The popularity of home schooling and failures of the public schools often present the need for parents to teach or supplement college preparatory math courses at home. A common sequence is Algebra 1, Geometry, Algebra 2, and Precalculus. In many cases, the challenges of these courses is beyond what parents themselves can muster, and the parents need to choose curricular materials to bridge the gap between the instruction they can provide directly and what their high school students need to be prepared for their college dreams.

The popularity of distance learning, the home schooling movement, entrepreneurial efforts, and non-profit organizations have combined to provide a number of high quality choices compared with what was available 10-15 years ago. A parent willing to consider the options and work to find a match for their students’ needs can likely improve their learning quality without having to relearn high school math themselves or hire a private tutor.

Learning math is hard, and while effort and careful consideration are appropriate when overcoming hard challenges, people of faith should recognize prayer is fundamentally more important. Parents should exercise faith through prayer when planning a curriculum or supplemental instruction and continue exercising prayer for their children as the children work their way through challenging coursework. Parents should also have faith that their children can succeed in challenging subjects, because their children are made in the image of God, and God said that what he created is good. Recalling their own struggles in math should give parents empathy for their children, but it should not shake the parents’ faith that their children can accomplish things that the parents did not. The “all things” that “are possible with God” certainly includes math.

One promise of Scripture is that “all hard work brings a profit.” There are no silver bullets in math education: no way to learn without hard work. The goal of selecting an instructional or supplemental program is to find a match between delivery methods and student learning styles so that the student will be motivated and willing to work hard to benefit from the desired outcome from working 1 hour or so per day for 180 instructional days per year over the course of a four year high school program. Scripture also says, “Many advisers make victory sure.” Each program has strengths and weaknesses, and the best way to ensure that the weaknesses in any single program are not a long term barrier to success is to employ more than one program over the course of a four year high school math education.

ALEKS

ALEKS is my favorite recommendation for both primary coursework and supplementation, because it is an intelligent learning system that quickly figures out which areas a student has already mastered and focuses practice and learning in specific areas of weakness and need. This greatly streamlines the learning process by focusing 80-90% of the material on the areas where it is needed the most. Repetition of material that has already been mastered is a frequent source of frustration for students who often feel like they are wasting their time. It can also be a source of false confidence if a student fails to gain competence in new material while working review problems correctly.

I’ve taught hundreds of students in introductory Calculus and Physics courses who were poorly prepared with a variety of traditional curricula and even earned As and Bs throughout their high school math experiences. Grades from brick and mortar schools are a poor predictor of success in college coursework. There is probably no better predictor of success in college Calculus and Physics than a complete ALEKS pie in Precalculus.

ALEKS Pre-Calc Pie

This figure shows a student “pie” from the ALEKS Precalculus course.

ALEKS can be very productively used either for original coursework or for assessment, refreshing, and review. A student who has already truly mastered the material from a good high school Precalculus course can complete their ALEKS pie in about 1 week, working one hour per day. Students whose high school coursework may not have been complete or rigorous (or who forgot some things) will take longer.

ALEKS offers progress reports in a number of formats that allows parents and teachers to monitor student effort and progress in ways to identify problems and provide accountability without needing a detailed understanding of the material. In cases where a student is stuck in a challenging area and the built in tutorials and hints are not helping, some alternate learning strategies may be employed such as: 1) Reading the relevant sections in a traditional textbook 2) Reading the relevant Wikipedia pages 3) Viewing the relevant Khan Academy videos or YouTube videos on the same material 4) Seeking help from a tutor or other subject matter expert.

I should admit that I was originally opposed to ALEKS, especially when it was touted as a replacement of the online assessment and remediation system in prior use at the Air Force Academy when I served on the math faculty there. I just didn’t believe it was capable of quickly identifying areas of student strengths and weaknesses. Fortunately, my colleagues prevailed, and I got to see first hand how good the system really is.

Saxon Math

Saxon Math is very popular among home schooling households, because the textbook series uses an incremental learning approach that only introduces one new concept and skill at a time and gives a lot of opportunity to review previously acquired skills. It is probably among the easiest textbook series for students to read and pick up skills in cases where they are relying much more on learning directly from a textbook without the benefit of a classroom instructor.

The downside of Saxon Math is that students often have difficulties converting the style and language used for teaching and exercises in the Saxon Math series when they need to use these math skills in other contexts. A strength of Saxon is that it teaches specific recipes for specific types of problems. But this can become a weakness when students need to develop their own problem solving recipes or when problems in a different context are more challenging to classify to recognize what recipe is needed.

