In a previous post, we explored data pointing to a homeschool math gap. What comes next? What can homeschooling parents learn from this information? In this article we use stories from homeschool graduates to examine the things that hold homeschooled students back in math, and to explore what can help them succeed. Our goal is to put a personal face on the homeschool math gap, and to give current and future homeschooling parents pointers on what can go wrong—and what can go right.
We should start with a few caveats. First, we know that public schooled students, like their homeschooled counterparts, can and too often do receive a deficient math education. We are addressing homeschooled students specifically, because that is what we do—we advocate on behalf of homeschooled students and work to bring their interests into the conversation. Second, we are aware that math can be done well in homeschool settings and that some homeschooled students can become especially proficient in math. We will turn to some of these individuals’ stories in the end of this article as we look at what helped them succeed.
We asked a focus group of homeschool graduates whose math education was subpar to tell us about their experiences, and to pinpoint the pitfalls they experienced. The information in this article comes from this focus group. In the last section we will cover the input we received from a smaller focus group of homeschool graduates who consider their math education especially excellent.
Many of the homeschool alumni in our focus group reported that their parents’ lack of math knowledge hindered them from being effective teachers. Some recounted not asking for help when they needed it because their parents didn’t know the answers either. In some cases their parents simply gave up. Some alumni reported that their parents became angry when they did not immediately grasp mathematical concepts, or interpreted their failure to learn as a sign of disobedience.
Rebecca: My mom’s narrative was that I was just more of an “English” person . . . . However, maybe it was that I wouldn’t ever ask my mom for help with math because she didn’t know how to do it either? . . . I think she just was unable to teach high school math and blamed me for lack of skill instead of helping me.
Acacia: The math I should have been learning was more than my mom remembered how to do.
Shae: My math experience had a lot to do with the fact that my dad was supposed to teach me that subject in middle and high school. He had anger issues, and would yell at me and my sister if we got problems wrong or didn’t comprehend concepts. Because of that, I resisted doing math in order to delay the anger. . . . I feel like I learned other subjects proficiently because my mom made sure I learned those subjects.
Jerusha: [My] parents gave up teaching me algebra. Mom couldn’t teach it and Dad didn’t have time or patience to explain it.
Bethany: It didn’t help that my parents used Roy Lessin’s spanking rituals when we were disobedient which included my not trying. My mother had a short temper and yelled, screamed, and cried when I didn’t get math. My father wasn’t able to teach me math because he never got it himself. . . . Later—much later—I was tested at a local College. I tested 5th grade level for math and I was 26 years old.
Jai: My mom would look at the [problems] I got wrong, spend about 5 minutes looking over the book and then tell me to go find my older siblings because she didn’t have time to re-learn it in order to help me. I had to take one remedial math class in Community College 6 years later in order to get up to Algebra 1 speed.
Katharina: I was fine with math until geometry—I have a bit of difficulty with spatial reasoning, in life as well as in mathematics. . . . So all the shapes just made me reflexively really nervous! My mom is the same way and I didn’t have access to any adults who could explain it well.
We can draw a variety of lessons from these stories. Responsible homeschooling parents need to either teach themselves the material, along with effective teaching strategies so that they can teach it, or seek out tutors or classes for their children. Parents who don’t feel strong in math need to seek out those who are to serve as their children’s teachers and mentors. It’s also important for parents to ensure that their own frustration with the occasional difficulties of teaching not bleed over to the teaching itself. Homeschool parents need to be careful that their own limitations do not limit their children.
Some alumni reported that their parents expected them to learn from a textbook or worksheets without any help or guidance at all. In many cases this led to frustration or to a failure to fully understand the concepts.
Savannah: My mother gave me workbooks to go through on my own, which were not well-done . . . . Though I am a perfectionist, the lack of quality teaching, lack of resources to go to for help, and habit of parents to push it under the rug and just explain it away as me just not being good at it, meant I ended up never mastering any mathematical concepts.
Anna-Brit: [From] fourth grade onward, I was given Saxon math textbooks with no other help, which worked well enough until trig and calculus. I missed some key concepts with calculus, and no matter how many times I patiently reworked problems and looked at old lessons, I could never get them to come out right.
Liz: Around junior high or so, when it was time to switch to Saxon Algebra 1/2 or 1 or something, math suddenly became super hard for me. . . . Mom didn’t have time to work on math with me any more at this point, or go over the thousands of problems I missed per lesson, so I struggled on through Algebra 1 in Saxon by myself (pretty much the one constant of school during those years was that I HAD to spend a couple of hours a day “doing math”). . . . My senior year, I worked my way through a geometry and a consumer math textbook with no help, and didn’t understand that either. With incredible optimism, I tried to test out of freshman algebra before my first year of college and unsurprisingly failed that test.
