Shormann Algebra 1: Results Matter

Posted July 31, 2015 by gensci
Categories: Uncategorized

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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!

How Shormann Math Teaches Proof

Posted June 17, 2015 by gensci
Categories: Teaching Mathematics

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Euclid’s Proposition 1 overlaying a pod of spinner dolphins swimming in a near-perfect equilateral triangle formation! The concept of proof applies to everything from building a rocket to the simple beauty of a pod of dolphins. Photo Credit clarklittlephotography.com

What is proof?

Proof is really nothing more than providing a reason for statements made or steps taken. In the standard American government school 3-year “layer cake” approach to high school math, the concept of proof is normally limited to some sections in the geometry layer. But proof is not a concept that is the exclusive domain of geometry. Shormann Math teaches proof in 3 main ways, by 1) studying Euclid’s foundational work on proof, 2) showing that proof is for all of math, not just a few weeks in geometry class, and 3) showing how proof applies in the real world.

Euclid and proof

Around 300 B.C., Euclid (330 – 275 B.C.) organized the previous 3 centuries of Greek mathematical work into a 13-volume thesis known today as The Elements or Euclid’s Elements. Scholars believe that only the Holy Bible has been more universally distributed, studied and translated. Starting with a foundation of 5 postulates, 5 axioms, and 23 definitions, Euclid proved 465 theorems, or propositions.While postulates are basically rules that are assumed to be true without proof, theorems are true statements requiring proof. Postulates are also referred to as self-evident truths.

Surprisingly, even though Euclid is considered the “Father of proof,” most American high school geometry textbooks mention little to nothing about Euclid. In Shormann Math though, students will learn who Euclid was, and the importance of his contribution to Western Civilization. Shormann Algebra 1 and 2 students will become very familiar with Euclid’s first 5 propositions, giving them a good understanding of proof technique. They will gain an appreciation for the deductive nature of geometry and geometric constructions, seeing how one proposition often requires the previous one. And they will also see the simple beauty and elegance of Euclid’s propositions.

Proof and mathematics

Perhaps one of the greatest flaws in the “layer cake” approach to high school math is that the concept of proof is almost always limited to a few weeks during the geometry year. In Shormann Math, we’ll do the standard triangle proofs and circle proofs, but we will also apply proof technique in other topics like algebra, trigonometry and calculus.

But how can proof be for more than just geometry? Well, proof is based on a type of reasoning called deductive reasoning (applying rules). Every single math concept begins with rules. And every single math problem can be solved by applying those rules. All of mathematics is deductive in nature, which means at any time, a student should be able to explain the rules (provide reasons for) they used to solve a problem.

Because Shormann Math is integrated, we’re able to help students make connections between the major concepts like algebra and geometry. This results in students getting a better feel for what mathematics is about, which will make it easier to learn. Instead of thinking that they are always learning something new and different, they will see how one lesson builds on previous ones, which makes it less intimidating.

Proof and the the real world

Sure, proof is important to mathematicians, but it’s also important in the real world. As we explain in Lesson 68 of Shormann Algebra 1,

“Supporting statements with reasons is a technique used by, and expected of, people that society refers to with words like professional, leader, wise, helpful, and trustworthy. People like Abraham Lincoln, the 16th President of the United States of America, known for his study of Euclid’s Elements and his application of the idea of proof to solving societal problems.”

We also helps students see the application of proof technique in the real world, as this table from Shormann Algebra 2 explains:

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Most importantly, proof is profoundly important in sharing the Gospel with unbelievers. God wants us to be ready to give reasons for the hope of salvation (I Peter 3:15). Our reasons should primarily be Scriptures we have memorized, or at least remember where to find them.

Conclusion

As you can see, proof is about a lot more than geometry! Shormann Math gives students a basic understanding of proof technique and it’s application to the real world. It’s a great tool to help them in their thinking, planning, designing and serving. If you think you would like your child to learn math in a more natural way that connects them to their world and their Creator, click here to learn more!

The New Shormann Math vs. Saxon Math and Common Core

Posted April 21, 2015 by gensci
Categories: Teaching Mathematics

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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.

Peacock Grouper

Posted February 25, 2015 by gensci
Categories: Uncategorized

peacockgrouper

Peacock grouper (Cephalopholis argus)

Peacock grouper, by Ellie Shormann

These beautiful fish (called Roi in Hawaiian) are commonly found around Indo-Pacific reefs. They are sometimes perched on top of a coral head or hiding in a cave. On the menu for grouper are small fish, crabs and shrimp. They can sometimes be seen following eels or octopus in hopes of catching a prey item that evades them! They have beautiful colors, too! They are normally brown with turquoise spots, with light brown or light yellow bars running vertically down their sides. They can even change color! They can change from darker colors to almost white. Isn’t that cool?

Click here for a printable coloring page.