Still, a student who has completed the high school Saxon Math series and truly mastered the material through Precalculus is well prepared for college math. I would recommend some level of practice for the relevant algebra and trig skills in a different context, such as a good year long high school physics class, a Coursera course in Precalculus or Calculus One, a review of Precalculus in ALEKS, or some suitable opportunity to begin a transition of what they have learned in Saxon Math to different contexts. Once a real college Calculus or Physics class is under way, the material is most likely coming too quickly to translate the math they know to the skills they need every day.

In my view, the big weakness in most book based programs (Saxon, Life of Fred, etc.) when administered by adults who don’t actually understand the material (and are not willing or able to really learn it), is that it is difficult for these adults to provide the needed assessment and accountability. Making use of answers in the back is very limited for those who can’t understand for certain whether those answers are right and who cannot explain to a student where they may have gone wrong when they obtain different answers.

Students are pretty adept at fooling parents when the best parents can do is ask “Did you do the practice work?” and “Can you show it to me?” Many purported efforts at completing math assignments are little more than copied answers from the back with (when required) mediocre attempts at a snow job showing the work to justify the answer. Real assessment and accountability requires the human teacher grading written work to be able to distinguish the snow job from legitimate work.

Derek Owens

Derek Owens is the king of distance learning high school math and Physics with a personal touch. Each section includes high quality instructional videos with practice problems to develop the skill. For students in the Atlanta area, in person classes are also available. Problems and exercises are worked with pencil and paper, scanned, and uploaded and graded in a traditional manner. Parents and teachers are emailed copies of results of every assignment and graded event and can log in and check a student’s complete course record at any time.

Topical coverage is very good, but not as exhaustive as ALEKS or something like the Glencoe series, which is the author’s favorite series to teach from. A student who winds up in a Calculus course using Stewart’s famous textbook may need to catch up on a few missed topics, but the high school preparation for many college Calculus and Physics courses will be far better than what passes as adequate in many public schools.

Derek Owens has degrees from Duke in Mechanical Engineering and Physics, and his approach to developing his high school math curriculum tends to reflect that. Teaching or supplementing a high school student bound to major in Mathematics probably requires a higher level of rigor and broader topical coverage. Yet, for students hoping to major in many other disciplines requiring college Calculus and Physics and having a strong preference for classroom style video lessons and pencil and paper assignments and tests, Derek Owens is probably a good choice.

Local Colleges and College Distance Learning

For students who have made a strong start with Algebra 1 and Geometry, the College Algebra course offered by most local colleges (either in person or distance learning) has enough overlap with Algebra 2 to serve as a functional equivalent in many ways. In many locations, dual enrollment programs are available to high school students starting in the 10th or 11th grades. And while earning an A or a B in College Algebra will have a student well prepared for Precalculus at the same school, there are a few caveats to recognize.

A student who struggled in Algebra 1 and Geometry will not be ready for College Algebra. A student who earned a C in Algebra 2 might productively take College Algebra as a review and refresher of the most important material. But most College Algebra courses cover most of the same material in 45-60 class days that most high school Algebra 2 courses cover in 180 days, so the rule of thumb that college classes require 2-3 hours of student work outside of class for each class hour is likely to be true and necessary for ample student learning to occur.

Likewise, a college Precalculus class also only spends 45-60 class days on the material that a high school Precalculus course spends 180 days on. There may be some compromise in coverage, but most of the difference is in the speed of delivery and need for student independence.

If these caveats are recognized, strong high school students can substitute College Algebra and/or Precalculus for Algebra 2 and/or high school Precalculus. I’d probably want to assess student preparedness with ALEKS assessments in Algebra 1 and Geometry (for College Algebra) and with an ALEKS assessment in Algebra 2 for Precalculus. Anything less than 90% on an ALEKS pie or assessment would indicate another route may be preferable. Alternatively, an ACT Math score above 28 likely indicates readiness for College Algebra and above 30 likely indicates readiness for College Precalculus, assuming the student is ready to make the extensive homework efforts required of real college math courses.

Coursera

Coursera offers a variety of college coursework either for free or at low cost. Offerings include Algebra, Precalculus, and at least two Calculus options. Although most courses are purportedly college level, at the present time, no real college credit is offered. My view is that the Coursera math offerings one might use in high school lack both the topical coverage and the academic rigor and quality assessment of real, accredited college coursework. Further, the quantity of work and learning from most single math courses in Coursera are less than one would desire to provide a full 180 days of math instruction for a high school student.

