approach in it's entirety, for all practice tests (even for SATs or GMAT practice-tests) can raise your test results atleast one letter grade, if not higher.
2 or more days before the test:
a) Take a timed practice test, then grade it.
b) Assemble a study guide based on all the skipped and wrong-answered questions.
c) Figure out how to solve them, using your answer key, notes, and textbook examples.
1 or more days before the test:
d) Retake the timed practice test, and grade again.
e) Consider solving other textbook problems that look similar to the test questions. Overworked teachers love using ready-made problems.
f) Get a good night's sleep. Leave the cramming for those who mis-manage their time.
“Did I get the right answer?” We’ve all asked ourselves this question. But how can we know for sure? It turns out that feeling unsure can have a big impact on our self-confidence. I'm here to say there’s a way out of the fog: Answer-Checks. It’s a powerful enough habit that those who use it for their homework can attain the highest levels of success in math.
Answer checks give students a clear view into how they are doing.
Personally I like instant feedback. I want to know right away if my answers are correct or not, so I can fix any errors in my thinking. This is especially true when the homework has no answer keys from online assignments, worksheets or even-numbered textbook problems. This is why answer-checks are such a crucial learning tool. They give students a clear view into how they are doing. So there is little need to rely on answer keys, comparing results with classmates, or waiting for teachers to return graded work several days later.
Below I've listed five methods for checking one's answers. Some are quicker than others in certain situations, so I recommend familiarizing yourself with each. This way answer-checking becomes a tool for insight rather than a drain on your time.
1) Solve a problem two different ways. Most any math problem can be solved atleast two ways, if not more.
Two different ways, same answer.
2) Convert an answer back to the original problem. Great for shorter problems.
Notice how the answer-check matches the original problem.
3) Plug the answer back into an equation. Our answer is correct when both sides of the equation match. Perfect for algebra problems.
Both sides of the equation match (13=13).
4) Use approximations to compare a problem with the final answer. This works well on problems involving decimals such as fractions, square roots, exponentials, logs, and trig functions.
When the decimals match, the answer is correct.
5) Insert a value into a variable. For algebraic expressions, we can choose any number we want. Caution: this will not work on equations because only one answer can be correct.
The answer is correct if both results match.
“But what if my answer-checks don’t match?” Then you've got a wrong answer. The next step is to find and fix any incorrect lines. To do this, I recommend re-tracing your steps, line-by-line until you find the mistake. Your goal is to catch any errors due to forgotten minus-signs, lost terms, or arithmetic errors. Once you’ve spotted your error, redo the problem at the corrected line to verify that both answer-checks match. Unless there are other hidden mistakes, the new answer should be correct.
Yes, checking answers is extra work. But if you want to be absolutely sure that your answers are correct, then it's the surest path to math mastery.
Word problems are a source of continual frustration for most math students. Decoding sentences into numbers and equations can trip up even the most prepared learners. Fortunately we can adopt simple habits to solve them more easily.
The first part of my advice combines four steps. These are exactly what I use to solve them. When reading a new word problem, I look up any words I don't know, using a dictionary. It helps if we know the meaning of all the words being used.
With most word problems I encounter, I draw a quick diagram. A train leaving a station accelerates to 40 km/hr? Draw a diagram. A circle is inscribed in a square? Draw a diagram. Drawings can organize a great deal of information into an easy-to-understand format. Often crucial insights pop up while I draw a diagram.
Next, I write down all generic equations that pertain to the problem. A car is travelling at a constant speed? Speed = [distance / time]. A box of volume V has a width, length, and height? Volume= [width*height*length]. I find it best to write down more equations and use less of them than to accidentally skip a crucial one. As the saying goes: Better to have and not need, than to need and not have.
Lastly, I find out exactly what the problem is asking. It's easy to get lost in the details of a tricky word problem. Writing an equation with a question mark helps me to focus my attention on finding that value, instead of getting lost in the details. How far did the plane travel after 2.5 hours? Distance = ?. When did the two joggers pass each other? Time = ?. It's yet another way of organizing our thinking.
Now, if a student feels completely lost with word problems, I recommend one final piece of advice:
Solve simpler word problems, atleast one math level lower, with the eventual goal of moving back up.
Let's say a student is having a tough time with Algebra 2 word problems. Trying to solve additional ones will frustrate them even more. The reason is that both their math skills and word problem-decoding abilities are shaky. This student could learn quicker by practicing word problems from Algebra 1 or even lower. Why? They already know the simpler math. This would free them up to decoding the words without slowing down from the underlying math. And once their skills improve, they can move back up to their current level.
If you're motivated to improving your word-problem skills, applying one or both approaches will have a huge impact on your results. Good luck!
To recap:
a) Look up unknown words in a dictionary.
b) Draw a diagram whenever possible.
c) Write all generic equations that pertain to the word problem.
d) Jot down the variable that the word problem is asking to solve. [(Variable) = ?]
e) If needed, solve simpler word problems, atleast one math level lower.
Teachers expect students to hold onto all class handouts, graded papers, and notes. But what's the point of keeping all these papers? Well, they contain every problem a student is required to solve. And they also contain every problem a student has answered incorrectly. Would it benefit us to learn from these past errors? Of course! In a sense, these incorrectly-answered problems form a roadmap pointing us towards better grades...IF we choose to learn from them.
