Posted tagged ‘David Shormann’

Shormann Math Builds Effective Study Habits

October 19, 2015

With Shormann Math, using 21st Century technology to create a math course allows us to obtain valuable information revealing that, regardless of skill level, students who want to learn math, can, and Shormann Math has the tools for them to do so.

For example, during quarterly exam week, students are provided with two full-length practice exams. Practice exams allow students to prove to themselves that they really do (or don’t) know the material covered that quarter. Besides the practice exams, they are given other guidelines on how to prepare for the exams. The guidelines are based on years of teaching experience, as well as observing university professors. Between my bachelor’s in aerospace engineering, and a PhD in aquatic science, I had a lot of professors and exams! And the best professors, the ones who really wanted you to learn the material, did two things: 1) they kept a file of previous exams in the library that students could check out and study, and 2) they had office hours so students could ask questions. Shormann Math provides both, with 1) practice exams that reward students for a good study effort and 2) free email Q&A any time.

But are the practice exams helpful? Well, see for yourself. The following graph displays the recent results of Quarterly Exam 1 scores for Shormann Algebra 1 and 2(beta) students.* The bottom line is that students with “Good” study habits made A’s on the exam. The graph is a display of the obvious fact that good study habits build fluency, resulting in good scores on the actual exam. Being fluent in math means you know how to use the rules to solve new problems. And the purpose of the Practice Exams in Shormann Math is to provide new problems so the student can prove to themselves whether they are fluent, and if not, what they need to review.

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At some point in your life, you will be tested on a large amount of information. Whether it’s for a job you really want, a driver’s license, an SAT, ACT, MCAT, etc., sooner or later, test day is coming. And if you really want that license, or that job, etc., you are going to put the personal effort into it to study. Shormann Math is designed to help students build effective study habits in a less important setting where the stakes aren’t as high. But, as the results above reveal, the best curriculum in the world won’t make a bit of difference if the student doesn’t put that personal effort into following directions and studying effectively.

*Graph details: Scores are from Quarterly Exam 1 taken by students in Dr. Shormann’s live online Algebra 1 and 2 classes, October 2015. The three categories are based on student performance on the 2 practice exams take prior to the actual exam. The students are allowed to take the practice exam, review mistakes using the solutions manual provided, and then take it again. Students who put the effort into retaking each practice exam were rewarded for their effort with a higher grade. Students are also encouraged to show work on their paper, solving each problem by hand. For the actual exam, they are required to submit handwritten work on each problem. The practice exams were counted as one of their homework grades, providing further encouragement to complete them. The three categories were broken down as follows: “Good” students averaged 95% or better on the practice exams, all of which took at least one of the exams more than once in order to get a higher score, which means they took the time to correct their mistakes and study the problems they missed. “Mediocre” students took each exam once, but averaged below 95%, and showed little to no effort to try the exam again, missing a valuable opportunity to review and build fluency. “Poor” students did not attempt either practice exam. Of special note is the fact that the trend was consistent, regardless of which course students were doing (Algebra 1 or 2).  Also, because the students had the opportunity to retake each practice exam until they received a 100, study effort, and not skill level, was the main factor influencing performance on the actual exam. Not all students are equally gifted in math (or any subject), but students who are less-skilled at math can do better by studying harder. These results provide good evidence that, with Shormann Math, students who want to learn math, can, regardless of skill level!

Shormann Algebra 1: Results Matter

July 31, 2015

Why do results matter?

Shormann Math builds on a solid foundation of time-tested teaching methods, including the incremental development + continual review format pioneered by John Saxon(1923-1996). And not just Saxon’s teaching methods, but his teaching thoughts as well, including his thought that

Results, not methodology, should be the basis of curriculum decisions.

One of the primary reasons John Saxon developed his math curriculum in the 1980s was because new ways of teaching math were not working. Math “educrats” at the time were promoting their untested “visions” of math teaching. But with 3 engineering degrees, John was a math user before he became a math teacher. Not only that, he was a test pilot. If anyone knew the extreme value and importance of testing a new product, it was John!

Results matter because they reveal whether or not a new product really works. And while statistics certainly don’t reveal everything about a new product, they can certainly reveal many things. Most math curricula don’t provide this level of detail on student performance. But with Shormann Math, each new course is beta-tested in a live, online setting first before releasing it to the general public. The following are statistics from the beta-test of Shormann Algebra 1. The results show that the majority of students made an A! The following statistics, plus other detailed information about the course, can also be found in our Shormann Algebra 1 teacher’s guide. To purchase Shormann Math, click here.