However, the instructional quality is very good for the topics covered, and if the educational goal is instructional quality rather than broad topical coverage or rigorous assessment, then Coursera courses might be a good fit for student needs. I would recommend the Algebra and Precalculus courses more for refreshing or review of earlier high school coursework or perhaps for a low-pressure practice before taking an accredited college course by the same name.

Since students often find accredited college Calculus courses to be a big step up in academic rigor from high school work, the unaccredited Calculus offerings may be considered as a lower-risk, lower-burden practice run for a high school student broadening their preparation for a more rigorous accredited college Calculus course. Alternatively, if a student has a gap of time between courses in a sequence, the Coursera courses may be a useful refresher before beginning the next course in the sequence.

Khan Academy

Khan Academy offers free online coursework in a wide variety of subjects, including the common high school math sequence, as well as Calculus and beyond. The courses are unaccredited, but offer high quality video-centered instruction. Students may enroll online and also gain access to practice problems and assessment tools. Alternatively, students enrolled in separate math courses can access Khan Academy videos (either at their site or through YouTube) for supplementary instruction as needed. Videos are available for nearly every topic in a typical high school math sequence.

My students have made great use of Khan’s instructional videos over the years. It’s great when a student finds a good fit between their learning style and a series of videos for supplemental instruction. However, since I have never known a student who used Khan’s math courses as the core of their math curriculum, I can’t say with confidence how students using Khan as the core of their high school math would transition to real college coursework. It is available and free, so I expect lots of folks will give it a try. I recommend employing alternate assessment methods on an annual basis to evaluate learning quality and ensure adequate progress before students matriculate to the next course in the high school sequence.

South Carolina State Distance Learning

South Carolina is now offering accredited high school coursework in an a la carte manner through a state-sponsored program. It is available both to South Carolina residents and to residents of other states, whether in public schools, private schools, or home schools. Their courses are aligned to rigorous state standards and are taught by highly qualified teachers who are appropriately licensed by the state of South Carolina.

Available math courses include the standard college preparatory math sequence, as well as AP Calculus and AP Statistics.

Conclusion

I’m sure I’ve probably missed a few of the available options, and others may have experiences, thoughts, and observations about the options I have discussed. Feel free to mention other options and observations in the comments below.

The popularity of distance learning, the home schooling movement, entrepreneurial efforts, and non-profit organizations have combined to provide a number of high quality choices compared with what was available 10-15 years ago. A parent willing to consider the options and work to find a match for their students’ needs can likely improve their learning quality without having to relearn high school math themselves or hire a private tutor.

Learning math is hard, and while effort and careful consideration are appropriate when overcoming hard challenges, people of faith should recognize prayer is fundamentally more important. Parents should exercise faith through prayer when planning a curriculum or supplemental instruction and continue exercising prayer for their children as the children work their way through challenging coursework. Parents should also have faith that their children can succeed in challenging subjects, because their children are made in the image of God, and God said that what he created is good. Recalling their own struggles in math should give parents empathy for their children, but it should not shake the parents’ faith that their children can accomplish things that the parents did not. The “all things” that “are possible with God” certainly includes math.

One promise of Scripture is that “all hard work brings a profit.” There are no silver bullets in math education: no way to learn without hard work. The goal of selecting an instructional or supplemental program is to find a match between delivery methods and student learning styles so that the student will be motivated and willing to work hard to benefit from the desired outcome from working 1 hour or so per day for 180 instructional days per year over the course of a four year high school program. Scripture also says, “Many advisers make victory sure.” Each program has strengths and weaknesses, and the best way to ensure that the weaknesses in any single program are not a long term barrier to success is to employ more than one program over the course of a four year high school math education.

ALEKS

ALEKS is my favorite recommendation for both primary coursework and supplementation, because it is an intelligent learning system that quickly figures out which areas a student has already mastered and focuses practice and learning in specific areas of weakness and need. This greatly streamlines the learning process by focusing 80-90% of the material on the areas where it is needed the most. Repetition of material that has already been mastered is a frequent source of frustration for students who often feel like they are wasting their time. It can also be a source of false confidence if a student fails to gain competence in new material while working review problems correctly.

