Battle Press

Let It Percolate

According to Merriam-Webster, percolate means “to pass slowly through something with many small holes in it” “Percolate.” Merriam-Webster, n.d. Web. 17 Nov. 2016.. It’s a wonderful analogy to the process of learning math, especially the more difficult concepts of higher math. Time and patience are required for a liquid to percolate through a fine sieve. Our brains are no different. But, we live in a time where expediency seems to be the measure of the facile brain. Kids that learn concepts quickly are viewed as the smartest in the class to the detriment of the slower learners who are left behind or marginalized.

My students work hard (for the most part) to master new concepts in math, and as they progress through a unit that builds upon itself they should be ready for the test. That’s not always the case. Often they get to the test, and the concepts are still a swirl of formulas and processes that haven’t settled into their appropriate home in their brains. They must work very hard to apply a particular concept or concepts to more difficult questions – the types of questions put at the end of a test that count for many more points than the easier rote questions testing skills mastery. For example, a student learning the concepts of factoring quadratic equations such as y=6x²-5x-4 into its factors (3x-4)(2x+1) is attempting to master a difficult new skill that uses math facts and integer mastery. There are processes I can teach them to make the task easier, but when this concept is placed into the framework of a word problem the task gets much harder. The typical word problems for quadratics are area problems and projectile problems. Both will require the student to use skills from other areas of math. The area problem will require the use of geometry formulas. In addition, they will have to recruit skills for building math expressions from word phrases, a very hard concept for some learners. If they fail at any one of these skills, then they will miss the entire problem.

Many of my students complain that they don’t get enough difficult questions for practice, so they can master blending concepts before the test. I agree with them. Skills work is not enough practice to help them harden concepts in their minds. They must play with the concepts and use them in a variety of situations, so the necessary connections are made across different areas of the brain. It takes time and patience for this type of learning to happen. And for some students, it will take longer than the rest of the class.

The US is lagging behind other countries in STEM scores, not because we aren’t capable of mastering these subjects, but because we don’t let kids play and explore with math. They have to see the applications for math, so the rote work will have a point.

My students ask me all the time, “when will I ever need to use the concepts of special right triangles or the unit circle?” I’ll respond by asking them what careers interest them – programming, engineering, business, doctor, or art (to name a few). I can see applications of math to all of these careers, even if they don’t. Jobs in the future will depend on students who have a passion for STEM, STEM jobs article. I am always trying to pass my love of math and science to my students. I think it is the most important part of my job, so I am patient. I wait for the ideas to percolate into their very capable brains (even the slower ones) because I want them to have every opportunity possible when they are adults. Learning shouldn’t always be about speed, some of our best and most creative minds take their time, letting ideas percolate before charging ahead with the first idea to pop into their mind.

This post is in response to the daily prompt, Percolate. Daily Prompt: Percolate


The Trouble with Math Facts

The first question is often, “What are math facts?” Math facts are the instant recall of addition, subtraction, multiplication, and division of whole numbers without the use of solving strategies. Basically, kids should be able to perform functions with whole numbers (2+3, 3×4, 8/2, and so on) from memory.

The students that come to me failing or have already failed a class cannot recall math facts. In some cases, they have reached high school and still struggle with basic facts such as, 9×8 or 12×8 (the 8’s table seems to be a big problem, and I sometimes wonder if there’s a conspiracy against it.) Add to that, starting in middle school (around seventh grade), teachers allow the use of calculators. The kids rejoice, and much to my dismay, they will use it for everything. We’ll be working a two-step equation, and they stop to input 5+3 into their calculator. It is unbelievably frustrating, and a waste of time. I pick my battles, but I usually call them out.

I understand how hard this can be. I struggled with addition and subtraction throughout elementary school. A friend, Laura, who is a fabulous middle school teacher nowadays, patiently spent a summer working on these skills with me. I am forever grateful to her for turning around a rough start in math.

Students bemoan that they never memorized their multiplication tables because they couldn’t learn numbers that way, so they’ve just accepted it. This excuse never sits well. I know without mastery of math facts, they will struggle to learn any new concept. It will take them twice as long to learn foundation concepts such as factoring quadratics, simplifying radicals, solving systems of equations, and so on. Most importantly, it is a major risk factor for them failing high school math.

The other question that I get all time, “How do I fix it?” There are no simple answers, and the kids weren’t wrong when they said rote memorization didn’t work for them. They may process information differently, so flash cards or writing out their tables a hundred times doesn’t stick. They need different strategies. There are songs for each of the multiplication tables, but most are geared toward elementary kids, and getting a middle or high school kid to use them is next to impossible.