Overall Performance

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Discussion: The average student in our beta test made an A in the class! Because each new Shormann Math course is beta-tested in a live online class setting, Dr. Shormann gets to know the students on more than just a “numbers only” basis. And we all know that God doesn’t make clones, so the fact that not every student performed the same should not be a surprise. Natural talent definitely matters, but so do things like attitude and maturity.  Dr. Shormann spends time during the video lectures encouraging students to develop fruits like patience and self-control (Galatians 5:22-23), as well as persevering with joy (James 1:2-3), and gratefulness (I Thessalonians 5:18).

Practice Sets

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Discussion: You’ve probably never seen statistics on student performance in a math class before, which is why it is important to discuss the data! The decreasing trend over time is exactly what we expected. Two big factors are responsible for the trend: 1) There’s more review of previously-learned concepts at the beginning, so it’s easier and 2) student effort tends to decrease the closer you get to the end of the year!

What we had hoped for was a Practice Set average above 85%, and that was achieved in all 4 quarters! 85% is a good cutoff for determining whether students are understanding, and retaining most of the concepts learned.

Note also the high first quarter average. Because Shormann Math is built on John Saxon’s method of integrating geometry and algebra, students using Saxon Math 8/7 or Saxon Algebra ½ will be most comfortable starting Shormann Math. However, not all beta-test students used Saxon previously, so the high first quarter average is a good indication that students who successfully completed any pre-algebra course should do just fine in Shormann Math.

Weekly Quizzes

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Discussion: Weekly Quizzes show a similar trend to the Practice Sets, challenging the students more as the year progressed. A score of 8 out of 10 or higher is a good indication of whether students understood the lessons covered that week. We are pleased that scores were well above this in all four quarters!

Quarterly Exams

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Discussion: Notice the Quarterly Exams do not follow the same trend as Practice Sets or Weekly Quizzes, with Quarter 1 having the lowest average. And this is where beta-testing a new product is so valuable. We realized that we were asking a lot for 9th-grade level students, most of which had never taken a cumulative exam like this. The solution? Practice exams! Just like when learning a sport, a musical instrument, etc., good practice results in good performance. The beta-test students clearly performed best on first quarter Practice Sets and Quizzes. Most likely, if they were given practice exams prior to their quarterly exam 1, this would have been their highest exam average. Now, all quarterly exams have two practice exams that students use to study for their actual exam.

85%+ is an indicator of good retention and understanding of concepts covered in a quarter. For all 4 quarters, student averages were at, or well above 85%. Because of Shormann Math’s format of continual review, we are basically asking students to be responsible for “all their math, all the time.” These results show that on average, students are responding very well!

The New Shormann Math vs. Saxon Math and Common Core

April 21, 2015

Summary: If mathematics is the language of science, then fluency should be the goal, which means the traditional “layer cake” approach to 3 years of high school math (Algebra 1, Geometry, Algebra 2) is probably not the best approach. The shapers of Common Core’s math standards realized this, and now states that adopt their standards can choose between two high school “pathways”, either the layer cake or integrated approach, where students learn algebra and geometry together. John Saxon* actually pioneered the integrated approach in the United States back in the 1980’s, but his integrated approach was only one small part of his textbooks’ successes. His method of “incremental development with continual review,” combined with a constant encouragement for students to learn by doing, were the keys. Shormann Math builds on John Saxon’s efforts to really teach math like the language of science that it is, by not just connecting students to their world, but, more importantly, to their Creator. In doing so, students learn to wisely mingle concepts like science and Scripture, faith and reason. Doing so makes it easier to learn subjects like calculus, which really does require a faith commitment in order to make sense of it. Because of its obvious connections to God’s attributes, secular calculus courses steer clear of this, and in so doing make it much more difficult to learn. Shormann Math will change that.

*John Saxon passed away in 1996, and the company he founded, Saxon Publishers, is now owned by Houghton-Mifflin/Harcourt. They have since created some Saxon-in-name-only Algebra 1, 2, and Geometry textbooks. Click here to read our review of the new books and to learn why we don’t recommend them.

The 10 Major Topics of Shormann Math

The 10 major topics of Shormann Math, compared to John Saxon's books and Common Core standards.

The 10 major topics of Shormann Math, compared to John Saxon’s books and Common Core standards.

Measurement is a topic that is a natural part of any math course seeking to teach math as the language of science. That it’s missing from three years of Common Core high school math is a huge problem. As a science class and lab teaching assistant during graduate school, one of the biggest math-related struggles I remember was students’ inability to convert from one unit to another. And it’s not just Common Core, most government school standards are weak in teaching measurement-related topics.