I’ve taught hundreds of students in introductory Calculus and Physics courses who were poorly prepared with a variety of traditional curricula and even earned As and Bs throughout their high school math experiences. Grades from brick and mortar schools are a poor predictor of success in college coursework. There is probably no better predictor of success in college Calculus and Physics than a complete ALEKS pie in Precalculus.

ALEKS Pre-Calc Pie

This figure shows a student “pie” from the ALEKS Precalculus course.

ALEKS can be very productively used either for original coursework or for assessment, refreshing, and review. A student who has already truly mastered the material from a good high school Precalculus course can complete their ALEKS pie in about 1 week, working one hour per day. Students whose high school coursework may not have been complete or rigorous (or who forgot some things) will take longer.

ALEKS offers progress reports in a number of formats that allows parents and teachers to monitor student effort and progress in ways to identify problems and provide accountability without needing a detailed understanding of the material. In cases where a student is stuck in a challenging area and the built in tutorials and hints are not helping, some alternate learning strategies may be employed such as: 1) Reading the relevant sections in a traditional textbook 2) Reading the relevant Wikipedia pages 3) Viewing the relevant Khan Academy videos or YouTube videos on the same material 4) Seeking help from a tutor or other subject matter expert.

I should admit that I was originally opposed to ALEKS, especially when it was touted as a replacement of the online assessment and remediation system in prior use at the Air Force Academy when I served on the math faculty there. I just didn’t believe it was capable of quickly identifying areas of student strengths and weaknesses. Fortunately, my colleagues prevailed, and I got to see first hand how good the system really is.

Saxon Math

Saxon Math is very popular among home schooling households, because the textbook series uses an incremental learning approach that only introduces one new concept and skill at a time and gives a lot of opportunity to review previously acquired skills. It is probably among the easiest textbook series for students to read and pick up skills in cases where they are relying much more on learning directly from a textbook without the benefit of a classroom instructor.

The downside of Saxon Math is that students often have difficulties converting the style and language used for teaching and exercises in the Saxon Math series when they need to use these math skills in other contexts. A strength of Saxon is that it teaches specific recipes for specific types of problems. But this can become a weakness when students need to develop their own problem solving recipes or when problems in a different context are more challenging to classify to recognize what recipe is needed.

Still, a student who has completed the high school Saxon Math series and truly mastered the material through Precalculus is well prepared for college math. I would recommend some level of practice for the relevant algebra and trig skills in a different context, such as a good year long high school physics class, a Coursera course in Precalculus or Calculus One, a review of Precalculus in ALEKS, or some suitable opportunity to begin a transition of what they have learned in Saxon Math to different contexts. Once a real college Calculus or Physics class is under way, the material is most likely coming too quickly to translate the math they know to the skills they need every day.

In my view, the big weakness in most book based programs (Saxon, Life of Fred, etc.) when administered by adults who don’t actually understand the material (and are not willing or able to really learn it), is that it is difficult for these adults to provide the needed assessment and accountability. Making use of answers in the back is very limited for those who can’t understand for certain whether those answers are right and who cannot explain to a student where they may have gone wrong when they obtain different answers.

Students are pretty adept at fooling parents when the best parents can do is ask “Did you do the practice work?” and “Can you show it to me?” Many purported efforts at completing math assignments are little more than copied answers from the back with (when required) mediocre attempts at a snow job showing the work to justify the answer. Real assessment and accountability requires the human teacher grading written work to be able to distinguish the snow job from legitimate work.

Derek Owens

Derek Owens is the king of distance learning high school math and Physics with a personal touch. Each section includes high quality instructional videos with practice problems to develop the skill. For students in the Atlanta area, in person classes are also available. Problems and exercises are worked with pencil and paper, scanned, and uploaded and graded in a traditional manner. Parents and teachers are emailed copies of results of every assignment and graded event and can log in and check a student’s complete course record at any time.

Topical coverage is very good, but not as exhaustive as ALEKS or something like the Glencoe series, which is the author’s favorite series to teach from. A student who winds up in a Calculus course using Stewart’s famous textbook may need to catch up on a few missed topics, but the high school preparation for many college Calculus and Physics courses will be far better than what passes as adequate in many public schools.

Derek Owens has degrees from Duke in Mechanical Engineering and Physics, and his approach to developing his high school math curriculum tends to reflect that. Teaching or supplementing a high school student bound to major in Mathematics probably requires a higher level of rigor and broader topical coverage. Yet, for students hoping to major in many other disciplines requiring college Calculus and Physics and having a strong preference for classroom style video lessons and pencil and paper assignments and tests, Derek Owens is probably a good choice.

