Jennifer Locraft Cuddapah and Christy Danko Graybeal
Associate Professors, Hood College, Frederick, Maryland, email@example.com and firstname.lastname@example.org
Although teacher educators often lament that teachers teach as they were taught, it is commonly assumed that future teachers of mathematics have had experience as students in typical mathematics classrooms. Yet, not all future teachers have had such experiences. An increasing number of teachers were homeschooled in contexts vastly different from traditional mathematics classes. So, if biography influences teaching centrally how do future teachers who were homeschooled as children plan to teach mathematics and how do they envision their learning experiences impacting their teaching? To begin to address these questions, four preservice elementary teachers, enrolled in a teacher preparation program, were individually interviewed at the end of their teaching internship semester. These candidates, who were on the cusp of teacher certification, were all homeschooled prior to entering college. Participants were asked about their experiences learning mathematics, why they decided to become teachers, and how they imagine their homeschooling experience will influence their teaching of mathematics. Then, midway through their first year of teaching, they completed a follow-up survey about how they were teaching mathematics in their current settings. Interviews and surveys were analyzed in order to better understand how this unique population of novice teachers’ experiences as homeschooled students influenced their thinking about teaching mathematics.
Keywords: teacher background, home schooling, homeschooling, mathematics instruction, elementary school mathematics, parents as teachers, individualized instruction, group dynamics, mathematics anxiety
Preservice teachers learn much of what it means to be a teacher through their experiences as students. What Lortie (1975) termed the “apprenticeship of observation” (p. 61) is cited as a reason for why education reform efforts fail. The value of teacher education programs is questioned because the trend is for teachers to teach as they were taught (Heaton & Mickelson, 2002; Smith, 1996). Howell (2012) writes, “The most persistent dilemma that remains a barrier to students of teaching becoming reflective knowers, thinkers, and doers, is their own narrow view of schools, children, and learning when they begin their teacher education programs” (p. 43). These views are crystallized through years of schooling experience from the student side of the desk. Other researchers (e.g., Boyd, Gorham, Justice, & Anderson, 2013; Grossman, 1991; Mewborn & Tyminski, 2006) point out that the cycle can be broken by giving preservice teachers opportunities to reflect on and analyze their experiences.
While researchers see the applicability of the apprenticeship of observation differently (Grossman, 1991; John, 1996; Mewborn & Tyminski, 2006; Rinke et al., 2013), they start with the premise that preservice teachers were students in typical classrooms. There is an absence of research on preservice teachers who were homeschooled and who had vastly different apprenticeship of observation experiences. Knowing the number of homeschooled students is steadily increasing and that many homeschooled students are likely to go on to college and perhaps major in education, it is important to build the research base about this particular profile of teacher.
Learning to Teach Mathematics
The National Council of Teachers of Mathematics (NCTM) outlined essential reform-oriented components for school mathematics programs in the early 1980s. Since then, NCTM has advocated for students to learn mathematical thinking. The movement towards reform-oriented mathematics instruction, where students are expected to generate and apply mathematical knowledge, has new legs with most states recently adopting the Common Core State Standards for Mathematics (CCSSM). One of the most challenging aspects of mathematics methods courses is helping preservice teachers recognize that they must teach both mathematics content and mathematical practices such as perseverance and the construction and critique of mathematical arguments.
Two teacher education learning experiences positioned to influence subject-specific pedagogy are the content methods course and student teaching. Ball (1990) writes,
A methods course is a particular curricular occasion, one that is different from other kinds of teacher education courses…. It is about acquiring new ways of thinking about teaching and learning. But it is also about developing pedagogical ways of doing, acting, and being as a teacher. And it is about a particular subject matter… (p. 10).
The student teaching experience is where, under the guidance and supervision of experienced educators, those learning to teach experience students and curriculum. There are many studies highlighting the practicum’s impact on learning (e.g., Cuenca, 2011; Torrez & Krebs, 2012).
One hurdle to learning to teach is the complexity involved in classroom interactions between students, teachers, learning, and curriculum (Grossman, Hammerness, & McDonald, 2009). Ball and Bass (2000) caution, “Because teaching practice is constructed in the interplay of mathematics, students and pedagogy, considerable parts of teachers’ work are embedded with uncertainties” (p. 90). Part of learning to teach is the process of not only understanding uncertainty but also feeling comfortable with it and knowing how to respond (Lampert & Ball, 1999). Belying the complexity and uncertainty inherent in learning to teach is how linear and predictable traditional mathematics instruction tends to be (Ebby, 2000).
When learning to teach mathematics, teacher candidates cannot be separated from their own mathematics learning experiences. This is a content-specific correlate of the apprenticeship of observation. Ball (1990) found that novices who were successful in mathematics were often not able or not interested in alternative ways of teaching and learning. Essentially, what worked for them should work for others. For novices who struggled learning mathematics, some either assumed that was just the way it was for some students or some instead sought to approach teaching mathematics alternatively. “But even if prospective teachers are critical of their own past teachers for teaching badly…, many of them lack alternative images of mathematics teaching, having had no other models” (Ball, 1990, p. 12). Additional complicating factors like the preponderance of females going into the lower grade levels of teaching coupled with the male/female discrepancies in mathematics achievement, anxiety, and course choice are reported in the literature (e.g., Bowd & Brady, 2003; Gunderson, Ramirez, Levine, & Beilock, 2012).