All Shormann Math high school courses will keep students fresh with working with measurements. Computers are also a very real part of every students’ world, so knowing about some of the mathematics behind them should be a priority. And, as mentioned in the Summary above, calculus becomes a normal part of high school math when one of the priorities is to connect students to their Creator.

Foundations and Pedagogy

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As Euclid famously said centuries ago, there is no royal road to learning. However, some methods are definitely better than others, and the Common Core’s integrated pathway (click here to read an Education Week review) is definitely a step in the right direction. However, the integrated approach has it’s own challenges. To really teach math like the active, hands-on language of science that it is, you have to teach it like languages are taught, or sports, or instruments, etc. You teach students a little bit about something, give them time to practice it, and then build on it. John Saxon called this “incremental development with continual review,” which is missing from Common Core.

Also missing from Common Core is the importance of math history. Understanding why they are learning the different math topics makes math more relevant to students. Learning some things about the people behind the math concepts they are learning, as well as some of the great, and not-so-great things they did, makes math more meaningful. And the connection to history also shines a bright light on the rich Christian heritage of mathematics, especially regarding algebra and calculus. Showing students how God’s attributes are clearly revealed in mathematics can make a huge difference in their comprehension and success in the course.

Shormann Math’s emphasis on math history means that, in developing the course, I dove deep into the classic works of Euclid, Newton, Euler, etc. Rather than reinventing the wheel, this study of the classics allowed me to develop a curriculum that stands on the shoulders of giants (a phrase often attributed to Isaac Newton). It should be a huge confidence-booster to parent and student alike to know your course is built on time-tested and proven methods for learning math.

What 3 Years of Math Covers

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By focusing on what matters most, Shormann Math does more in 3 years than either Common Core or Saxon. In the first two years, Shormann Math covers all the concepts presented on the SAT (the new 2016 version), the ACT, and both the CLEP College Algebra and CLEP College Math exam. A full credit of geometry is integrated into the first two years as well. This is different from John Saxon-authored texts, which include the geometry credit in years 2 and 3 (Algebra 2 and the first 1/3 of Advanced Math). And before you think Shormann Math couldn’t possibly have enough geometry, consider that we will cover all the standards, like perimeter/area/volume, similarity and congruence, circle and triangle theorems, and proofs. In addition, we will show students how the proof technique is not some isolated subject you only learn in geometry class, which is what most students, and parents, think it is. We’ll introduce students to proofs by studying the master, Euclid, covering several of his propositions. We’ll do the standard triangle proofs and circle proofs, but will also apply proof technique in other topics like algebra. And students will learn how proof is used in the real world. They’ll even learn how geometry is used in art and architecture. And on top of all that, we’ll introduce non-Euclidean geometry in Algebra 2, diving deeper in Precalculus. We’ll also use CAD programs like Geometer’s Sketchpad to complete proofs and more.

Finally, Shormann Math will introduce calculus fundamentals. By year 3 (precalculus), Shormann Math students will be very comfortable finding limits, and will have a solid grasp of derivatives and integrals. We hope all students will continue on to Shormann Calculus, but if not, they will be more than ready for college-level calculus. Of all the courses in college, calculus is the subject that opens the door to virtually every college major, or if the student cannot pass the class, closes the door on about 80% of majors. The first three years of Shormann Math will give students the confidence they need to take college calculus, and be at a level to help their peers learn it, which can also open up opportunities to build relationships and share the gospel. And completing 4 years of Shormann Math will allow students to possibly prepare for and pass either the CLEP or AP Calculus exam, receiving college credit for their efforts.

But Saxon + DIVE Lectures do a lot of this already. Why make a new curriculum?

There are many reasons, here are a few:

  • We can build the curriculum on a Christian and historical foundation, rather than bringing these fundamentals in from the side, like we do with the DIVE Lectures that teach Saxon Math.
  • The one topic John Saxon didn’t integrate was calculus. We think it just might be the most important topic to integrate, and our current Shormann Math students are proving Algebra 1-level students can learn some calculus fundamentals!
  • We don’t know how long Houghton Mifflin/Harcourt will continue to sell John Saxon-authored textbooks.
  • We can take advantage of 21st Century technology and e-learning to provide more efficient and effective learning. Our self-paced e-learning format includes many powerful learning tools, including video lectures and video solutions to homework, all for about the same price as the Saxon home study kits. The following table lists some detailed differences between Shormann Math and Saxon Math.

