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Fuzzy Mathematics If you’re not old enough to remember the old "Ma and Pa Kettle" movies, you will have to ask grandma or grandpa about them. Their movies were among the best of the funny classic black and white movies made back then. The kind of movie the entire family could watch and laugh together over.
My brother and I often went to see the same movie more than once.
Storehouse of "Useful" – or Perhaps "Useless" – Information, Whatever the Case May Be! (PART 2) 10. SAXON MATH HONORS COURSES: I do not know why I did not address Honors Courses in my book, but these past several months I have had numerous calls from homeschool educators as well as high school classroom teachers using Saxon math books. They were asking me if any of the Saxon Math courses qualify as Honors Courses. So, I thought I had better address that situation quickly.
13. COURSE 1 and COURSE 2:While these two textbooks were created for use by the public and private schools – and while their presentation format of the content is different  their lesson order and concept content are identical to their home school soft cover counterparts. Math 76, 4th Ed has the same order and concept content as the Course 1 textbook and Math 87, 3rd Ed has the same order and concept content as the Course 2 textbook. So a student can successfully go from Course 1 to Math 87 or from Math 76 to Course 2. However, because of the two vastly different presentations of the concepts, I would not recommend their use unless you are on a tight budget and acquired the books at a reasonable used rate or free of charge.
Storehouse of "Useful" – or Perhaps "Useless" – Information, Whatever the Case May Be!
Could a Saxon Math Grading Website Help You? I was recently contacted by Ken, the creator of My Math Assistant to discuss his Saxon Math online grading tool. At first, I was unsure of the benefit of his website since one can simply buy the answer keys and use those to evaluate one’s progress. However, after some explanation, I can see the value for both the student and teacher/parent  and it may be something you might want to consider using whether you are homeschooling or using Saxon Math in a school setting. Here’s how I understand it works: The student types in their answers to each problem and receives immediate right/wrong feedback. They don’t have to wait for their parent or teacher to evaluate their work and know how well they understand the concepts. The student also has the opportunity to immediately rework the homework problem and try again  a great solution for those simple arithmetic mistakes that can mask the child’s true understanding of the material. It also works on the answers to the individual test questions. By the time you sit down with your student to go over their work, you both know exactly what you need to work on together and what concepts they are not grasping. The parent/teacher receives email reports on their child’s progress and scores, including how many attempts it took them to get each problem correct or if they just couldn’t figure it out. The website also keeps records of their grades on each lesson, test, and their overall score. A Concept Mastery report shows areas of potential weakness in the student’s understanding as they progress through their Saxon math book. This should be a HUGE time saver eliminating the back and forth between the students correcting individual homework questions, and returning to you to check them again. I can imagine homeschool parents and teachers alike benefiting greatly from this service and being able to focus their time on each student understanding and mastering the individual math concepts. There is an option to turn off the tests and my recommendation would be to turn that off and still grade tests by hand to insure mastery of the concepts. The cost is very reasonable at $5/month for one student or $9/month for a family  and you can cancel any time. By paying annually  you can receive two free months. Group discounts are also offered for homeschool coops and schools.