What has been proposed as part of reform efforts to improve teacher learning about mathematics is to purposefully interrupt past experience to make future changes (Ball, 1990; Ebby, 2000). Learning occurs from both good and bad experiences. Negative learning experiences, particularly those involving mathematics (Bekdemir, 2010; Boyd, Foster, Smith, & Boyd, 2014), can impede a novice’s experience learning to teach mathematics.
Through the apprenticeship of observation, “What students learn about teaching, then is intuitive and imitative rather than explicit and analytical; it is based on individual personalities rather than pedagogical principles” (Lortie, 1975, p. 62). Teacher education programs, therefore, can help candidates explore assumptions to become better equipped to respond to classroom situations (John, 1996). Grossman and McDonald (2008) call for teacher education practicums to focus on domain specific expertise. They describe “pedagogies of enactment” (p. 189) where teachers not only understand the structure of the content but they also discern what is happening and what needs to happen in a given moment based on that content and those interacting with it. This is the bridge between the university coursework and the internship experience where pedagogical content knowledge can be honed.
Approximately 3% of school-age (ages 5-17) children in the United States were homeschooled in 2011-12 (National Center for Education Statistics, 2014). This percentage has increased steadily for the past few decades and is predicted to continue to rise (Kunzman, 2012; Ray, 2010). The legal right to homeschool in all 50 states, the expansion of internet access, circulation of curricular materials, and online courses has led to increased incidences of homeschooling (Isenberg, 2007).
Much of the homeschooling literature attempts to characterize those who choose it (Hanna, 2012). Van Galen (1988) wrote about two categories of homeschoolers which is still a common construct used to describe the motivations of this population. The ideologues, which include conservative Christians, are those with philosophical clashes with schools who seek to homeschool in order to opt out of the moral and political stance of public schools. The pedagogues are those who critique teaching methods used in public schools and desire more creative teaching approaches.
The notion that families are motivated by conservative political and religious forces through a movement to reject public schooling (Apple, 2007) has been critiqued by some (Bauman, 2005; Davis, 2005). Davis (2005) highlights reasons such as health and special interest and learning needs, which inform the very personal, deliberate choice of a family to homeschool. Davis writes about other reasons such as peer pressure, family commitment and lifestyle, geography, safety, religion, pedagogical philosophy, and money. “One of the most significant things that I think the non-homeschooling public needs to understand about the motivations for homeschooling is that in almost every case, the reasons are multiple” (Davis, 2005). No matter the reason for homeschooling, 60% of Gallup Poll respondents support it (Bushaw & Lopez, 2013).
In terms of who chooses to homeschool, some authors have noted the increasing variation within the population. Bauman (2005) writes about the profile of homeschoolers and indicates that “homeschoolers are not at the extremes of education or income.” Homeschooling is increasing in the Black community, cutting across racial and class lines (Coleman, 2003; Mazama & Lundy, 2013; Sampson, 2005). Kunzman (2012) highlights the variability of culture, ideology, and practice of the homeschooling population. Homeschooling families are not necessarily utilizing a single schooling approach for all grade levels or for every child in the home. Rather, families who homeschool are likely to send one or more of their children to a school or may opt to send a homeschooled child to school part-time or for other grades (Bauman, 2005; Isenberg, 2006).
Further, when Martin-Chang, Gould, & Meuse (2011) initially sought to research academic achievement of homeschoolers, they anticipated comparing homeschoolers with traditional public schoolers. Yet, the homeschooler population was not as homogeneous as they thought. Some parents utilize prescriptive lessons or curricula and follow a structure while some opt for an open-ended approach. In a similar vein, Anthony and Burroughs (2012) report in their case study of four homeschool families that homeschooling planning is akin to restaurant menu ordering; families select from among the offerings.
In the current accountability era, it is not surprising that some researchers seek homeschool student achievement data. The use of large databases, such as the Trends in International Mathematics and Science Study (TIMSS) and the National Assessment of Educational Progress (NAEP), is a challenge because homeschoolers are not included in these data sets (Nemer, 2002). The one national assessment which reports out homeschooler performance is the Scholastic Achievement Test (SAT) (see Belfield, 2002), but the drawback of these data is that the test-takers are not a randomized group (Isenberg, 2007). Despite the challenges, there has been research reporting high achievement of homeschoolers (Ray, 2010; Rudner, 1999). Notably, much of this research acknowledges that the data gathered is from volunteer participants who openly homeschool and that there is a large homeschool population operating outside purview. Additionally, because the methodology of the studies is limited in generalizability and reliability, there are calls for more research to better understand homeschooled students’ achievement (Kunzman & Gaither, 2013).
