*About Mathematics*.

AN UNDERGRADUATE LIBERAL ARTS CLASS

Here is what 23 students had to say about this text and the associated course. What follows was written by freshman and sophomore students at Buffalo State College in a class taught fall semester 2010 by Professor Rising. The excerpts have been taken from required daily single page commentaries that were solicited to assist in the revision process. (The full set of commentaries is available for review.)

At the outset:

"I am not ashamed or embarrassed to admit that math is not my strong point. In fact, I somewhat strongly dislike the subject."

"When I discovered the class was math-based, I have to admit, my heart did skip a beat."

"I am always the first to admit math is not my forte, however, after reading the Preface and Introduction my attitude changed. I am not planning on becoming a mathematics major but I am willing to give it a fair shot."

"I agree how math is usually taught as just how to solve a specific problem with a specific method. Then, if a student comes across a slightly different problem they become confused. That is how I was taught in Middle School and High School. It seemed boring to me because it was just solving problems and equations one after another."

"The textbooks we use for my other math classes are absolutely awful. It's as if the book expects us to already understand the concepts and just tries to show them to us from an alternative viewpoint. The way you are going about writing your book is phenomenal."

"The word 'mathematics' and many of its associations petrify me. The only thing I enjoy that is even remotely related to math is Sudoku puzzles."

Along the way:

Getting Started

"So far I have learned a lot of information I did not know about my calculator. Before taking this course, the use of my calculator was limited to doing basic math and figuring out trigonometry problems. Furthermore, in last week's reading in Appendix 1 I felt that the statement that calculators are 'admired but rarely accessed' was an accurate statement when it came to my use of my calculator. I have this expensive piece of equipment yet I have never really had the faintest idea how to use it."

"So far I really like the readings we are doing. Normally textbooks do not address the reader and are just dull and boring. This textbook attempts to insert humor which makes required reading monumentally more fun to do."

"I am very grateful that I have found the readings for this class to be very clear and concise. Math is often a difficult subject to explain in written words, but so far I have been able to understand the text very well. After reading the Preface and Introduction of our text, I was glad to discover how understanding Professor Rising is in regards to his students' feelings about math, purposely writing this textbook in an easily comprehensible and accessible manner. Also I was pleased with myself that I was even able to run the program WHAT without a problem, as it was my first time running a program on a calculator on my own."

"I am really enjoying this class. It's not that it is easy, but it is just very different from any other math class I have ever taken. I was very scared to take this course because of what I had heard about last semester's class, which seemed to be geared to math and science majors. This class is more for everybody."

"The textbook for this class is extremely new material to me and very informative."

"My last experience with math in high school left a bad taste in my mouth but I am having more success with your class than before. I find the text accessible and your teaching method direct. In previous classes teachers emphasized formulas and semantics to no end. The shift away from that in this class allows me to see the points more clearly."

"This homework assignment had to be my favorite thus far. I can actually say that I enjoyed running the programs on my calculator. They were quick and fun. My favorite programs were POLYGONS and SIERPINS, because of the beautiful designs they created.... After completing this homework assignment, I can honestly say that I am no longer afraid to embark on my homework assignments."

"In class I was especially interested when we discussed the problem with the 1980 and 'x years old in x squared'. One thing I've liked about class is the fact that I hear about old things I've learned but also new concepts like 'the butterfly effect' and the 'four color problem.'

"I am starting to feel more comfortable with how class is going. If you remember, at first I was worried about the subject matter being over my head and the workload being too heavy. Now, however, I'm feeling better about it. So in all, I am good with going forward with what I have learned so far."

"I liked the homework for this week. I thought the last 2 questions were especially interesting. I spent almost half an hour on the POLYGON question because it was so entertaining. I loved looking at all the different shapes."

"I was really excited that I was able to do this homework without struggling and hopefully that will continue. Thank you for your help."

"This class was one of my favorites to date. I have been using a graphing calculator since my freshman year of high school and yet still I learned more about the graphing function than I had previously known."

"So far I am really enjoying this class because it is the first time in a while that what I am learning is completely new to me. Normally I have some idea of what is going on in a class but with this class, every single thing is completely new to me since I have never done anything on a calculator."

"I'm extremely happy that I decided to take this class. Not only is it teaching me a lot of information about my calculator, it's also opening my eyes to what else is out there in the world of mathematics. Also, I love using both the POLYGON and SIERPINS programs. I love seeing the different designs appear and try to guess what they are going to look like."