I like the idea of math games much more. The site Math4Love has many free games available for download. There are iPhone/iPad apps; search math facts games, and the list is extensive. My family loves board games, and a few games that help with math are Machi Koro, Incan Gold, Splendor, and Manila. If you’re playing a game that needs a banker, then give your kid the job. They may take a little longer, but it encourages them to work on addition and subtraction (no calculators allowed). Playing with numbers is a much better way to learn math facts than boring memorization work.

When you’re at a store or restaurant figuring out a discount or a tip, give the problem to your child. They need to see the importance of math in everyday life. They may argue, “I have a calculator on my phone, and I always have my phone. I don’t need to do this stuff in my head.” Again, they’re right. We do always have a calculator handy, but their success in higher level math depends on this skill. Sneak math into as many situations as possible, be persistent. They have to use math to get better at it.

Next Week: Finger perception and building a better math brain.


Get the Most Out of Tutoring

Some of the suggestions in this post will seem elementary, but trust me, they need to be addressed. A few students show up with nothing, not even a pencil. I immediately question their commitment. I’m willing to invest time and energy in my students, but they must meet me halfway. When I have more invested in my student’s grade than they do, the sessions can be painful for both us.

Student Responsibilities

Attempt every assignment. Homework can be a tedious chore. However, you cannot succeed without practice. Repetition helps students memorize formulas, master processes, and improve basic math facts. It is impossible to prepare for a test when they haven’t completed any of their homework. At this point, the student is hopelessly behind, and I cannot teach an entire unit the night before a test. The most important responsibility for a student is homework, even if the teacher doesn’t collect it for a grade.

Know what you want to work on. On average, I meet with my students once a week, sometimes less. During the intervening week, their class can cover a large amount of material. It isn’t feasible to cover everything from the previous week in one session, at least not in any great detail. Students should maintain a list between sessions identifying problems or topics they found challenging. This way students are in control of their session, and they feel more invested in the process. In addition, we don’t waste time on easier topics. We only have an hour together, so make the most of it.

Be prepared for the session. Each student, at a minimum, should have pencil and paper. I’m happy to provide supplies every now and again, but not every session. (Side note to parents. Assume that if your kid takes nothing with them for tutoring, then they probably walk out without learning anything. They aren’t taking it seriously, and you’re wasting money on an exercise in futility.) Make sure you have the calculator you will use on tests charged and ready to use during the session. Some topics require more advanced computations or programming, and I prefer teaching these steps on the student’s own calculator. Know your login information for any web supported class features (eclass, schoology, etc). Try to get plenty of rest. High school kids start class very early, and their sessions come at the end of an already long day. Bring a snack, or something to drink to help you stay awake.

Parental Responsibilities

Check progress often. There is a temptation with high school kids to pull back and hand responsibility solely to them. They’re starting to look like adults, so we expect them to behave like adults. Their brains aren’t always up to the task, and they need help from us to stay on track. There’s a wonderful book about this issue, The Teenage Brain, by Frances Jensen, a neuroscientist who looks at how the teenage brain functions differently from adults. (I plan to do a post on some of her findings.) Most schools give parents access to their child’s grades. Make it a habit to check progress every few days.

Engage with your child. It’s not enough just to check their grades. Follow up with them, so they know you’re checking their progress regularly. My son quickly learned that I go through the roof if I see an NTI (not turned in) on his class portal. So he checks his own grades more often, and when I point out NTIs, he’s already in the process of addressing them. It takes some of the bluster out of my rants. Ask them what they learned during tutoring, and if they have any additional or follow-up homework for the night. Encourage, or harass, them into doing their homework every day.

Address concerns. Get in contact with me as soon as possible with any concerns about the progress of your student. Let me know if something major is going on with them. The same applies to their teachers. If you aren’t sure why they’re failing all their tests and doing well on quizzes, then reach out to their teacher and ask. If you don’t like the answer you receive, then contact the head of the department or the counselling department, be a pest if you have to. You are your child’s best advocate.

Next Week: The importance of math facts.

Role of a Tutor

Parents search for a tutor for one reason, improving their child’s grade. I can’t always accomplish that, but it is my goal. There are many factors affecting my students’ grades, and I am just one component. On average, my students see a marked improvement in their grade, but I do not guarantee this result.