Ray (2004) explains how qualities like self-discipline, motivation, and initiative contribute to research showing “that the home-educated college applicant is very likely to succeed in college, both academically and socially” (p. 10). Martin-Chang et al. (2011) administered the Woodcock–Johnson to a total of 74 children and found that “structured homeschooled children achieved higher standardized scores compared with children attending public school. Exploratory analyses also suggest that the unstructured homeschoolers are achieving the lowest standardized scores across the 3 groups” (p. 195). Regarding mathematics achievement in particular, Kunzman and Gaither (2013) reviewed homeschooling literature. The authors tentatively conclude that “there may be at least a modest homeschooling effect on academic achievement—namely that it tends to improve students’ verbal and weaken their math capacities” (Kunzman & Gaither, 2013, p. 17).
Despite the growth in popularity and support of homeschooling, there is a dearth of research on teachers who were homeschooled. It is unknown how many students in teacher preparation programs were homeschooled as children. This study seeks to contribute to the literature by focusing specifically on homeschooled teacher candidates’ learning about mathematics.
Seeking to better understand the experiences of teacher education candidates who were homeschooled, we employed interview methods and present findings as case studies of four participants (Merriam, 2001). Because we two researchers are teacher educators in the college preparing these candidates, we came to the study through our own interests and experiences. Author 2 is the mathematics methods instructor for students in the early childhood and elementary/special education programs so she knew each participant. Author 1 coordinates the secondary initial certification program. As she has taught courses in the early childhood and elementary/special education programs, she worked with one of the four participants in the study. She met the other three for the first time during the interviews.
We engaged in collaborative research after we realized we had a mutual interest in knowing more about the impressive homeschooled candidates we were teaching and how surprised we were that they wanted to become classroom teachers. Because neither of us was homeschooled, we knew we had assumptions about it and what students from it might be like in the “real world of public schools.” We decided to focus on mathematics because it is an area where the calls for change have been slow to be realized (CCSSI, 2010; NCTM, 2000). We undertook a descriptive case study inquiry to learn from the four homeschooled teacher education candidates who were enrolled in the initial certification programs across the two years during which we gathered data. Our research questions were, “How do future teachers who were homeschooled plan to teach mathematics and how do they envision their own learning experiences influencing their teaching of mathematics?”
Research took place at a small, private four-year liberal-arts college in the mid-Atlantic. Serving approximately 2400 undergraduate and graduate students, the college is well-known in the state for its teacher preparation programs. The Education Department offers initial certification programs in early childhood, elementary/special, and secondary education. Each year, there are approximately 45 initial certification graduates, and of these, typically one or two of them was homeschooled prior to enrolling at the college.
National Council for Accreditation of Teacher Education (NCATE) accredited initial certification programs at the college consist of coursework and teaching experiences leading to eligibility for state licensure. Courses are typical teacher preparation ones which include child development, working with diverse learners, instructional methods, and assessment. Every semester preservice teachers are enrolled in education courses; they are also assigned a field experience in a partnering public school district. They begin with observation and assume more classroom responsibility culminating in full-time student teaching during their last semester.
In order to explore the learning experiences of homeschooled teachers, we sought input from all of the initial certification candidates enrolled in our teacher preparation program who were homeschooled. Thus, our sampling was purposive and homogeneous (Miles, Huberman, & Saldaña, 2013). The four participants (pseudonyms used) are white females in their early 20s who were homeschooled for a significant timeframe prior to entering college. Three participants were in the early childhood preparation program, and one was in the dual certification program for elementary/special education. What follows are descriptions of their homeschooling experiences written from their interview data.
Joanna attended a small, private, Christian school for kindergarten and first grades. Before Joanna entered second grade, her mother felt called by God to homeschool Joanna and her two sisters. Joanna calls her mother a natural teacher. Joanna’s mother had always wanted to become a teacher, but she became an accountant instead. She was Joanna’s sole teacher for grades two through eight. Joanna’s mother was very structured and had a schedule to ensure that the three girls would rotate through different disciplines. In the beginning, her mother was very involved in instruction, but as Joanna got older, she became more independent and began to learn more through the reading of textbooks. At the end of every day, she would meet with her mother for an hour or two to discuss what she learned that day and to address any questions. For high school, Joanna continued to be homeschooled primarily by her mother, but she also took classes with other homeschooled students. These classes were taught by other mothers. Joanna described this as similar to a college format where they would have class once or twice a week and then work on homework between classes. Joanna attributes her preparation for college to this schedule. She learned “how to be independent and how to manage my time well.” Since graduating from her teacher preparation program, Joanna was hired to teach third grade at the private Christian school she attended as a kindergartener and first grader.
Andrea was taught by her mother for her entire educational career until she was in the 12th grade and began taking mathematics courses at the local community college. Her mother chose to homeschool Andrea, her older brother and her younger sister after a school administration change at the Christian school her brother was attending at the time. Andrea’s mother graduated from high school, but did not finish college. Andrea’s mother loves learning and has a strong work ethic that Andrea admires. Until seventh grade, Andrea and her mother would read textbooks together and work through problems together. After that, Andrea learned on her own for the most part. Andrea took art classes with other homeschooled children and dance lessons at a local dance studio. She fondly remembers the individualized instruction that her mother was able to provide and the many day trips to museums and science centers that they took. Now, as a novice teacher, Andrea frequently discusses teaching ideas with her mother. Since graduation, Andrea has been teaching kindergarten at a public elementary school.