"I completely understand synthetic substitution and enjoyed learning the purpose of it versus just going through the steps and accepting the process for what it is. I understand the program SYNSUB completely and understand the process it's undergoing."

"This may be strange to hear this, but I really do find reading this textbook enjoyable. It doesn't have an overly serious tone like most textbooks, which makes it easier to read, and frankly a whole lot easier to understand."

"I still like the fact that the readings are not written in such a way that one feels like they are actually reading a textbook, but instead being led through a process. I feel like I am starting to understand and following along and understanding more."

"The reading we had I found quite interesting because I had never really thought about the programs that have to be included in the calculator for them to work. I always thought when you punched in the numbers in the calculator they just appeared and the calculator just knew."

"My favorite problem was Exercise 4.3, because of all the beautiful designs I was able to experiment with. I also enjoyed watching my calculator draw out the triangle from Exercise 4.4, considering it took such a long time. It was rather interesting toknow that Sierpinski had been able to develop something as interesting as the Sierpinski Triangle."

Algorithms, Functions and Equations

As for the algorithms, I thought they were something much more complicated than they are. I thought they were complex equations, I did not realize they are basically like recipes. I wondered at first how we were going to use those programs in the calculator and what their use was but now I understand more and feel more comfortable using the calculator."

"In class we also went over square roots. I thought that the way we were shown today was very easy and a lot more helpful than the way I was taught in high school. I understood this method and now I am definitely not afraid to find the square root of a number and solving it out on paper instead of using the calculator (although, if it saves me time, I will still always use the calculator if we can, ha ha.)

"It is very fascinating to me to see how many different methods you can use to come up with the same answer and to solve the same problem, just in different ways."

"It took me a bit to figure out the homework problems, but the reading before the exercises definitely helped explain and helped me understand."

"I really enjoyed learning about the algorithms. I remember my high school math class asking the teacher how to do square roots by hand and she told us there was no way to do it. It didn't make sense to me, because I knew square roots existed before calculators existed.

"I also liked the reading for this homework assignment. I think it is very good for students who are not good with math. It really helps you understand where numbers come from and how they work. It also shows a more advanced view of the places (ones, tens, etc.) In most math books I find it hard to follow their work, but I thought it was very easy to follow this."

"I liked the SYNSUB program too. That will definitely be one I keep on my calculator after this class."

"I liked writing the numbers out in that calculator way: (((4 x 10 + 9)10 + 6)10 + 8)10 + 2."

"One thing that I have noticed in the text that I particularly like is the presence of detailed examples. Although sometimes the examples can be long, I don't mind reading them and following them all the way through because I know that they help me with the homework problems."

"I used the programs on the calculator to help me check my work and was actually comfortable with it. Score!

"I started picking up synthetic division quicker as we reviewed it in class and really wished I could've taken a class like this in high school. I honestly feel that high school students would benefit exponentially from taking a course like this. It's sad to acknowledge the truth that with each generation, calculators are becoming increasingly prevalent in ALL studies of math. It's coming to a point where people can hardly do simple functions without the help of a push of a button. What I like about this course, however, is learning how the calculator solves the simple functions."

"I easily understood the synthetic substitution on this assignment and the program made things that much easier. Where was this when I went to high school?"

"This portion of the text we read and the assignment that followed were very well written. The text directly supported exactly what we had to do and the examples were a good reference point.

"I've never used synthetic substitution before. I think it's quite the neat little trick. I wish I had been introduced to it back in high school when I was learning how to solve equations such as this. I'm sure this won't be the last new thing I haven't seen. I can't wait to see what else you have in store for us."

"I loved the reading this week. As with the introduction and preface, it felt accessible and explained the concepts vey well. The other units were helpful but I felt this one was exceptional."

"I'm not sure if I mentioned earlier, but I wanted to comment briefly on your textbook. Your writing style is very straightforward. I appreciate that. It is refreshing to understand the material first hand without a supplemental dictionary at every word. Nicely done."

"For a class that is at 8 a.m. in the morning, I sometimes fear that I'll be exhausted for class and unable to retain any of the information. That was how I felt this morning was going to be. Luckily, I love the information that we are learning, which makes it easier for me to pay attention."

"I liked the reading for this week. I thought the steps for the square roots were easy to follow. I also liked the humor in the introduction to the section."

Calculus

"I'm glad we are doing calculus now although this is not necessarily a calculus class. I have an immense fear of math and I feel that although I am not understanding everything 100% I am still understanding a lot more than I used to. The thought of calculus has always terrified me so having it broken down for me is really good. I have always thought I was just terrible at math but I think with a little more effort on my part I could start understanding a lot more than I used to. This is the first class where I feel like I am really learning new things."