So why don't more students learn from their mistakes? Probably because they have math folders that are disorganized to some degree or other. It isn't uncommon to see an underperforming student having a math folder spilling with papers. So a crucial study guide, worksheet, or practice test that really could've helped out, gets lost in the abyss. Students who habitually misplace papers can expect to see their grades drop atleast a letter grade, if not more. This can be avoided if they take small daily actions to organize their math folder and learn from their mistakes.
How then can one stay organized with minimal effort? It's a two-step process. 1) Write the date on every incoming piece of paper in the upper right hand corner: handouts, homework, tests, and class notes. Everything. 2) Then hole-punch and order all incoming papers from oldest to newest into a 3-ring binder. Now all is organized. Owning a portable hole-punch and stapler help to keep loose papers to a minimum. The real power is in a binder of date-stamped papers which allows students to easily find problems to work on. And tackling our old math mistakes is where the real magic happens.
Most every student knows the feeling of math anxiety. It’s the impending doom right before a test. Or that sinking feeling when homework stops making sense. Some educators view math anxiety as a fear of failing. Yes, that’s part of it. But there’s a deeper force at play. The underlying cause comes from holding one particular belief. And when a student lets go of that belief, they are free to succeed again. In this article, I’ll go over what that belief is and why it debilitates us so much. Then we can talk about how to succeed again.
The cause of all math anxiety comes from holding one particular belief.
We often convince ourselves that outward factors are the cause of a learner’s decline. Yes, skipping problems, not learning from mistakes, and putting in minimal effort all contribute to low grades. However, I maintain that one single factor is at the root of all math struggle. It can be summed up as follows: Students who believe they are “smart” eventually set themselves up to struggle in math. Whereas those who avoid that belief can steer clear of disaster.
So how does believing you’re smart cause math anxiety? A student who believes they are “smart” is connecting their own self-worth to their successes. “I aced that test… because I’m smart”. “The homework was easy… because I’m smart.” As long as the results support their belief, all is well. The problem is when the inevitable failures occur.
When the “I’m smart”-student experiences large stretches of failure, then they begin to re-evaluate their self-worth. Some give up and resign themselves to the belief that “maybe I’m not so smart”. Others adopt a resentful attitude of “I hate math!”. In either case, the learner works less and less, in order to protect their self-worth from further decline. So the struggling student sits in limbo, unable to quit and unwilling to move forward. They are now stuck in the math trap.
Every wrong answer, low grade, or moment of confusion is a reminder that they might not be as smart as they originally thought. But the core issue is not how much intelligence they possess; the issue is that they feel pain at every failure.
By contrast, those who avoid the “I’m smart / not-smart” dynamic don't suffer such pains. Failure to them is a necessary part of learning. It guides them to know what not to do, so they can more quickly discover what they need to do. For them, failure is a guidepost pointing towards success, not a road block against it.
Failure lets us know what not to do, so we can more quickly discover what we need to do.
Here are two questions worth asking ourselves: If connecting achievements to our self-worth is causing so much suffering, then what’s a possible solution? What could I accomplish if I let go of the beliefs causing my math anxiety?
The approach I take to math is about cultivating the fun. Figuring out how to have fun is the only way I've found to sustain the high levels of energy and focus needed to excel at math. Having fun makes the hard work bearable. Without it, we fixate on our confusion, wrong answers, and less-than-perfect grades. Fun makes all the small inconveniences bearable, even enjoyable. And when you are really having a blast with your studies, you will enjoy seeing math where ever you go.
What does self-deception have to do with math? My view is that self-deception blocks students from improving their math skills. But what is it anyhow? It's the practice of believing that a false idea is true. And it occurs everytime a student thinks they understand math more (or less) than they really do. The result tends to be low grades and an equally low desire to study. My goal with this article is to help students avoid this mental trap, for improved math success.
“Nothing is more hostile to a firm grasp on knowledge than self-deception.” -Diogenes
Normally while learning a new topic, we think one of two main thoughts: "I don't get it" or "I do get it". As long as these correspond roughly to reality, then all is well. However for some, there is a feeling that they understand a topic more than they really do. And for others, they believe they can't understand a topic, when really they could. I call these two types the over-confident and under-confident student.
The over-confident student feels little need to learn beyond the easier parts of a topic. They prefer to put in just enough energy to finish their assignments. Deep down they hope that the homework and tests stay easy, and the teacher grades generously. This wishful thinking allows them to avoid working harder. It also blinds them to the likelihood they will struggle with future assignments.
On the other side, we have the under-confident student. Their eyes gloss over when looking at new math problems. Where other students put in the effort to make sense of a new topic, they give up. To them, confusion and frustration aren't natural parts of learning that everyone goes through. Instead these are signs they will never be good at math. So they avoid studying, and their learning stops. What all this negative self-talk does is blind them to the possibility that they can do better than they believe.
In both cases of the over and under-confident, the end result is giving up. Both do this to protect themselves from the pain of struggling. The irony is that their choice to avoid pain comes back in the form of low grades.
Fortunately there is a way out of this cycle of frustration. Here are a few ideas and questions worth considering.
a) What would happen if you replaced wishful thinking ("I bet the test will be easy") or negative self-talk ("I'll probably fail the test") with: "The more I study, the better I'll do on this test"?
b) How would it benefit you to become more aware of your abilities, no matter how unpleasant the reality? "What problems are holding me back from doing my best?"