Amy began school in the public school system. In first grade, her teacher was ill, and she had a long-term substitute teacher who frequently called on students who had not raised their hands. When Amy did not know an answer, she would become embarrassed and upset. She particularly hated not being able to answer mathematics questions and begged her mother to not make her go back to school. So, in the middle of first grade, Amy’s mother began to homeschool her. Amy’s mother had worked for the public school system in a variety of supportive positions such as instructional assistant but had no formal training in teaching. Her mother continued to homeschool her through fifth grade. In sixth grade, Amy reentered public schools. She described this reentry as traumatic and she especially hated mathematics class. She begged her mother to continue homeschooling her, but her mother insisted that she stick it out. Unlike the other prospective teachers, Amy has four older siblings who all attended public schools for the duration of their educational careers. Since completing the teacher preparation program, Amy has been hired as a special education teacher at a public elementary school.
Unlike the other participants, Elizabeth’s homeschooling experience was negative. She is the eldest of three. Elizabeth was born prematurely, is deaf in one ear, and has difficulty tracking with her eyes when reading. She did not attend preschool and entered kindergarten at age four. She struggled in kindergarten and first grade, and midway through first grade her mother was frustrated with the school so she pulled Elizabeth and her sister out of school. Elizabeth’s mother attended college but did not graduate. Until Elizabeth was in grade four, her mother followed a homeschool curriculum but near the end of fourth grade everything fell apart. Elizabeth’s father was struggling with addictions and abusing her, her mother was struggling with mental illness, and her parents were not able to ensure that Elizabeth and her siblings were receiving the support and care they needed to learn and grow at home. Occasionally Elizabeth, her siblings, and her mother would need to check in with the local school system. One time her mother told Elizabeth and her siblings not to say anything negative about their situation. “If you tell them anything about our [home]school, they’re going to take you away and they’re going to put you in a bad place. They will make you go to school and you’re going to hate it. You’re going to get bullied and bad things are going to happen.” This was the last check-in that Elizabeth remembers. After that, Elizabeth’s father was arrested for abuse and her mother stopped teaching them. Elizabeth and her siblings spent their days watching television. Her mother taught the children what to say when in public so that no one would know that they were not learning. Despite there being no record of her education between grades four and twelve, when Elizabeth was 17, and her peers were graduating from high school, her mother gave her a piece of paper saying that she is a high school graduate. This was not an official document, so Elizabeth does not have a valid high school diploma or General Equivalency Degree (G.E.D.). Soon after this, she was working three jobs and trying to care for her brother, sister, and mother when one of her employers told her about community college and then helped her to navigate placement testing and enroll in some basic courses. After earning 60 credits with a 3.8 G.P.A. and writing essays explaining her life experiences, Elizabeth’s resilience stood out more than her lack of formal schooling. She was able to transfer to our four-year school to complete her teaching degree. Since graduating from college, she has been working as a first grade teacher in a public school and has begun work on a graduate degree in educational leadership.
Data Collection and Analysis
The four homeschooled candidates in the teacher preparation programs were contacted individually through informal conversation and more formally through a follow-up email. Each expressed eagerness to participate. Individual, in-depth interviews were scheduled during the candidate’s full-time student teaching semester and took place at the college in Author 2’s office. At each interview, informed consent was explained and signed, and permission to audio record was ascertained.
The interview protocol included specific questions (see Appendix A); however, additional probes stemming from each interview were added where appropriate. Participants were asked to talk about their experiences and thoughts about being homeschooled, what they remembered about learning mathematics, why they decided to become teachers, how they might approach teaching a particular Common Core standard in mathematics, and about their mathematics teaching and learning coursework and field experiences. Amy, Andrea, and Joanna had interviews lasting about 45 minutes, and Elizabeth’s lasted about two hours. Audio recordings were transcribed for analysis.
Transcript data were analyzed individually and comparatively. First, each transcript was read to look at each individual’s experiences holistically. Next, places where experiences and ideas overlapped were identified. A summary of each participant’s interview was written, and initial thoughts about what findings stood out most prominently as well as what questions still lingered were captured in researcher notes. These notes were used to compile a follow-up survey (see Appendix B), which was sent to the four participants halfway through their first year of teaching. The survey asked about fathers’ roles in homeschooling, anxiety levels about mathematics at different points in schooling, current mathematics teaching practices, and advice for other homeschoolers considering teaching. Surveys were analyzed comparatively not only looking for intersections with interview data but also across the participants for repetitive ideas expressed. Themes emerged from the transcripts and surveys in the repetitive codes.
Findings and Discussion
Each participant shared her own experience of being homeschooled and becoming a teacher. Common themes which permeated these individual experiences included the role of the preservice teachers’ mothers, the importance of personalized instruction, discussion of student collaboration and generation of solution methods, and anxiety about mathematics. Presentation and discussion of each theme follows.