In the first session, we review their current grade and relationship with math. I want to know; did they ever like math, or consider themselves good at math. If so, when and why did that relationship change? Also, what are their goals for each session? (This question is especially important for high school and college students.) My top priority is to identify weaknesses in foundational math. I can’t devote an entire session to addressing these weaknesses because we need to stay on top of new concepts. For example, if fractions are a problem, then I take every opportunity to work on them. I scan the assigned problems to see if they address weak spots. If not, then I look at the ones not assigned and pull from those.

Typical sessions include work on assigned homework and test prep. For my focused students, they come prepared with specific areas of concern, and we focus on their list first. With the time left over, we preview new concepts that will be covered in the next week. A lot of my students only want to work on the assigned homework for that night. They want to be done with Math when they leave the session. I understand this goal, but I’m rarely in favor of it. I select representative problems from the current assignment and then review previous assignments for problem areas.

Quiz and test preparation are another focus. And again, my focused students come with questions in hand because they’ve already worked on the review prior to the session. The other half haven’t bothered to look at the review. I try to work the entire review with them. We usually run out of time, and the topics we do cover are not as in-depth as I hoped.

Teachers can’t tailor their style to each student’s needs; it isn’t feasible with large numbers of students. They don’t get the feedback of sitting next to their students while they struggle with a problem. Tutoring sessions afford me that luxury. I can slow down when my students really struggle. I know which students can skip steps and which ones need detailed step-by-step instructions. Sometimes, I present a topic five different ways before hitting on the method that works best for them.

I love math and try very hard to share my passion. Many kids come to me apathetic about math. They don’t like their teacher and hate the subject; motivation is a huge problem. Parents have asked me to threaten their kids into studying more. There is nothing I can take from them that will impact their study habits outside of tutoring sessions. I take responsibility for presenting the topics in as many ways as a student needs until they can understand it, but I do not take responsibility for their study habits. I am a tool the student can use to improve their understanding of math, but they must choose to use the information I give them. It’s not possible to reach every student, but I try every time one of them sits in the seat next to me. I never give up on them, even when they give up on themselves.

Coming next week: How to help your kids get the most out of tutoring.

Hope you’ve all been enjoying my posts. Remember to follow my blog if you want to be notified of new postings. Feedback and suggestions are always appreciated.

Tests, tests, and more tests

Students live or die by tests, at least it feels that way to them. Parents dole out praise or punishment based on the results. Teachers measure students against each other and determine mastery of different skills. The school passes or fails students based on test scores. Expand even further, the state bases teacher pay and ranks schools according to the results. No wonder kids feel so much pressure at just the mention of an impending test.

Are tests the best way to assess the capability and understanding of a student? Most of the time probably not, instead we are conditioned to accept tests as the gold standard for determining the success of our kids. It’s only a snapshot, so many factors can influence the picture you see on that day. The test doesn’t care about any of the outside variables impacting the performance of the student. They could be sick, tired (a chronic problem with high school kids), upset, anxious, or depressed. They might have had the worst fight of their lives with their best friend or broken up with a girlfriend/boyfriend. As adults, we can call in sick and take the day to deal with any of those issues. Kids don’t get that luxury. None of that matters to the test. The only thing that counts is the work on the page.

I know I’m leaving out some big reasons for performing badly. They didn’t try hard enough. They were lazy and didn’t study. Kids can make some bad choices, but I would argue so do we. I know I’ve procrastinated about getting my tags renewed and had to pay a fine. I’ve had days where I’m so tired I can barely function because I went to a concert on a work night. Their job is school, and some days they stink at it just like us.

Most of my tutoring sessions consist of test prep, and the tests don’t always capture the true picture of a student. They may come to me the day before the test with a swirl of formulas swimming in their head, but walk out confident and ready for the test. The student knows some of the concepts, but they haven’t really cemented the information into their brain. When they get to the test, they swap formulas or blank on word problems; the grade is not what they hoped it would be. Add to that test anxiety intensifying after each failure, and it’s a recipe for subpar test performances.

I always go over tests with students when they get them back, if they get them back. (That’s a pet peeve of mine. How are the kids supposed to correct what they did wrong if they can’t analyze the test and take it home?) They can be so embarrassed to show me a bad test and focus only on what they did wrong. I want to know what they understood. Did they miss a concept, or was it a simplification error such as losing track of a negative? I ask them what went wrong, what was hard, what was easy; and then we re-work the problems they missed. They are much more responsive than my own kids when I just yell them.

A neurological study about brain growth during learning shows a marked increase in growth when a mistake is made. It is an opportunity to learn even more. They need to know that failures do not always mean more failures. And, it happens to all of us, even adults.