Jessica: Around 9th grade I begged for algebra, it was the only higher math I knew about, I literally did not know there were things called geometry, trigonometry, calculus . . . . My mom ordered Saxon Algebra 1 and the answer key, handed them over and that was my class. I was motivated, I wanted to go to college, I loved science and wanted to have the background in math, but that wasn’t enough to teach myself algebra. I gave myself a placement test a few years ago and my math was at a 6th grade level. I couldn’t even pass the GED practice test.
It’s worth noting that sometimes self-taught math can work. Breanne, a participant in the focus group, wrote that she struggled with teaching herself math but ultimately succeeded. Jeffrey, a homeschool alumnus who received a good math education, gave reasons he feels he was successful in teaching himself math.
Breanne: My mom helped with math in elementary grades, but in high school I was just given Saxon books to teach myself. She’d grade the tests. It took me a long time to do math every day because I had to work hard for it. . . . I did end up with A’s and B’s though, because I actually cared about learning.
Jeffrey: I taught myself Calc I and learned it well. . . . [W]hen you write a terrible paragraph, you might not ever figure out how bad it is on your own. But when you get a math problem wrong, you usually can compare it to the answer and immediately find out that it’s wrong. Not that this makes math easy, but it is a significant factor helping self-taught math to be more doable.
Breanne may have learned the material, but she nevertheless described her self-taught math education as a “struggle.” And while Jeffrey was able to use an answer key to figure out the concepts, this is not always possible. In my own experience, the answer key rarely gives any information about how the answer was arrived at, and it’s that process that is so important when learning math. Similarly, different people have different learning styles.
Homeschool parents should not assume that their teenagers will be capable of teaching themselves Algebra or Calculus out of a textbook. Many students need a parent, tutor, or teacher to provide guidance and motivation, especially for a subject like math. Parents who plan to have their children work through a textbook should make an effort to learn the material alongside their children, answering questions and explaining concepts as they go along.
Other options include hiring a math tutor (or arranging a trade with a homeschooling parent who is particularly good at math), or finding a class. In some states homeschooled children are permitted to take one or two classes at their local public high school without enrolling full time. In other states community colleges are open to high school students at a discounted price.
When children attend school, they will likely have a range of teachers that vary in quality. Their teacher one year may be terrible at math or may even tell them that they’re bad at math, but the teacher they have the next year may work to inspire them. For some homeschooled students, however, a parent who dislikes math or discourages them from pursuing the subject may be the only math teacher they ever have. This means what a homeschool parent tells their children about their math ability or about the necessity (or lack thereof) of math takes on an oversized importance.
Some alumni in our focus group reported being actively discouraged from pursuing math by their parents. In some cases this was fairly general—the alumni were told that math was unimportant anyway, or simply that they weren’t good at math—but in other cases it had a gendered aspect.
Rebecca: [My mom] also discouraged me from wanting to study [math] by talking about how useless it was, and that practical math for cooking would be better for me anyway.
Melissa: My mother wasn’t good at math and told me I wasn’t very good at math either.
Jennifer: I was told over and over again from about 3rd grade forward [that I wasn’t good at math] by one or both of my parents. Oh my gosh it made me want to quit altogether.
Jessica: I was in public school from first through fourth grade. My lowest grades were in math,but still ranged in the 90s to a low of 88. For some reason my mom took this to mean math was my weakness. She repeated this to me almost daily my first year of homeschool. She even had me start off in a fourth grade math book to help me “catch up”. I was bored out of my mind by all the divide and check.
Jerusha: [My parents] said I wouldn’t need [math] as a housewife anyway.
Heidi: My mom finally stated that, “Hey . . . what do you need algebra for anyway? You are a girl,” and that was that. At the time I felt happy and relieved. After all, I was going to marry and have babies happily forever after . . . what did I need it for?
Breanne: Mom always said [that] girls’ brains aren’t wired for math. That made things worse, it felt like my struggling was futile.
Homeschool parents need to be aware of the oversized input their feedback has on their children’s math motivation and ability. Parents who don’t like math themselves need to be careful not to pass that on to their children, even accidentally. Children need to be inspired to thoroughly pursue each subject as they search for things they like and are good at. Giving children a negative outlook concerning math closes doors that should remain open.