Mother as Teacher
The mothers of the four the prospective teachers were their primary caregivers and teachers. For example, Andrea’s mother used her knowledge of each of her children to structure their homeschool days. Andrea recalled,
“With my brother, he’s nocturnal so she would allow him to sleep in because I mean she could’ve gotten him up and had him do his work in the morning but was he really going to learn well? No. She knew that. She would let him sleep and then he still had to get his work done… it didn’t matter what time it was…. Not having those time constraints was really helpful. My sister and I were in the morning and she was able to balance us both out. She knew when there was something that I could do independently, she would be working on something that my sister needed help with and then she could flip flop.”
Today, Andrea and her mother have teaching in common, and they talk frequently about their practices. Andrea surmises that had her mother had access to the internet and some of the more modern practices and knowledge about manipulatives, she would have certainly used these in her homeschooling. “She would’ve been using all those things. She would’ve gone online. She would’ve been able to go to these different places, give these resources….She’s very open to new things.”
In a similar way, Amy’s mother used her knowledge of her child in her approach. Amy recalls, “I just remember it being a lot different with my mom, because she didn’t seek to embarrass me or make me feel bad, and I was more comfortable with her. She knew I was a shyer kid, so she was in tune to that.” Amy’s mother frequently incorporated cooking into mathematics instruction bringing a real life authenticity to her learning.
Although this was a short-lived positive experience in her otherwise tumultuous homeschooling life, Elizabeth briefly joined other homeschooled students to be taught by other mothers. She said, “We joined a co-op, which a lot of homeschoolers do.… We had one mom that had a doctorate in some kind of science, and she was wonderful….” Joanna participated in similar experiences where a mother would teach a group of homeschooled students. She said, “It’s similar to how the college format is set up where we’d have class once or twice a week. Then we’d have homework that we would do in between the classes.”
Absent from these homeschooling experiences with their own or other mothers is the mention of fathers. The implementation of school was seen as the mother’s work. When collaborations happen, these are between and amongst mothers. When probed about this silence, participants shared their perception of their fathers’ involvement in their schooling. Joanna’s father was the financial provider of the curriculum and learning materials. Amy’s father read to her every night and worked with her on mathematics. When Amy was in middle school and high school (in the public school setting) her father provided help with mathematics, science, and social studies. Andrea’s father always traveled to museums, science centers, and historical landmarks with the family. He also helped Andrea with mathematics. In contrast to the supportive side roles of these three participants’ fathers, Elizabeth’s father played almost no positive role in her education. Elizabeth shared,
“When I was little and he was still in the home, he kept my mother on track, ensuring that she was teaching my siblings and I. However, he worked 80 hour weeks on average and was rarely around. By late elementary school, he was more and more distant in my education. When he was home, he was drinking, impossible to interact with, and abusive. Without him to encourage my mother to keep trying to teach me and my siblings, she soon stopped. I struggled to learn to read and understand mathematics by then. In what would have been middle school, he was arrested for abusing me. After that, he played no part in my education.”
The centrality of the mother in the teacher role is interesting to consider as these homeschooled women become teachers themselves. Because their mothers served as their teachers, the mothers were the role models of the homeschool apprenticeship of observation experiences. What they learned about teaching and approaching the learning process was shaped by a teacher figure who also embodied other roles and qualities with the home/family structure. Traditionally schooled children do not readily have access to the home lives of their teachers nor are they likely to be privy to the roles and family life qualities that teachers have outside of school. Whether those roles and qualities were mostly positive (as was the case for Amy, Joanna, and Andrea) or whether these roles and qualities were more dysfunctional and alarming (as was Elizabeth’s experience), the attention to individual child needs and caregiving permeated what was learned from these mothers and valued enough to be brought into their own descriptions about teaching.
One of the values each participant holds, carried over from what she learned from being homeschooled by her mother is the importance of individualized instruction. For example, Andrea believes that homeschooling helped her because she was able to take time to master a skill. “I did get it eventually, I just needed more time… Being homeschooled gave me that opportunity….” On the other hand, if something came easily to her, she was able to quickly move on to the next topic. Andrea knows that the individualized pacing of homeschooling is what helped her learn best and seeks to incorporate this in her classroom teaching.
Amy shared the following advice for other homeschooled students wishing to pursue a career in teaching:
“I would ask them to take into consideration how important individualized instruction was to their educational experience and always keep in mind that individual students need different strategies, approaches and contexts for learning in order to be successful. And most importantly, I would advise them to always teach with the patience, compassion and love they likely received in their homeschooling experience in order to nurture and cultivate the young minds they encounter and foster a love of learning through risk-taking and trying new things, rather than anxiety over the unknown or fear of failure.”
Although Elizabeth withstood the negative side of homeschooling, she still values the personalized mindset that characterizes the practice. She believes her perspective will help her identify neglected or abused students. She shared,
“Coming out of what I’ve come out of, I see what they’re going through. I can spot a kid that’s being neglected, who’s being abused, who’s struggling to learn because I’ve had all of those things. My heart goes out to those kids. The challenging ones that have behavior off the wall, those a lot of the time are the ones that I enjoy working with the most because something is going on.”
Elizabeth was in an interesting position to observe positive homeschooling practices when she went to live with her aunt, uncle and cousins when she was a young adult. Her aunt homeschooled her cousins.