My kids have pointed out the hypocrisy of all this. How I’m really patient with my students and never berate them for a low test grade. With my kids, there is often a punishment for low grades. So, I try really hard to take a deep breath when one of them brings home a big fat failing grade. I try not to have a knee jerk reaction to take away phones or limit their video games. Instead, I look at why they failed. It’s the why that is really important. Their grades do not define who my children are. The CogAT does not define whether my child is gifted or not. The Georgia Milestone does not tell me how good or bad my child is at a subject. They may indicate areas that need work, but they do not define them. Instead, I try to help them learn from their mistakes. Sometimes I still yell, but I’m working on it.

This blog is in response to The Daily Post prompt Test.

Warning Signs: High School

Many of the problems discussed in Warning Signs: Middle School still apply to high school. But, high school has four distinct paths with different areas of concern. Average paced students face very different challenges and demands than accelerated students.

As a freshman, students enter Algebra I, Geometry, or Accelerated Geometry. Respectively, they will top out at Pre-Calculus, AP Statistics, AP Calculus, or Advanced Calculus (or possibly a higher level math offered at a college). In a future blog I’ll go into more depth on the different tracks.

Freshman in Algebra I are on the lower end of math proficiency. They probably struggled throughout middle school, and the jump to Algebra will be a challenge. The students who ask for my help with Algebra I are lacking fundamental concepts going all the way back to elementary school. They have yet to master math facts, fractions, integers, and applied problems (word problems). These kids are at extreme risk of failing as freshman. My recommendation would be to get a tutor immediately. You can start with free tutoring session offered at the school, but these are group sessions. They may not work for every student. Peer help can also be a good resource. Don’t let them disengage and give up on math, get them support.

Freshman in Geometry are a mixture of students pushing and coasting at this pace. If they’ve dropped down from accelerated, then it’s a fairly easy class. At first, they will be reviewing concepts they’ve already learned. I don’t get too many of these kids as they just needed a slightly slower pace to do well. The other half are kids who were capable at Algebra in middle school, but they may already be struggling to keep up. I stated in my middle school post that grades are often inflated, and this is where I really see it. Kids that had B’s and even A’s may still have big weak spots in their fundamentals. Parents should be checking grades frequently. Pay close attention to quiz grades; low quiz grades presage low test grades. The time to intervene is early in the semester before too many test grades are in the book. Far too often, students come to me late in the semester failing and desperate to recover their grade, a nearly impossible task with so few tests remaining.

Freshman in Accelerated Geometry are the high achievers. Many of them have been in the gifted program since elementary school, and high school is where math gets challenging. Up to this point, they weren’t tested too much by lower math, so for some, they will have to work hard to get the same grades as in middle school. The teachers are distilling one and half years’ worth of material into one year. The pace will seem very fast on the harder concepts. Most of these students have good fundamentals, but the speed may prevent them from fully grasping the concepts before the test. Pay attention to how long they spend on homework and early test grades. Do not let them get behind. Concepts build on each other and failing to master even one will compound into greater difficulties in Pre-Calculus and Calculus. Another issue with this group is the tremendous pressure they often put on themselves. Stress and frustration can impede them further, and the support of a tutor can help lighten the load.

Next week: The role of a tutor.  

Feedback and recommendations for future topics would be greatly appreciated. Have a great week.

Jump Discontinuity

Jump discontinuity is something my calculus students encounter when they learn about limits. They study graphs and try to determine if a function approaches a limit at distinct points along that function. Limits are a hard concept for my calculus students, as they are in life. And jump discontinuities seem to give them particular fits.

They are created by piecewise functions where a function is defined at specific points along the domain. They look like the graph above with lines jumping across the graph.

Being a math lover, they’re a wonderful way to view the graph of our lives. Each jump is a major change.

My students experience a jump between middle and high school. For a moment, they stand with one foot in each world. They dream about the future while looking at it through the lens of their past. Middle school had its own particular set of rules imposed by their friends, teachers, and parents. Those rules will change when they enter high school. So for a brief moment in their lives, they wonder about the possibilities and freedoms that will come with those new rules.

My son is navigating this process as he begins high school. There’s so much for him to learn and master, and from my perspective he’s embracing each challenge with grace and humility. I marvel at him. He’s often overwhelmed by the experience, but he doesn’t let it discourage him from the future he’s envisioned for himself.

I tried to identify all the big jumps in my life – graduating college, marriage, the birth of my children, buying a new home. The one that really sticks out was the decision to move to Bangkok, Thailand, when my kids were in elementary school. It was one of the scariest things I’ve ever done. We didn’t even have passports.