JOHN SAXON'S LEGACY John Saxon was, among other things, a teacher, a leader, a graduate of West Point, and a great storyteller. I first met John and his wife Mary Esther in the late 1960’s in my motherinlaw’s kitchen in Enid, Oklahoma, while I was on leave preparing to go to Germany. While his motherinlaw and mine had been members of the same sewing club and also the same Presbyterian Church for almost forty years, our military careers took us our separate ways, and I never had a chance to know him very well until I started teaching several years after he had already published his first algebra book in 1981. That night in the kitchen, John told the story about when he flew the supply route from Japan to Korea – in between B26 bombing runs – during the Korean War. He said he had not had much sleep in the preceding five days, and he was concerned that he would doze off while piloting the aircraft, so he instructed his enlisted crew chief to make sure he stayed awake. “I told him that whatever it took, keep me awake! I woke up the next morning and I could barely move my right arm, the pain was so intense. I looked at my right shoulder and it was a dark purple color,” John said. “I learned later that day that the crew chief kept punching my shoulder every time I started to doze off  all the way from Japan to Korea! I told him, Chief, you almost broke my shoulder. So he says to me, ‘Kept you awake, Sir!’” The high school where I had done my student teaching had been using John’s math books for several years. I liked using them, so when I started my first job as a high school math teacher, I asked for and received approval to buy his math books for two of my three math courses. The first year I taught, I finished all the lessons in John Saxon’s first Algebra 2 book. When school was out, I drove to Norman to visit with John. When I bragged to him that we had finished his book, he smiled and, pitching me his new second edition, said, “Here. Try this new edition. It’s seven lessons longer.” John and his finance officer loaded seventy of the new second edition Algebra 2 books into the trunk of my car. As I drove home later that evening, I wondered what I would say to the highway patrolman if I were stopped and he looked in the trunk. John had given me the books, and I did not have a paid invoice for them. I remember in the early days of his company, John had a personal policy that if a student found an error in one of his math books and wrote to him about it, John would send him five dollars for each error he found. That fall, when we started using these brand new first printings of the new second edition of Algebra 2, one of the students had found four problems  with wrong answers. Checking the answers, I verified that the student was indeed correct. The four answers were wrong! The young man then asked about the twenty dollars that I had mentioned he would receive. So using my classroom telephone, I called John at his office. I had placed the telephone on the speakerphone, so the class could hear the conversation. They appeared excited that they were actually sitting in their classroom, talking to the author and owner of the publishing company that had published their math book! John asked me if I had verified that the answers were indeed in error, and I told him the student was correct, that the answers were in fact wrong. Without hesitation, John immediately asked the young man his name and congratulated him for finding them. I reminded John about his “five dollar” policy. He agreed that the young man deserved the twenty dollars and that he should not have to wait around for the money. Then John, in a loud and clear voice said, “Art, you pay him,” and hung up! A warm summer evening in June and a free trunk load of seventy Algebra 2 books flashed before my eyes as I gave the young man my only twentydollar bill. John was both a mathematician and an engineer. After retiring from military service, while teaching mathematics at Rose State College in Oklahoma City, he was appalled to see that the incoming college students could not handle simple math concepts. So John decided to write his own math books to correct this. I soon learned what John meant by “atrisk adults” when, some twenty years later, I also encountered college students who still did not understand fractions, percents or decimals. They were failing their basic algebra course at the local university where I taught mathematics. Throughout John’s years of publishing his math textbooks, he always used the words “students,” “educators,” and “responsibility” when speaking about his books. He had designed them to teach the basic concepts of mathematics. They were not designed to teach just “critical thinking” or “higherorder thinking” at the expense of this critical subject matter, as many books still do today to meet requirements of textbook selection committees. One of John’s favorite analogies of what was wrong with this idea was instances when he would tell his audience, most often teachers and administrators, "Understanding should follow doing, rather than precede it. If you’re going to teach someone how to drive an automobile, don’t lecture him on the theory of the internalcombustion engine. Get him to drive the car around the block." John was always aware of and deeply concerned about our high school students as they continued to fall behind in their understanding of the basic concepts necessary to be successful in mathematics and science. He believed so strongly in what he was doing that, in 1980, so that he could publish his first math book (an Algebra 1 textbook), he borrowed money from his children, from his bank, mortgaged his house, and also borrowed against the value of his future military retirement pay! More than twentyfive years later, we all know John and his company were a tremendous success! And we all know the legacy that John Saxon has left the field of mathematics – especially for homeschool families. In July of 1993, in an open letter to then  President Clinton, John Saxon warned of the pending disaster in the areas of mathematics and science. He was concerned that educators were advocating teaching critical thinking when they should be teaching basic math concepts. He complimented the President on the fact that, while still Governor of Arkansas, he had supported a bill in the Arkansas Legislature that returned control of textbook selection to the local school boards. Local control was something John felt would keep the “unknowing” at the state level from being able to control the local school boards and administrators, and allow them to solve these problems locally. John Saxon passed away on October 17, 1996. His children continued management of Saxon Publishers until it was finally sold to Harcourt Achieve in the fall of 2004. I remember the warm sunny day in 2004 when John Saxon’s children announced the acquisition of Saxon Publishers by Harcourt Achieve at the newly constructed Saxon Headquarters in Norman, Oklahoma. Just a few minutes after the children had made their announcement, dark ominous clouds swept in, and in the midst of a torrential downpour, one of the biggest electrical storms in Norman’s history knocked out all the electrical power and telephone lines to the Saxon Corporate headquarters after lightning had struck the building. I told you John was a great storyteller. It appears, again, that he had the last word that day!