“When my aunt taught her kids and I watched it, I was like, ‘Oh my gosh, this is what homeschooling is supposed to be? Wow.’ Her day was very structured. It was structured like a school day was. You got up. You did your work. You played. It was the coolest thing I’d ever seen, especially now. Now, I get to go back through her resources and her lesson plans and see what she did. Home schooling can be awesome. You can completely tailor your instruction to each child’s individual needs. You can’t do that in a classroom.”
Elizabeth’s perspective is particularly valuable because she experienced the horrific side of homeschooling but is able to articulate and explain the valuable side that she knew she missed. Despite this and because of this, her own homeschooling experiences position her as quite a gifted and empathetic teacher.
Individualized instruction was a normal, unquestioned aspect of the participants’ apprenticeships of observation. As such, their own individualized learning experiences instilled in them the belief that personalized education is necessary. As Andrea so aptly characterized it,
“One of the most beneficial parts of being homeschooled is being able to differentiate and personalize instruction, learning style, pace of learning, and interests. I think that my experience of knowing how essential differentiation was in my education is reflected in my own teaching within a classroom setting. Although it is more difficult to implement differentiated instruction within a classroom setting, it is essential to make every effort to give students in a classroom the same opportunity to have an individualized approach to education.”
Collaboration/Multiple Solution Methods
Although the homeschooled teachers appreciated their individualized instruction, they also feel they missed some of the benefits of having peers with whom to collaborate. As Joanna articulated,
“I would’ve really liked to have had a little bit more experiences, just sharing different ideas….I was socialized, but I think it would’ve been nicer to have been able to bounce off different ideas from classmates….I definitely see the value of learning in the classroom… I remember growing up thinking I only want to homeschool, but now going through this program it’s like there’s a lot you can learn in the classroom, too.”
She and others acquired this next level of perspective from their teacher preparation coursework and student teaching experiences. Because they were somewhat sheltered, they are surprised by the diverse thinking of their students and see the value of helping their students consider multiple problem solving methods. They formed a more astute sense of what collaborative thinking and problem solving can do to facilitate student learning.
Andrea shared, “When I learned how to solve math problems, I learned how to complete the problem using one strategy. Typically, I did not understand why or how this strategy worked. Now as a teacher, my goal is to provide students with several strategies to solve one problem.” In a similar way, Elizabeth sees her role in the classroom as going beyond one-dimensional mathematics teaching. “You don’t just have to teach your kids math with the standard algorithms. There are different ways to do things. Letting them exploratory learn and… connecting everything to real life experiences.”
Joanna’s mother used Saxon textbooks and rarely used manipulatives or other physical models, instead focusing solely on the algorithm. In high school she used a program designed for homeschoolers which had lessons on the computer and problem sets. Joanna looks back on this and says,
“It was very much, ‘This is the algorithm. This is what you do.’ I did well in math. I was able to follow, but I would get frustrated a lot. I remember asking my mom, ‘Why is it like that?’ She would be like, ‘That’s just the way it is. That’s how it is.’ I was like, ‘But why?’ Even now, I didn’t really learn the why until I did the [mathematics] methods class.”
In hindsight, Joanna infers that learning mathematics would have been more fun if she had had more opportunities for collaboration and more hands-on experiences. Thus, as a teacher, she considers ways to infuse fun and collaboration into her instruction. She realized her teacher preparation professors were using practices they wanted her to acquire.
“You [professors] model how to teach as you’re teaching us how to teach, so just the whole group collaboration and the coming up and sharing, like how to talk to the person next to you. I never had that before, but the fact that you organize your class that way… [professors] are teaching us how to teach.”
Later she explained,
“As I continued to learn how to teach, it was all education professors. Same format, just how you [education professors] talk, even different than English professors. It wasn’t just ‘I’m going to stand up here and give you a lecture.’ It was ‘How can we all learn together? Let’s all share ideas.’ That’s how I prefer learning too….I like talking about [information], discussing it.”
In their current teaching, the teachers purposefully build time into lessons for students to collaborate and share student-generated solution methods. Joanna says, “When I teach, I don’t like having my students just sit there and do work for a long time because I remember what it was like. It got a little boring, so I like to involve my students and have them share ideas with each other.” In describing her own mathematics instruction in her first year of teaching, Andrea says, “The conversation that takes place in small groups allows students to demonstrate the how and why components of problem solving…Students are also provided with the opportunity to work with their peers to problem solve and share their own understanding.” It seems that their individualized learning experiences have helped them come to appreciate the positive role peers can play in mathematics education.
When participants were prompted to share their mathematics learning experiences in homeschooling, we did not specifically ask them to talk about anxiety —a topic permeating the literature on females and mathematics (e.g., Bowd & Brady, 2003; Gunderson et. al., 2012)—but each of them did so. Their own feelings and experiences shape how they approached later mathematics learning opportunities as well as how they plan for mathematics instruction with their own students.
Amy began being homeschooled midway through first grade and recalls her stress being directly related to mathematics. She remembers,
“We had a long-term sub,…and she was not the nicest teacher…I just remember her embarrassing us…I used to get really upset. So, I would go home and just tell my mom, ‘I don’t want to go back. I don’t want to go back. I hate it.’ And I remember it being specifically math-related, because I didn’t know, and I didn’t understand, and I was like, ‘Don’t call on me,’ the whole time. That’s when my mom pulled me to be homeschooled.”