Local Colleges and College Distance Learning

For students who have made a strong start with Algebra 1 and Geometry, the College Algebra course offered by most local colleges (either in person or distance learning) has enough overlap with Algebra 2 to serve as a functional equivalent in many ways. In many locations, dual enrollment programs are available to high school students starting in the 10th or 11th grades. And while earning an A or a B in College Algebra will have a student well prepared for Precalculus at the same school, there are a few caveats to recognize.

A student who struggled in Algebra 1 and Geometry will not be ready for College Algebra. A student who earned a C in Algebra 2 might productively take College Algebra as a review and refresher of the most important material. But most College Algebra courses cover most of the same material in 45-60 class days that most high school Algebra 2 courses cover in 180 days, so the rule of thumb that college classes require 2-3 hours of student work outside of class for each class hour is likely to be true and necessary for ample student learning to occur.

Likewise, a college Precalculus class also only spends 45-60 class days on the material that a high school Precalculus course spends 180 days on. There may be some compromise in coverage, but most of the difference is in the speed of delivery and need for student independence.

If these caveats are recognized, strong high school students can substitute College Algebra and/or Precalculus for Algebra 2 and/or high school Precalculus. I’d probably want to assess student preparedness with ALEKS assessments in Algebra 1 and Geometry (for College Algebra) and with an ALEKS assessment in Algebra 2 for Precalculus. Anything less than 90% on an ALEKS pie or assessment would indicate another route may be preferable. Alternatively, an ACT Math score above 28 likely indicates readiness for College Algebra and above 30 likely indicates readiness for College Precalculus, assuming the student is ready to make the extensive homework efforts required of real college math courses.

Coursera

Coursera offers a variety of college coursework either for free or at low cost. Offerings include Algebra, Precalculus, and at least two Calculus options. Although most courses are purportedly college level, at the present time, no real college credit is offered. My view is that the Coursera math offerings one might use in high school lack both the topical coverage and the academic rigor and quality assessment of real, accredited college coursework. Further, the quantity of work and learning from most single math courses in Coursera are less than one would desire to provide a full 180 days of math instruction for a high school student.

However, the instructional quality is very good for the topics covered, and if the educational goal is instructional quality rather than broad topical coverage or rigorous assessment, then Coursera courses might be a good fit for student needs. I would recommend the Algebra and Precalculus courses more for refreshing or review of earlier high school coursework or perhaps for a low-pressure practice before taking an accredited college course by the same name.

Since students often find accredited college Calculus courses to be a big step up in academic rigor from high school work, the unaccredited Calculus offerings may be considered as a lower-risk, lower-burden practice run for a high school student broadening their preparation for a more rigorous accredited college Calculus course. Alternatively, if a student has a gap of time between courses in a sequence, the Coursera courses may be a useful refresher before beginning the next course in the sequence.

Khan Academy

Khan Academy offers free online coursework in a wide variety of subjects, including the common high school math sequence, as well as Calculus and beyond. The courses are unaccredited, but offer high quality video-centered instruction. Students may enroll online and also gain access to practice problems and assessment tools. Alternatively, students enrolled in separate math courses can access Khan Academy videos (either at their site or through YouTube) for supplementary instruction as needed. Videos are available for nearly every topic in a typical high school math sequence.

My students have made great use of Khan’s instructional videos over the years. It’s great when a student finds a good fit between their learning style and a series of videos for supplemental instruction. However, since I have never known a student who used Khan’s math courses as the core of their math curriculum, I can’t say with confidence how students using Khan as the core of their high school math would transition to real college coursework. It is available and free, so I expect lots of folks will give it a try. I recommend employing alternate assessment methods on an annual basis to evaluate learning quality and ensure adequate progress before students matriculate to the next course in the high school sequence.

South Carolina State Distance Learning

South Carolina is now offering accredited high school coursework in an a la carte manner through a state-sponsored program. It is available both to South Carolina residents and to residents of other states, whether in public schools, private schools, or home schools. Their courses are aligned to rigorous state standards and are taught by highly qualified teachers who are appropriately licensed by the state of South Carolina.

Available math courses include the standard college preparatory math sequence, as well as AP Calculus and AP Statistics.

Conclusion

I’m sure I’ve probably missed a few of the available options, and others may have experiences, thoughts, and observations about the options I have discussed. Feel free to mention other options and observations in the comments below.

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