WHAT ARE THE DIFFERENCES AMONG THE VARIOUS SAXON MATH TUTORIALS ON THE MARKET TODAY? While at Home School Conventions, I was repeatedly asked by homeschool educators to explain to them the difference between the “DIVE” CD’s, the “Saxon Teacher” CD’s, the “Teaching Tapes Technology” DVD series, and my DVD series “MASTERING ALGEBRA, John Saxon’s Way.” That is an excellent question because some companies confuse the situation when they advertise their CD’s as being “video” products when in fact they are not DVD’s, but only CD’s containing a graphic presentation with audio. The abbreviation DVD stands for “Digital Video Disc” and these DVD products will work on either a computer or a television DVD player, while CD products will only work on a computer with a CD player. Basically, here are the differences: DIVE CD’s: The product covers John Saxon’s math books from Math 54 through Calculus. Each level textbook has a single CD containing instruction corresponding to each individual lesson in that textbook. The presentation is a whiteboard presentation which means there is no teacher to watch at the board. The student hears the voice in the background and watches writing appear on the screen. The product will not work on a television DVD player. The CD will not work in a television DVD player because it is not a true “Digital Video Disc (DVD),” but rather a graphic presentation with audio. As a CD, it is restricted to being played only on a computer. Each individual CD math series costs $55.99. They are available for the current editions of Saxon Math from Math 54 through Calculus—and for some of the older Saxon editions as well. The CDs will work on a PC or a Mac. THE SAXON TEACHER CD’s: The product is sold by HMHCO and supports John Saxon’s math books from Math 54 through Advanced Mathematics. Similar to the DIVE CD, these CDs are a graphic whiteboard presentation which means there is no one to watch presenting the lessons. The student hears the voice in the background as the writing appears on the board. The individual in each of the individual series of CD’s goes over every problem in the textbook and the individual problems on the tests as well, which is why there are four or more CD’s to this product as opposed to the single CD sold by DIVE. HMHCO sells these CD graphic “audio” solutions for $103.00. There is a printed version of the solution for each of the daily problems. The printed version is called the “solutions manual” (which contains the same “stepbystep” information as the more expensive CD). The printed solutions manual sells for between $56.75 for the Algebra 1, 3rd Ed manual to $58.40 for the Advanced Mathematics course. If you have purchased the new soft cover editions of Math 54, 65, 76 or 87, the solutions manuals are included in the price of the Homeschool Kit for these four courses. Don’t forget, these are CD’s – they are not DVD “videos.” And as CDs they can only be used on a computer. They cannot be viewed on a television set that has a DVD player. The CDs will work on a PC or a Mac. TEACHING TAPES TECHNOLOGY: The product is a DVD “video” set of lessons which means they can be used on either a television or computer DVD player. The entire series covers Math 54 through Calculus. As advertised by the company, the individual lessons are taught by a state certified math teacher. The individual series for a particular math book in the upper level math series sell for anywhere from $175 for the Math 54 series to $200 for the Algebra ½ series to $245 for the Calculus series. The Calculus series requires the first edition of calculus. Each DVD series for a specific textbook contains from 14 to 20 individual discs. Like the Saxon Teacher CD series, the teacher on these videos goes over every assigned and practice problem in the book, which explains why there are so many DVD’s in each individual series. Unlike the DIVE or HMHCO CD’s, these are DVD “Digital Video Disc” presentations and as true DVDs they will work on either a television or a PC running on Linux or Windows operating system—or MAC computer—as long as they have a DVD player (internal or external). MASTERING ALGEBRA “John Saxon’s Way”  by Art Reed: This product is also a DVD video presentation which means the DVD’s will work on both a computer as well as a television DVD player. This capability would enable a group of homeschool students (or a CoOp) to watch together, on a single television set, as they would in a regular math classroom. The concepts of every lesson are taught by an experienced Saxon math teacher with over twelve years teaching experience using Saxon Math books in a rural public high school classroom. The students see an experienced Saxon math teacher at the board teaching the concepts contained in that lesson. There are ten to twelve DVD’s in each of the series which run from Math 76 through Calculus. Each individual series from Math 76 through Calculus sells for $59.95 (which includes postage within the U.S.A. and its Protectorates—including APO and FPO addresses). The teacher does not “read the book” to the students. Using different problems than the examples from the book, he teaches the concepts presented in the textbook taking time to explain each concept in terminology more easily understood by the student. As any good classroom math teacher, the teacher on these DVDs explains in terminology more easily understood by the student than the often encountered complicated terminology of a math textbook. The DVDs will work on a PC or a Mac. In April of 2019 online tutorial lessons for all seven series of these DVDs – from Math 76 to Calculus were added to the DVD product line. The lessons  identical to the lessons on the DVDs  can be reviewed and/or subscribed to by going to: https://teachingsaxon.com/shop/. The online lessons will work on a PC or Mac and on any device (e.g. laptop, cell phone, tablet, etc.) that has access to WIFI. A two year subscription sells for $59.95. Before you buy any of these products, sit down with your student and look at each of the samples provided by the companies on their websites. Make sure the student is comfortable with the instructor’s voice and demeanor and how the material is presented by that instructor. Here are the four websites: https://diveintomath.com/cdromfordivemath764thedition/ https://www.hmhco.com/search/shop/homeschool?subcategory=math http://teachingtape.com/tapes.htm https://www.homeschoolwithsaxon.com/ For more information on my DVD series, you can also read last month’s news article.