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What is the prerequisite for Shormann Math Algebra 1?

Students who have successfully completed a standard pre-algebra course, including either Saxon 8/7 or Saxon Algebra Half, are ready for Shormann Math Algebra 1.

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Do you have any questions? Feel free to leave a comment!

Click here for a detailed description of Shormann Math, including sample video lectures and pricing information.

How to Be a Mature Math Student

January 29, 2015

At the beginning of W.M. Priestley’s book, Calculus: A Liberal Art, is a page titled For Anyone Afraid of Mathematics. Here’s the first paragraph:

Maturity, it has been said, involves knowing when and how to delay succumbing to an urge, in order by doing so to attain a deeper satisfaction. To be immature is to demand, like a baby, the immediate gratification of every impulse. 

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Gabriel Medina, 2014 winner of the Van’s Triple Crown of Surfing, maturely surfs a wave at the Banzai Pipeline. Maturity, whether in surfing, learning math, etc., involves knowing when and how to delay succumbing to an urge.

I am learning to surf, and every session reminds me how immature I am at this sport! I need instruction, and lots of it. I make bad choices on which waves I should try to catch and which ones I should let pass. More often than not, I do not know when and how to delay succumbing to that urge to ride a wave. But with repeated practice and instruction, I hope to gain a better sense of making mature wave selections.

In a similar way, an immature math student has many urges to overcome. One of the biggest is fear of failure, and when students feel that urge, they often respond immaturely by cheating, asking for help too soon, or just giving up. Do you want to be a mature math student? Here are some suggestions to help you achieve that goal.

  1. Failure is an option. In a math course, there is a reason that you are the student, and not the teacher! Students are the ones who need instruction. So when you are learning, humble yourself and be ready to make lots of mistakes.
  2. Learn from your mistakes. Homework is your time to practice new concepts and to expect some mistakes. When you grade your homework though, and you miss a problem, don’t just mark it wrong. Correct it. Review your lesson and your notes. Look for similar examples in the book. How were those examples solved? If your course has a solutions manual, study the solution carefully and work the problem again.
  3. Set a time limit. Some students give up too easily. Others don’t know when to give up. Both responses are immature. There is a difference between taking 10 minutes to solve a complex problem that you know how to do, and spending 10 minutes searching aimlessly for clues on how to solve a problem. If you can’t figure a problem out after 10 minutes or so, move on. Try it again later. Sometimes, after you’ve rested, you will find that you can figure a problem out.
  4.   Pray for maturity. Ask God to make you a humble, dedicated learner. Math is a tool for studying His creation, and He definitely wants you to use it to know Him better, so talk to Him, and ask Him to lead you. Some students will spend all their years of schooling blaming others for their poor math performance. They will blame the teacher, the textbook, their parents, everything but themselves. If that is you, well, most likely, the main problem is you. Ask God to show you how to have a grateful attitude for the gift of education. Ask Him to help you know when and how to maturely succumb to that urge to know the answer to a problem, and do your work in a way that gives Him glory!

Do you have any other suggestions on how to be a mature student? Feel free to leave a comment.

It Only Takes an Instant

December 1, 2014
Two images of a wave in Waimea Bay, Hawaii, taken 0.1 s apart, reveal how quickly things can change from beauty to chaos (or vice versa).

Two images of a wave in Waimea Bay, Hawaii, taken 0.1 s apart, reveal how quickly things can change from beauty to chaos (or vice versa). © 2014 David E. Shormann

I never cease to be amazed by the technology of today’s digital cameras. By pushing a few buttons, anyone crazy enough to bob around in a 6-8′ high shore break can capture some amazing beauty in God’s creation! But as the photos above reveal, the beauty only lasts for an instant.

It seems impossible that things can change from beauty to chaos, or vice-versa, in so short a time. But big changes can and do occur in even less time than the tenth of a second that elapsed between these two photos.

Strangely enough, instantaneous change, something us humans really can’t fully comprehend, is behind almost every major technological achievement of the past 300+ years!  How can that be? How can something we will never fully understand help us make all sorts of useful devices? Well, some things we just have to take on faith. Faith is at the heart of the branch of mathematics known as calculus. And calculus is all about the study of instantaneous change.

Subjects like calculus are easier to grasp when we consider the Author of every instant of time, and Creator of the biggest  and best instantaneous changes of all. Paul writes in 1 Corinthians 15:52 how we will be changed “in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised imperishable, and we shall be changed.”