After elementary school, Amy returned to public school for middle school and she still experienced anxiety about mathematics. She said, “It was just always a source of embarrassment, and I was always so not confident in it. I was never confident in math. I remember being terrified in math class.” The hands-on mathematics her mother did with her, related to using fractions in cooking, were the only concepts with which she felt more comfortable. She attributes this to the fact that her mother was “just disguising it.” Amy has brought these experiences into her own approach with her current students. She strives to make the learning environment low stress and focuses on each student as an individual. She says, “I really try to get a grasp of how my kids are going to learn math best for them, not what works for me.”
When asked about what her highest level of mathematics, Andrea chuckles about ever having the desire to take pre-calculus or calculus.
“No (laughing). I think that I could just because I’m so determined and if I’m given a task I’ll get there eventually. It may take me a little longer and it may be a struggle, but eventually I will get there and I will figure it out. Could I? Yes. Did I have the desire? No (laughing). I’m good with my elementary mathematics.”
Her knowledge about herself as a learner conveys the confidence she has. Her response indicates that she did not avoid higher levels of mathematics because of anxiety.
Elizabeth remembers not liking school much when she was in the early elementary years because she did not learn to read until fourth grade. This was likely due to her deafness in one ear and not having a structured homeschooling routine. She remembers that none of her subjects made sense to her. But, then she recalls how her mother
“started reading Laura Ingalls Wilder books to me, and I got caught up in the story and I loved it. I realized that reading could be fun, and I started reading. Once that piece came together, the math started coming together, because I could read what I was supposed to be doing. I remember her using a lot of manipulatives in math, and I think that I remember liking using them. It’s about all I remember. Unfortunately, though after fourth grade stuff just went south with my family. Everything fell apart over a matter of years.”
Had her family life not been so tumultuous, she may not have continued to slip behind in her schooling. Elizabeth says she stopped learning mathematics after long division. As a child, she never was taught fractions. “I learned fractions when I came to [college] and took [the two mathematics for elementary teachers courses].” She became acutely aware of an anxious moment when she dabbled in an online learning curriculum as a middle school aged student. She shared her experience of looking at one of the mathematics classes. “There’s this algebra class on there. I’m like, ‘Why are there letters in math? When did this happen?’ I got really confused.” She confronted her own anxiety again in community college where she tested at the pre-algebra level. Instead of being discouraged about how far behind she was, she says, “for the first time in my life I realized I wasn’t stupid, I could learn and I had every opportunity at my fingertips.” She took advantage of these learning experiences, worked hard, and performed well in a structured schooling environment. Elizabeth did not have to unlearn or relearn mathematics; she just picked up with concepts she had never seen nor learned before and embraced them. Referring to the successes her siblings and she experienced in their college performances, Elizabeth surmises, “I think we knew what a privilege an education was. Once we got the opportunity to learn, we ran with it.”
Because anxiety was mentioned by all participants during the interviews, we followed-up with a short survey. Participants shared their anxiety levels about mathematics at various points in their lives being prompted, “On a scale of 1-5 (with 1 being the least and 5 being the greatest), how would you estimate your own level of anxiety about math at different times in your life?” Results can be seen in Table 1.
The anxiety levels are lowest for the elementary years, both when they were elementary aged and learning the mathematics as well as now when they are teaching this level of mathematics. Middle and high school level mathematics are associated with the highest levels of self-reported anxiety. College level is mixed, although it should be noted that most of the mathematics these teachers took in college is mathematics geared towards elementary teachers. The same prompt was not asked of non-homeschooled teachers, so results cannot be compared. Yet, from this initial analysis, these homeschooled teachers have less anxiety about mathematics they are teaching, than is typically presumed and reported in some articles (Bowd & Brady, 2003; Gunderson et al., 2012). Perhaps this is a result of the individualized, personalized nature of the mathematics instruction they received in homeschooling. Perhaps this is due to the teachers they had, who were primarily their mothers. Perhaps this can be attributed to the elementary levels of mathematics being something their mothers were skilled at and comfortable teaching. No matter what the greatest influence is on their lack of anxiety, unlike reports of other early grades teachers, these four homeschooled teachers are not shirking away from teaching mathematics in their current professional roles.
Table 1. Self-Reported Anxiety Levels about Mathematics.
Note: 1 indicates low levels of anxiety and 5 indicates high levels.
Our initial foray into exploring the experiences of homeschooled teachers, albeit a sample of four, has important implications for research and practice. First, in terms of research implications, it is important to build the literature base about the different kinds of teachers coming into the profession. Understanding the experiences of the homeschooled teacher candidate can enrich what is known about the profession and who chooses to enter it. It is critical to examine how different schooling experiences of teachers influence their approaches to pedagogy, and particularly pedagogy in certain content areas. Linked to what Ball (1990) reports, this sample of homeschooled teachers drew from their methods course learning in shaping the value of particular content pedagogy because it was so different from the more linear, predictable approach (Ebby, 2000) they experienced. Knowing that this group of homeschooled teachers sees the value in individualized instruction as well as collaboration because of their homeschooling experiences adds to what we know about the narrow views of schooling that teachers from traditional forms of schooling have learned through their apprenticeship of observation experiences (Howell, 2012; Lortie, 1975).