WHAT HOMESCHOOLERS ARE SAYING ABOUT THE DVD MATH TUTORIALS Several years ago, I completed a random survey of homeschool educators who had purchased the DVD math tutorials I had created. Over ninety percent of those who responded to the survey indicated they wanted DVD math tutorials created for the Math 76 and Math 87 textbooks also. Since the DVD math tutorials from Algebra ½ through the Advanced Mathematics textbook (which include the first twentyfive lessons of the Calculus text through limits and derivatives) had already been created, I made the decision to follow the homeschool educators’ advice, and immediately completed production of DVD math tutorials for Math 76 and Math 87. The DVD math tutorial series are now available for all seven levels of John Saxons math books from Math 76 through the first twentyfive lessons of the calculus textbook. A sample lesson from each of these seven different math tutorial series is available to review elsewhere on this website. If you would like to review one or more of the sample lessons when you are finished reading this news article, here is the link to them: usingsaxon.com/onlinevideo.php It is difficult for homeschool educators to evaluate the varied math tutorials on the market without actually purchasing them and that can become quite expensive and sometimes disappointing. On a daily basis, I receive telephone calls and email from homeschool educators posing questions about how the varied math CD and DVD math tutorials for John Saxon’s math books are presented and how they compare with each other. To assist in making a decision regarding which product to purchase as a math tutorial for students using John Saxon’s math books, several years ago I asked The Old Schoolhouse Magazine staff to review my DVD math tutorials as they had previously reviewed my book several years earlier. They agreed. Excerpts from those reviews are reflected below. Next month I will compare the various Saxon Math Tutorials on the market today. 1. Excerpts from the review of Art Reed’s Algebra ½, 3rd Ed DVD Math Tutorial. “In the past few years, our family has used the DVDs from Teaching Tape Technology to give additional instruction in Saxon Math for grade levels 4th through Advanced Math . . . so when I had the opportunity to review the Mastering Algebra John Saxon's Way Algebra ½ (3rd edition) DVDs, featuring seasoned mathematics instructor Art Reed, I was intrigued . . . Could these videos measure up? Could I be objective? I can honestly answer ‘yes’ to both of those questions . . . Art Reed is a fantastic instructor. He is engaging and inspiring, but his approach is also straightforward and no nonsense . . . he also has a great sense of humor. He is a professional through and through . . . he knows his stuff. It is obvious that he enjoys teaching math and wants his students to succeed and master the material. I like his confident way of presenting each lesson . . . He does not spoon feed, but he does explain each concept thoroughly and give encouragement. He gives extra tips and information to make everything easier to understand . . . I also like the way he uses visual aids and manipulatives when needed to reinforce certain concepts . . . Overall, I think this is a wonderful set for homeschool families who use Saxon Math . . .The students have access to an experienced instructor, and they can replay the videos as many times as they need to master the material . . . I highly recommend Art Reed and the Mastering Algebra John Saxon's Way DVDs as a great investment in your child's mathematical education.” ******************************************************************* 2. Excerpts from the review of Art Reed’s Algebra 2, 2nd or 3rd Ed DVD Math Tutorial. “Mastering Algebra is a tutorial course designed to work with Saxon Algebra 2, either the 2nd or the 3rd edition. It is 12 DVDs, containing 129 lessons and 2 review lessons to brush up before you begin. The lessons are correlated with Saxon Algebra; for those who want the tutorial benefit but are using another curriculum, a detailed scope and sequence of the lessons is available online so that you can select the lesson or skill you need to work on . . . Mr. Reed, the teacher, stands at a podium at the front of a classroom with a real white board behind him and teaches the class. He even has an oversized calculator that he uses to show exactly what you do with various calculator functions. There are no people in his classroom, however, so he interacts with the listener, not students in front of him. This adds a personal touch to the tutorial, in my opinion. . . The lectures are very understandable, and Mr. Reed has a way of breaking down and illustrating the concepts so that they are easy to comprehendeven for the ‘mathchallenged.’ . . . The series is specifically geared for the home educating parent/student, and it would probably set many a homeschool mom's mind at ease to have such a competent math tutor for her high school student. At $56.95 for the entire set (which includes free shipping) – this is the most inexpensive math tutoring you will ever find as well . . . I highly recommend this tutorial course—even if you aren’t using Saxon Algebra.”