Some children have learning disabilities. Unfortunately, while teachers are trained in recognizing learning disabilities and providing intervention, many homeschool parents may not understand that they are dealing with a learning disability until much too late. Homeschool parents need to educate themselves in warning signs that may point to learning disabilities and be willing to have their children tested for learning disabilities should such signs appear. Once a learning disability is identified, parents need to provide support and look for resources.
Bethany: My learning disability got in the way of my ability to learn math. . . . For a short time when I was in grade school, I had a specialist teach me math and I performed well. . . . He seemed to understand me and my dyslexia. He had me doing math above my grade. I fell behind again when I was homeschooled. Later–much later–I was tested at a local College. I tested 5th grade level for math and I was 26 years old. I went to the class they held as the lowest one could take in college. I felt deep shame. . . . Like my earlier learning specialist, they seemed to get my brain. I aced the class. . . . The bottom line was that I require explanations and practice that are more suited for my manual brain.
Melissa: There is no doubt based on what I do on a day to day basis that I am fairly mathematically inclined, though I think it’s possible I have some kind of learning disability since I can be a bit slow at times to pick certain things up. Based on kids I’ve worked with I think I may have dyspraxia, which would explain why I suddenly seemed so skilled once I had access to computers, since people with this disorder have trouble with writing out equations and that kind of thing.
Jennyfer: I have dyscalculia. My private school couldn’t deal with it, the public school in the area would have put me in the special ed holding tank, so I was homeschooled due to it. I was never able to achieve more than 5th grade, even with lots of tutoring. They eventually just gave up.
Some children are homeschooled due to learning disabilities. In these cases, parents hope to give their children better than what they were receiving in the local public schools. But doing this isn’t easy, and requires a lot of effort and the willingness to look for a new solution when one thing isn’t working. Homeschooling parents of children with learning disabilities need to be careful not to give up before they have sought out and exhausted the resources available.
Homeschool parents have a variety of math curriculum available to them, and can easily shop around online or at homeschool conventions. Parents need to work to educate themselves on best practices and ensure that they thoroughly review each curriculum they choose. Some alumni in our focus group spoke of using curricula or math programs that simply did not work for them.
Melissa: My mother’s version of math education was . . . not good and mainly focused on memorization, which never stuck anyway. My mother said I had to do them over and over again because “you won’t always have a calculator.”
Liz: Eventually, Mom purchased this program at a homeschool conference called “Algebra VideoText”, where the instructor explained everything on VHS tapes and there was a hotline to call if you had problems. For the rest of high school I slogged through that program by myself, dutifully watching all the videos and completing the modules, and eventually “completed” it, without understanding much of what was being presented or retaining it at all. The help-line guy was MEAN (“What’s the matter with you? This is basic! There’s no reason you shouldn’t understand this!’) and after a while, I quit calling him.
Once a curriculum has been selected and purchased, homeschool parents need to pay attention to whether or not it is working for their children. This can be more difficult when a child is working more independently, but should be possible through frequent communication and through working through a curricula alongside a child. Homeschool parents need to be willing to changed their curriculum plans when a given program is not working.
In many cases, homeschooled students who struggle with math may have the ability to do well but not the interaction or resources they need to excel. This was the case for a number of alumni in our focus group, who were eager to speak of their experiences in college, where having a class and a teacher turned things around for them.
Jerusha: I tested into a remedial class and loved it. Turns out I’m really good at learning algebra from a teacher.
Jai: I had to take one remedial math class in community college six years later in order to get up to Algebra 1 speed, but I had a teacher that was amazing and spent time to answer my questions and look over my work with me.
Katharina: Having a teacher and college tutors really changed things for me.
Liz: The math course I had to take in college was what my mom called “math for dummies,” but I did OK in it because there was an actual teacher who explained stuff. I think I got an A.
Acacia: The summer before I entered public high school, I had to go to Sylvan Learning Center to catch up on everything I missed, even though I was relatively good at math and picked it up way faster than they expected.
Unfortunately, while many homeschool alumni who previously struggled with math may find themselves able to succeed with an actual class and teacher once in college, this does not mean that their deficient homeschool math education does not shape their future and their career choices.
Melissa: I LOVED science, so I wanted to be good at math. But I didn’t have a good background in math or how to study it, so I floundered once I got to school in high school and ended up giving up on my dreams of being a scientist. In college I was finally able to take some remedial classes, but still didn’t quite catch up. By accident I ended up doing tech for a living, which I do OK at, but I feel I regularly get passed up for promotions and have hit a ceiling because of my deficient background.