More Thoughts on Furthering the Dialogue on Creation

Posted February 14, 2015 by gensci
Categories: Creation/Evolution

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Appearances can be deceiving. How old do you think this canyon is? How long did it take to form the layers that were carved out? If I told you the majority of what you see took less than 5 years to form, would you call me a liar?

Appearances can be deceiving. How old do you think this canyon is? How long did it take to form the layers that were carved out? If I told you the majority of what you see took less than 5 years to form, would you brush that off as a pleasant fiction?

It’s been my pleasure to read some recent posts by Doug Wilson and Gavin Ortlund regarding Creation and Earth history. Doug started with this post, to which Gavin responded here with 4 points. Wilson then responded here, to all but Gavin’s 4th point. Wilson wisely left point 4 unanswered, suggesting that someone should respond who has more of a science background. And, while I’m more at home swimming with whales in the open ocean than writing blog posts, I felt compelled to respond. So, here goes this scientist’s attempt to further the dialogue on Creation.

Before I start, I want to say that I really appreciate Gavin’s effort to make a “friendly appeal” towards dialogue on Creation. Well done, and I hope to follow his lead with some friendly iron sharpening of my own.

Discern Between Scientific and Historic Research

Gavin’s point 4, the one Wilson left unanswered, was a call for young earth creationists to get “specific with the scientific evidence.” But this has been done, and is being done, in a thousand different ways (see below).

More importantly, the “scientific evidence” is not the problem at all. The problem is the interpretation of the evidence, which leads to another big issue. If anyone, young-earth, old-earth, or other, is truly interested in furthering the dialogue on Creation, they will put a greater effort into discerning between scientific research and natural history research. Scientific research is testable, repeatable, and verifiable. Natural history research involves drawing unverifiable conclusions from data. Natural history research is about interpreting unobserved past events.

In my opinion, a more scholarly approach to the Creation dialogue involves making a clear distinction between a scientific thing and a historic thing.  It’s been over a decade now since the call was made to move beyond scientific creationism, so young-earthers and old-earthers alike should be putting more effort into properly discerning between the two.

You don’t have to be a scientist to discern between the two types of research. You just need to know how to read a recipe. If you cannot, or just refuse to, acknowledge the difference between scientific research and natural history research, then you are not furthering the dialogue on Creation.

Energy or time?

Gavin wrote that “one step that will greatly help the dialogue about creation in the church is for young-earth creationists to pay more attention to the specifics and particulars of the evidence for an older earth and universe.”

If any Christian writes, speaks, or preaches like they have no clue of the vast amount of material published by young earth creationists regarding “specifics and particulars of the evidence,” then they are not furthering the dialogue on Creation. I am trying to say this in as friendly a way as possible, but a statement like that shows a lack of effort to research a matter before writing about it. It is the glory of kings to search a matter out (Proverbs 25:2), so act like a king.

Remember also, we are talking mainly about history here, and conclusions about the unobserved past depend on interpretation. For Christians, the biggest differences between old and young earth views stem from our presuppositions. Were high-energy, short term events the dominant shapers of earth’s surface? Or was it low-energy, slow, and gradual? The interpretive differences result mainly from how much emphasis the researcher places on catastrophism (high energy, short duration) versus gradualism (low energy, long duration).

Do you want to learn about what creation researchers are saying about the Grand Canyon? Starlight and time? Ice layering, etc? Then click here, or here, or here, or here, or many other places. If you would like, you can also read about some of my natural history research. I conducted an age-calibration experiment of the Ar-Ar radiometric dating method, and found that method overestimated the age of my sample by a factor of 55,000.

Read, and you will find that there are many reasons, good reasons, to be skeptical of the methods and models used to speculate about billions of years of earth age.

Here’s some advice for old-earthers who are serious about furthering the dialogue on Creation. It’s the same advice my advisor gave me when I turned in the first draft of my PhD research proposal. Across the top of the proposal in big red letters was the word READ. Read young earth creation research. Search the matter out.

And to that I would add, PRAY. Ask God to give you wisdom and discernment to further this dialogue in the best possible way, which is the one that will bring Him the most glory.

Unsettle the (Secular) History, Burn the “Fictitious History” Strawman

As Doug mentioned, “the science is always settled until somebody unsettles it,” and this is true. But, keeping on track with discerning the scientific from the historic, it might be better to say, regarding earth age, that “the history is always settled until somebody revises it.”

In Gavin’s post, he quotes Robert Newman, who said “In harmonizing the revelation God has provided us in his Word, the Bible, and in his world, the universe, it seems to me that it is much preferable to spend our efforts on models that do not require us to believe that God has given us fictitious history.”

Newman’s argument is a logical fallacy. He sets up a straw man by portraying young earth creationists as a group that sees a lack of harmony between His word and His works, and seeks to harmonize the two with fictitious models. If Christians are truly interested in furthering the dialogue on Creation, then they need to rain burning sulfur down on the “fictitious history” strawman.