These same lessons are now also available in online classes at www.teachingsaxon.com/shop/
DO YOU REALLY HAVE TO DO THE DAILY “WARMUP” BOX AND “PRACTICE PROBLEMS”? I receive several emails each week about the excessive amount of time some home school students spend on their math assignments each day. In almost every case, the students have spent between thirty minutes and an hour on the “WarmUp” box and the six to eight “Practice Problems” before they even get started on the thirty problems of the Daily Assignment. It has been a little more than a decade since I have been in a public classroom, and I am not sure if public school middle school math teachers still lean on what they used to call a math “WarmUp” at the start of each class. The purpose of the “WarmUp” was to settle their students down and get them ready for the math regimen of the day. Using the “WarmUp” box at the beginning of each lesson in the Saxon Math 54 through Math 87 textbooks can become quite frustrating to students who do not have the advantage of a seasoned classroom math teacher gently guiding them in the direction of the correct solution for the problem of the day – knowing that problem might come from a concept not yet introduced to the students. But what about the “Daily Math Facts Practice” and the “Mental Math”; how will students receive training in those areas? While these two areas are essential to the student becoming wellgrounded in the old pen and pencil format of adding, subtracting, multiplying and dividing, graded by the teacher, that format has been improved with a computer model. Using the computer format allows the students to instantly know whether their answers are right or wrong. Additionally, while the home educators can easily spot the results tallied on the computer as the student moves along, it saves them the time spent manually grading the documents. I have placed a link to a wonderful Math Facts site on my website. Readers can find it by going to my home page, and from the list on the left side of the home page, click on “Useful Links.” When the new window appears, select the second link from the top labeled “OnLine Math Facts Practice.” That link takes you to a math facts practice site that allows the student to select from seven different levels of difficulty in adding, subtracting, multiplying and dividing. Five to ten minutes on this site every day at the appropriate level for the student to be challenged without being frustrated is just as good as the mental math or facts practice found in the “WarmUp” box. While the Math 87 book still reflects the same “WarmUp” box that the previous three math textbooks do, a student should have mastered the facts practice by this time. If this is the case, skipping the entire box is acceptable – unless – the student particularly enjoys the challenge of the “Problem Solving” exercise. Now let’s see if I can explain why I am recommending you stop having the student take time to do the six to eight practice problems at the front of each of the mixed practices (the daily assignments). The original purpose of these practice problems was for the classroom teacher to use all or some of them in explaining the concept on the board so that the teacher did not have to make up their own or use the homework problems. Sometimes teachers would use some of them to have students come to the board to show their understanding of the new concept. My experience in teaching John’s method of mastering math has shown me that there are basically two possibilities that can exist after the student has read and/or had the concept of the daily lesson explained to them. Possibility 1: The student understands the concept and after doing the two homework problems dealing with that new concept, completely understands what to do and has no trouble doing them. Mastery of this concept will occur over the next five to six days as the student does several more each of these for the next few days. If this is a critical concept linked to other steps in the math sequence, they will keep seeing this concept periodically throughout the rest of the book. Possibility 2: When students encounter the two homework problems that deal with the new concept, they have difficulty doing them. So, on their own, should they go back to these practice problems and get another six to eight more problems wrong? If they did the practice problems before they started their daily work, would anything have changed? If they cannot do the two homework problems because they do not understand the new concept, why give them another six to eight problems dealing with the new concept to also get wrong? This approach ultimately leads to more frustration on the part of the student. Students will have spent thirty minutes or more on these additional six to eight practice problems and still not understand the new concept. Not every student completely grasps a new concept on the day it is introduced which is why John’s books do not test a new concept until the student has had five to ten days to practice that concept. Those practice problems were not placed there to give the student more problems to do in addition to the thirty they