My husband was offered a one-year job in Bangkok (turned into 2), and he accepted it with about four weeks to get us there. We had very little knowledge about Bangkok, and I spent the next weeks arming myself with facts about our new home. Three weeks to go we still needed to pack up our house and transfer the kids to their new school.

When I look back on this time, I can’t believe we managed it. We jumped with both feet into the deep end. The flight to Bangkok is the literal jump between these two worlds. It was a long one, about twenty-four hours of traveling. That’s a lot of time to worry and wonder about the possibilities awaiting us. It was the unknown that I really feared. The experiences in my life couldn’t prepare me for the challenges I would face in Thailand.

Bangkok overwhelmed me in every way possible when we first arrived, but eventually I embraced my new home and grew to love it. For my kids, the experience opened their eyes to different cultures in a way they never could have experienced from the suburbs of Atlanta.

I’m learning to embrace the jumps in my life. Those moments where I can wonder about the possibilities to come while appreciating the experiences I have had in my past.


Warning Signs: Middle School

Math grades in middle school are inflated. The teachers are very supportive, and the kids have multiple opportunities to retake tests. This is a good thing, and I’m not dogging middle school teachers. They have a lead role in laying the foundation for upper level math.

When I begin with a student, we always go over their current grade. For middle schoolers, I take their class average and deduct five to ten points off the top to get a better picture of where they are. If your child has a low B or C, then they need help. Anything below a C, and your child is in crisis. They are missing fundamentals and need help assessing their weaknesses.

Elementary school taught the basics – math facts, fractions, and decimals. Middle school begins a more rigorous application of these skills. In addition, fundamental concepts are introduced – integers, algebraic expressions and functions, linear functions, quadratic functions, and the basics of geometry. These concepts are the foundation for higher maths. If they fail to grasp any of them, then it will come back to haunt them. And in high school, the grades stay with them, impacting their GPA. The time to course correct is middle school.

Pay attention to how long it takes them to complete their homework. If it takes more than an hour, then there is a problem. These kids are at risk of quitting their homework all together. While parents may think their child is lazy, I would argue many of them are so discouraged they give up. Homework is a punishment because even when they attempt it they aren’t getting it. And as one concept builds on the next, in a matter of days, they are left behind. Imagine sitting in a class every day and feeling hopelessly lost and stupid, like the teacher is speaking in a language you can’t understand. It’s boring and humiliating, and they fall even further behind. It is a vicious cycle, and they need help to break out of it.

Middle school is the time when many parents struggle to help their kids with math. It’s just been too long since they used some of these concepts. Moreover, I know from personal experience working with your own child can be difficult. There is a history between the two of you that can get in the way of meaningful learning.
Coming next week: The warning signs for high school students

Does my child need a math tutor?

If you are even considering the question, then get help. Don’t wait! Far too many kids are not getting the support they need to be successful, and the cycle of poor grades and even poorer mastery of vital skills crushes confidence. This cycle establishes a lifelong belief that they are horrible at math, missing some gene that the gifted kids have. Once a kid falls into this trap, it’s very hard to reach them. They give up and accept failure.

Many of my students think math is an inherit gift, either you have it or you don’t. It is simply not the case. Math is a skill, and like any skill, practice leads to mastery. While it is true that some kids have a natural affinity for math, even they must practice the necessary skills in order to achieve at a high level. They just like doing it, so they practice more often. For them, it’s a positive feedback loop, and they become even more invested in doing their homework and honing their skills. The results are better grades, and they rise to the top.

Kids that struggle have the opposite experience. They do their homework as best they can, but they still fail quizzes and tests. Their failures pile up, reinforcing that studying is a waste of time. So, they study less and fail more. The pattern is set and very hard to break. A tutor can help to rebuild confidence by shoring up deficiencies in fundamentals and helping them prepare for quizzes and tests.

If you polled kids and asked do you need a tutor, most would say no. They often believe only “stupid” kids have a tutor. This stereotype is a problem, and holds them back from asking for help. Many students who use tutors are very good in math and want to achieve even more. Most fall in the middle, they are “okay” at math (their words, not mine), but need a little support to maintain their GPA.

Most of my students like tutoring once they are here. None of them want to fail, they just can’t see a way around it. They believe it’s impossible to get a B or an A in math. Many surprise themselves, and do just that. I love seeing their eyes open to the possibility of success. They need a little boost, so their hard work is rewarded with good grades. Success is possible.

Coming next week: The warning signs for middle school aged kids.

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