Personally, I think most young and old earth Christians are honestly searching for truth. In that search, we all need to be curious and open minded, not “settled,” having a healthy skepticism of any manmade models that speculate about earth’s past. Are you putting too much faith in the models of men? If so, consider that you may be closing the door on adventure and exploration, and stifling the curiosity of the next generation. I don’t want to be the one responsible for closing that door, do you?

I am not exactly sure what it is in our human nature, maybe pride, but it seems like there is a desire among some that, before they die, they are required to come up with their own personal “theory of the universe”. For the vast majority of old earth creationists, I think one reason they are unaware of young earth arguments is because they believe the history about the unobserved past is settled history. The big bang is their cosmology, and they have probably never thought to search out alternative models. They are probably unaware of the assumptions behind the big bang model, like the universe is homogenous, and no one place is more special than another.

But what if that’s not true? Are we really so arrogant to believe that here, in the 21st Century, we have all of history figured out? A 6,000+ year old universe sounds like a really, really old universe to me, but if you think it’s billions, not thousands, then it seems you should be more, not less skeptical that your model is valid. You have a lot more history to explain than I do!

Are you familiar with the big bang model? Could you list 4 other models of cosmology? Have you heard of Einstein’s metrics? If your answer to the last two questions was “no”, then it would be a wise move on your part to do a lot of research before you write any more about why we need to doubt the creation days were 24 hour periods, like Justin Taylor did recently.

Don’t hamstring the dialogue on Creation like a wolf on an elk calf, leaving it hobbled and helpless. Find ways to nurture it instead. Understand at least something about the young earth position. One presupposition of a young earth creationist is that, regarding history, God’s word is authoritative. It is an axiom to build our understanding of all history on, including natural history.

Like Justin Taylor’s article, it seems the most common theme among old earthers is they place too much emphasis on doubting biblical history. Not enough emphasis is placed on doubting manmade models like the big bang, plate tectonics, gradualism, etc. I find that old earth Christians are often enthusiastic about doubting evolutionism, which is wonderful. But the same people who rightfully acknowledge problems with evolutionism, like the lack of transitional fossils, at the same time fail to acknowledge the fact that the majority of those fossils are buried in water-deposited sedimentary rock found almost everywhere on earth’s surface, and averaging one mile thick. But where is the doubt about the old earth assumptions of all that rock being formed slowly and gradually over millions of years? Why not show a little skepticism about that, too? After all, rapidly-buried creatures preserved in thick, water-deposited rock layers all over the earth sounds very much like something we would expect from a worldwide cataclysm like the Genesis Flood.

In the 1900’s, J. Harlan Bretz was skeptical that the Channeled Scablands were formed slowly and gradually. He was able to show how they formed rapidly from floodwaters released as late-Ice Age dams burst. Or take the photo above, which shows where the River Lethe carves through layered deposits from the 1912 Novarupta volcano. By the time Robert Griggs explored the area in 1917, the canyon was already carved through all that material!

Sometimes, what may sound like just a pleasant fiction, turns out to be reality after all. Acknowledging that our eyes and our minds often deceive us will do much to further the dialogue on Creation.

Avoiding Endless Genealogies

In I Timothy 1:4, Paul warned Timothy to avoid “endless genealogies, which promote speculations rather than the stewardship from God that is by faith.” Think about the book of Genesis. Think about the genealogies in other places in the Old Testament, or in Matthew and Luke. Think also about the unfolding story of God’s relationship with man in Scripture. And think about your own family’s genealogy. When pondering your own family tree, you would think it strange to insert a million+ year gap in the middle of it. The main message from any genealogy is a message of continuity.

Continuity is also at the heart of the idea of covenant. A covenant is about an agreement, a relationship. A wise pastor I know described covenant in Scripture like this:

The gospel set forth in the context of God’s eternal plan of communication with His people as it unfolds in the historical outworking of the redemptive plan of God. Covenant theology is central to the message of the Scriptures, which testify to God’s redemption of His people in and through the finished work of Jesus Christ.

Christian, what do you believe? Is God’s plan of redemption, as revealed in Scripture, continuous and covenantal, or broken and discontinuous?  If it is broken and filled with gaps, what will you put in those gaps? How long were they? Do your beliefs about history promote speculation of God’s word more than they do speculation of man’s word?

In my opinion, furthering the dialogue on Creation means that some pastors and theologians need to take more care to avoid endless genealogies and the speculations they promote. I’m praying more teachers of the Word will focus on encouraging Christians to be scientists and engineers and doctors, developing new technologies and other things by using what God made to serve Him and serve others. Furthering the dialogue on Creation will mean spending a little more time focusing on what God called us to do in Genesis 1:26-28, and a little less time on what God meant by “day”, filling in the supposed gaps with an endless supply of speculative claims.

How to Be a Mature Math Student

Posted January 29, 2015 by gensci
Categories: Teaching Mathematics

Tags: , , , , ,

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

Posted December 1, 2014 by gensci
Categories: Teaching Mathematics

Tags: , , , , , , ,
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).


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