Anna-Brit: There was 110 point gap between my critical reading and math scores on my SATs. I ended up minoring in statistics in college, but fear of the prerequisite four levels of calculus prevented me from majoring in it, to my shame.
Liz: To this day, I stay far away from math. Maybe I would be good at it if I’d had some actual instruction, I don’t know.
Heidi: I went on to conquer statistics for my Bachelors and am now happily working on my Masters. But to pass the algebra I got help from everyone I could think of . . . school tutor, my drummer from worship team, and my baby brother who also put himself through school.
Savannah: This experience [failure to teach myself high school math from a textbook] has ingrained my fear and hate of all things math and science related, and in turn pushed me away from higher education in embarrassment of my skills.
While experiential learning can often be extremely helpful, it should not be a replacement for more academic study of math. There is only so much math that can be learned from cooking, or from balancing checkbooks. For most children, higher-level math like algebra will require more than experiential learning.
Jerusha: One year my “math” was to make an answer key for an antiquated book on arithmetic for agriculture. I think it was used by the Amish. Balancing my parents’ checkbooks, paying the bills, and keeping my dad’s business ledger also counted as math.
In some cases, children’s success in other areas may mean that their parents do not notice their struggles and deficiencies in math. Parents need to be proactive and pay close attention to their children’s progress in math.
Katharina: I do remember feeling quite defeatist in high school, and my poor math skills were the reason I never finished my chemistry course either, too much math…but as my outstanding strengths were in verbal reasoning/writing, it never occurred to me or my mom to address those deficits, you know?
Finally, while a deficient math education can hold young adults back and make their lives more difficult, some will push through in spite of it all.
Savannah: I have turned a new leaf and am in my first ever math class (remedial college course) catching up with things I never knew! I am determined because I am sure once I am able to understand it from a qualified teacher, I will cease to be so unnerved!
And now we turn briefly to our smaller focus group of homeschool alumni with good experiences. Our main focus in this article has been how things can fail, so we want to finish with a brief picture of how things can go well
Emilie: My mom was passionate in teaching all subjects, and mathematics was no exception. In elementary school, she used a conceptual math curriculum which we worked through together using manipulatives and other various real life examples to understand arithmetic. We were not tied to this curriculum, however, as we found its algebra book confusing. For algebra and geometry we carefully switched to another program that was well-reviewed and also emphasized conceptual understanding. For my last two years of high school, I took Precalculus Algebra and Trigonometry, followed by Calculus I and II at the community college, as they were beyond my mom’s expertise. The teaching I received there was excellent and allowed me to take Calculus III and Differential Equations as a freshman. (My younger sister also took calculus-based physics and an introductory engineering class while still in high school.) Mathematics may not have been my mom’s favorite subject, but it ended up being mine, and she opened all the necessary doors for me and my siblings to explore it.
Nathan: I was mostly self-taught from Saxon textbooks, my parents weren’t in a position to teach me anything advanced. I joined a MathCounts team made up of other students from our regional group. There was one engineer dad in the group who really accelerated our progress, and some of the other parents were really good at teaching us to assess every problem from a logical perspective and find not just the solution, but the best, fastest path to that solution. Everybody on that team was a total math dork by the end. We even took turns teaching each other on occasion (with supervision), because it helped us solidify the concepts in our own minds AND helped us all pick up things that the others were good at, which improved both our math skills and our ability to optimally function as a team during the cooperative portions of the competition.
Isaac: In retrospect, I think the mathematical education provided by my parents was highly successful. I think there are two particular aspects of my math instruction that were unique and provided immense benefit. First, my parents had a strong emphasis on understanding my learning style and providing curricula tailored to me. My parents were not tied to a single textbook and were attentive to my feedback, as well as maintaining their own assessments and backing them up with external standardized tests. Second, my parents stringently insisted that I absolute master a concept before moving on. I was able to take Algebra early, but struggled with the abstract concepts and was required to re-take the entire course. With a different curriculum and another semester to work on the material, I began to thrive and even enjoy the concepts. Having now worked with professional mathematicians, I see some of my parent’s weaknesses; they could have focused more on enabling independent discovery as a child and answering my sometimes more probing questions in deeper ways. However, they recognized their limitations and sought professional external math instruction after Algebra, which was also superlative and placed me in the very beneficial relationship with math I enjoy today.
Strong levels of parental involvement, a willingness to change curriculum to suit a child’s learning style, community college courses, math clubs or other extracurriculars—these things can provide children with the guidance and motivation they need to not just succeed at math but actually excell. Yes, all of these take more effort than simply handing a child a textbook and telling them to learn it. But then, whoever said homeschooling would be easy?