Leonhard Euler (1707-1783), a devout Christian man considered the best mathematician ever, wrote that “it is God, therefore, who places men, every instant, in circumstances the most favourable, and from which, they may derive motives the most powerful, to produce their conversion; so that men are always indebted to God, for the means which promote their salvation.”

Euler understood God’s relationship with man and creation very well. He also understood mathematics really well, too! Much of the way we teach mathematics today comes from Euler’s textbooks on the subject.

In our new Shormann Mathematics curriculum, we believe that all 10 major topics covered, including and especially calculus, are best understood by connecting the study of mathematics to Jesus Christ, the founder of all knowledge, and the founder and perfecter of our faith (Hebrews 12:2).

The 10 Major Concepts of Shormann Mathematics

August 26, 2014

The following is the fifth in a series of posts covering Shormann Mathematics, Algebra 1, the newest product from DIVE Math and Science! Click here to read the complete document that covers Shormann Math core ideas, course description, and Algebra 1 table of contents.Screen Shot 2014-08-26 at 7.57.55 AM

After years of teaching mathematics, researching math curricula and math history, and applying mathematics as a scientist and engineer, I concluded mathematics can be taught by covering 10 major concepts. The 10 major concepts are: number, ratio, algebra, geometry, analytical geometry, measurement, trigonometry, calculus, statistics, and computer math. While all 10 concepts can be taught in any K-12 course, specific concepts will be emphasized more or less at appropriate times. For example, number and ratio will be emphasized in younger grades, algebra in Algebra 1 and 2, etc.

I know what you are thinking right now, and that is “But CALCULUS is one of the 10 major concepts! How can you possibly teach calculus to an Algebra 1 student?!” Well, if you have even an 8th grade level of math proficiency, you know that if it took you exactly one hour to drive 60 miles, your average speed would be 60 mph. If you understand that, you already understand something about calculus, because calculus is really nothing more than studying rates of change. And yes, it gets more complicated than that example, but it also gets less complicated, too, so much so that there are things about calculus you could teach a kindergartner!

Most state mathematics standards do not include calculus, and none that I know of require calculus in high school. And the federal Common Core math standards include no calculus, and almost no precalculus either! However, the discovery of calculus is one of the greatest mathematical achievements ever! All the great technological achievements of the last 300+ years are in some way or another related to calculus! And proficiency in calculus opens the door for a student to choose any college major, while an inability to pass calculus limits a student to about 20% of college majors.

For high school mathematics, most home schools and private schools simply parrot whatever their state standards are, which means they complete Algebra 1, 2, and Geometry, and check off math on their transcript, not really knowing why they did math this way. With Shormann Math though, we want you to know why you are doing math differently. We are going to paint a broader brush than most math curricula, teaching math like a language, while at the same time helping you become proficient in standard Algebra 1, 2 and Geometry concepts. Along the way, rather than avoiding calculus because you heard it was scary, you are gently introduced to it. And, before you know it, you will be understanding more calculus than all your peers, and probably even your parents, ever did! Rather than an afterthought or a scary thought, Shormann Math makes calculus a normal, natural part of the curriculum, and culminates with a formal (and yes, it’s optional!) calculus course that will prepare students to receive college credit via CLEP or AP Calculus.

Done in a thoughtful and age-appropriate way, all 10 major concepts listed above can most definitely be represented in one way or another in a K-12 mathematics curriculum.

Shormann Math Core Ideas: Jesus Christ is the “Common Core.”

August 5, 2014

The following is the third in a series of posts covering Shormann Mathematics, Algebra 1, the newest product from DIVE Math and Science! Click here to read the complete document that covers Shormann Math core ideas, course description, and Algebra 1 table of contents.

Jesus Christ is the “Common Core” of Shormann Math

Perhaps you have heard of the United States government’s “Common Core” curriculum. Perhaps you have also heard that a lot of people are concerned about it. Leading experts believe the Common Core’s mathematics standards will not prepare students to study science, technology, engineering, and math (STEM) in a selective four-year college. And a white paper by the Pioneer Institute concludes by saying

“At this time we can conclude only that a gigantic fraud has been perpetrated on this country, in particular on parents in this country, by those developing, promoting, or endorsing Common Core’s standards.”

Unfortunately, man and his ever-changing ideas are at the core of this curriculum. At DIVE, we strive to place Jesus Christ at the core of all our products, and we pray that this will result in students learning math and science for His glory and the service of others. So, even though our primary goal is NOT to prepare students for STEM, we believe by putting Christ at the foundation, just like the world’s original universities did, students will naturally learn to use mathematical tools that will connect them to their world and their Creator.