are assigned every day. They were placed there for the classroom teacher to use on the blackboard to teach the new concept so they did not have to develop their own or use the student’s homework problems. There is nothing wrong with a home school educator asking a student to do one or two of them to show them the student does understand the new concept; however, doing more than that could be a waste of time and effort in either possibility. Not every child is the same and I realize that because of a particular child’s temperament, there may be some instances where the parent has to go over more than one or two of the practice problems with the child – and this is okay – but for most students this is not necessary. If the student really enjoys the challenge of the daily “Problem Solving:” that is okay – except parents should make sure that the student does not spend an excessive amount of time on that individual challenge and allow the real goal of completing the thirty problems of the Daily Assignment to become a secondary goal – and later a bother to the student.
DO MATH SUPPLEMENTS REALLY HELP STRUGGLING STUDENTS? Before addressing that question directly, let me first relate a story about a man walking across a bridge spanning a river. As he looked down at the water, he noticed a boy who had fallen into the swift current. It was apparent from the boy’s struggle that he could not swim. The man realized he had only two alternatives. He could shout instructions to the boy on how to overcome the swift current and perhaps enable him to dog paddle to safety on the shore, or he could dive into the water and rescue him. Without hesitating, the man dived into the water and immediately swam to the side of the struggling boy. Now the man had to face another dilemma. Should he pull the struggling boy to safety or should he immediately try to teach him how to swim? Everyone would agree that when people are drowning, that is not the time to try to teach them how to swim. All one can do at that time is try to get them to a place of safety where they can overcome the swift current of the river. So it is with mathematics. In any of John Saxon’s math textbooks from Math 54 through Calculus, if student’s begin struggling before reaching lesson thirty or sooner, it is a sign that they will drown in the later lessons of the book unless they are taken to a place of safety where they can better manage and learn the concepts that they are now unfamiliar with. Concepts that are dragging them into deep water! It should become apparent that they are not prepared for the book they are in, and no amount of supplemental material or expensive tutors will overcome those shortcomings. Mathematics is like the swift current that challenged the drowning boy. Like the river, upper level mathematics is challenging and can easily become unforgiving. Looking for a slower moving or shallower river may create a temporary solution, but eventually that water will again become swifter and deeper and unless one is prepared, all the advice and assistance given at the time of the struggle will come too late. While it is a noble goal for students to strive towards taking a calculus course in their senior year of high school, it is critical that they first master the algebra. The calculus is easy! It is the challenge of the algebra and to a lesser degree the trigonometry that causes students to fail calculus. Any student with a solid algebra background, entering any college or university, will pass that school’s math entrance exam and will be successful in a calculus course should they choose to do so. When classroom teachers or home school educators take shortcuts with one of John Saxon’s math books, they are not adequately preparing the student for the deeper water ahead. More than a quarter of a century of experience with Saxon Math textbooks has shown me that classroom teachers and parents who take shortcuts with his curriculum (instead of going slowly and deliberately through as John intended) cause students to “flounder” as they encounter the “deeper” water. At this point, they find it easier to blame the book – and they look to switch to an easier math course! The classroom instructions contained within my DVD “video” tutorial series – as well as the online lessons – are not math supplements. They contain actual classroom instruction on each concept in the book. Like the book, the classroom instruction is designed for the homeschool student who is in the appropriate level math book. The instruction enhances the written word they have already read from the textbook. Many of the lessons present a different explanation by an experienced Saxon math teacher that helps the student through the difficult reading of the lesson. However, regardless of who creates them, neither the CD whiteboard presentations nor my DVD classroom tutorials – or online lessons – will help students who are taking a course they are ill prepared for. They will eventually find themselves frustrated and floundering in the “deeper water” of a math course they are not prepared for! Have a Blessed and Happy New Year


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