Second, it would be interesting to further explore the role of the fathers in the education experiences of homeschooled teacher candidates and particularly their influence on the preservice teachers’ learning about mathematics. The focus on the mother as the central figure in the education of the children is common in the literature (Anthony & Burroughs, 2012; Apple, 2007; Mazama & Lundy, 2013) and is seen in the experiences of the teachers we talked with. The gendered nature of teaching as a profession as well as the gendered experiences of mathematics teaching and learning warrants specific attention in future research.
A third area for future research is a comparison of preservice teachers’ anxiety levels about learning mathematics as a homeschooled versus a traditionally schooled student. Participants shared how they had less anxiety in their elementary level years which increased steadily throughout middle school and then high school. Then, in college and currently they have less anxiety about mathematics, which is congruent with Bowd and Brady’s (2003) findings. In light of Beilock, Gunderson, Ramirez, and Levine’s (2010) finding that female teachers’ mathematics anxiety affects the achievement of their female mathematics students, there are interesting prospects for future research to probe whether homeschooled teachers’ lessened anxiety is the result of the nature of the content they are learning and teaching–elementary level material–and the familiarity and comfort they already experienced with it or if there is something unique about the way it is taught and understood while in a teacher preparation program that makes it more accessible to these teachers.
Findings from this study indicate that the perspective homeschooled teachers bring to the profession, one which embraces individualized, personalized instruction (Romanowski, 2001), is valuable for practice. Although our participants did not experience traditional classrooms for the entirety of their pre-K-12 schooling, they were drawn to and became dedicated to the profession, embracing the necessity of differentiation for their diverse students. Three of them experienced the tremendous benefits of individualized learning, and in Elizabeth’s case, one felt the profound effects of not having individual needs met. These experiences were assimilated in their apprenticeships of observation (Lortie, 1975). They were successful preservice candidates who performed well and were readily hired after graduation. In terms of practice for teacher preparation programs, homeschooled teacher candidates might be a particular profile to be targeted for education program recruitment.
Another implication for practice is for teacher education programs to include multiple field experiences, particularly for the homeschooled candidate, who might not otherwise have experiences with public classroom settings. This highlights the critical role mathematics methods courses and preservice clinical experiences play in the development of the homeschooled candidate, particularly for their enactment of mathematical understanding and pedagogy (Ball & Bass, 2000; Grossman & McDonald, 2008). Since most homeschooled future teachers’ mothers have a particular depth of mathematical content knowledge (Kunzman & Gaither, 2013), the college practicum is positioned to be particularly influential. Selection of appropriate mentors/cooperating teachers for student teaching must be mindful, since homeschooled teacher candidates need to observe role models who are teaching in the reform-oriented ways NCTM and CCSSM call for as being particularly effective for developing deep mathematical understanding. Having such role models can enrich their apprenticeship of observation experiences as they learn about and apply their pedagogical knowledge about mathematics.
Appendix A. Interview Protocol
- Talk to us about your homeschooling experiences.
- Tell us about your experiences learning mathematics specifically.
- Who taught you? Alone or in groups?
- Describe a typical day/week.
- What curricular materials did you use? Manipulatives? Assessments?
- What did you find easy about math?
- What did you find difficult about math?
- Why did you decide to become a teacher?
- What do you imagine will be your biggest challenge with regard to teaching mathematics?
- Thinking about a specific standard from the Common Core, how do you imagine that you would teach this topic? What resources would you use to plan? Walk us through a lesson.
- For example: CCSS 2NBT.5: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
- Thinking about your coursework here at [our college] and your field experiences, what has surprised you about mathematics teaching and learning?
- In what ways do you imagine that your home schooled experiences will influence your teaching of mathematics?
- If you have kids, do you think you will homeschool them? Why or why not?
Appendix B. Survey Questions
- What was your father’s role in your education?
- Why did you decide to major in Education as an undergraduate (as opposed to doing a Master of Arts in Teaching or non-traditional certification program like Teach for America)?
- What advice would you give another homeschooled student who is interested in becoming a teacher?
- On a scale of 1-5 (with 1 being the least and 5 being the greatest), how would you estimate your own level of anxiety about math?
- Highlight in grades K-2
- in grades 3-5
- in grades 6-8
- in grades 9-12
- in college
- What grade level(s) are you currently teaching?
- How does teaching compare with what you thought it would be before you started?
- Are you responsible for teaching math this year?Highlight
- Thinking about your math teaching, how many times in the past week did you:
- Highlight teach a math lesson?
- have students use manipulatives?
- have students discuss math ideas with one another?
- have students work on a true problem (one that students don’t already know how to solve)?
Author 2 emailed you the copy of your transcript where you talked about how you would plan to teach a math lesson. Please look at what you said before you had started teaching. Now that you are teaching, please comment about what, if anything you would change from what you said before.
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