"A piece of the reading I enjoyed was Warwick Sawyer's passage. I would've never guessed calculus was so significant to life, mostly because I had no idea what it entailed prior to this course. I was one of those students you referred to in the previous reading -- I scoffed at anything with the word calculus about it. I completely shut down over my pre-calculus tests, blanking on all of the material we had covered. Now, I feel much more confident and comfortable with the subject."

"Well, this homework took no effort at all thanks to the programs TANEST and F3. These programs are easy to use and take no time at all to come up with the answers. As for the program quiz that is due tomorrow, I finally feel that I can follow the programs. I am more confident using and working with my calculator, and you're right, it is way easier."

"As for the calculus, so far so good. It's all new to me, but I have been able to follow the class lessons and text very well. I especially like how the text includes many visual examples of graphs, as it definitely helps me to look at the graph when something is being explained rather than trying to visualize it and have a mental image of the wrong picture. I also like how the program TANEST was used to find the derivative before complex math was introduced. This way, I have a clear idea of what the derivative is, and I'm not confusing myself with the math associated with it. It is very important to understand main ideas and concepts first, and then go into more detail later."

"As for the calculus, so far so good. It's all new to me, but I have been able to follow the class lessons and text very well. I especially like how the text includes many visual examples of graphs, as it definitely helps me to look at the graph when something is being explained rather than trying to visualize it and have a mental image of the wrong picture. I also like how the program TANEST was used to find the derivative before complex math was introduced. This way, I have a clear idea of what the derivative is, and I'm not confusing myself with the math associated with it. It is very important to understand main ideas and concepts first, and then go into more detail later."

"I really am enjoying this calculus stuff we are doing."

"I think it is really interesting how we can find the area of (sic!) a curved line and how exact our measurements can be. I never really thought any aspect of math was particularly interesting, however, this new material has somewhat begun to interest me. I can't imagine all the work that any calculus problem must have been before calculators. Problems that take us a few minutes must have taken a few hours or something depending on what needed to be figured out."

Geometry

"I like refreshing on the geometry aspect of math. The reading provides more insight on the history of these proofs, naming people and providing their accomplishments gives me more knowledge behind the math that I've never known before."

"I am really enjoying this new unit that we are doing. I hated geometry in high school, but I am enjoying this unit."

"I think that this geometry chapter will appeal to a lot of the students in the class. With all the planet earth and math, I think it will be eye-opening. I feel that many people's aversion to math comes from the idea that there is no point to it or they can never see themselves needing to know it. I think that the way that the chapter discussed the connections will answer that annoying and discouraging question for many of my classmates."

"I thought the last class was really interesting and I enjoyed it a lot. I had never really understood latitude and longitude. Furthermore, I never realized how important it really is. I had never heard about how those English sailors had died. I find it incredible how much we have advanced so that now we have little computers that help us figure out where we are and how to get from one place to the next. Sometimes I wonder what it would be like to show these technological advances to the early explorers. It would blow their minds I am sure."

Mathematical Models

"I didn't know that probability could also come to use with the calculator. I never used the program rand before this class so it's interesting to see how the calculator generates those random numbers."

"So far I like this chapter on modeling. I find that the arithmetic and calculator work is very appropriate and everything we have gone over in class and what is written in the text is clear. I especially liked the lesson on Tuesday when we were introduced to matrices."

"I must say that so far I am enjoying this segment of the class. I'm not quite sure as to say why this section "Modeling" interests me, but I think is because this is material that I've never really touched on before. The ideas of random numbers, probability and matrices all seem to capture my attention. And not to say that your class sessions are boring, but I found the last class session actually enlightening. I'm the type of person to enjoy learning new things and the fact I walked out of class with this new wealth of information that I actually understand is a bit of a perk for myself."

"I would like to say that this class was by far my favorite of the semester. I loved getting the game in my computer. I also liked how it connected probability with a real-life situation, even if it is gambling. I had actually just asked one of my friends if they had games on their calculator and then I found out that I already had one. Needless to say, this was the most entertaining class of the year."

Money Matters

"I am so glad that we are doing a unit on money. I never really went over any banking and things like that in high school and I get crazy confused with these types of things. I have always been concerned that once I have to start handling my finances by myself that I will have no idea what to do or what is going on."

"The homework was very interesting. I really enjoyed it because the book used very real life situations."

"I think that this section of the class will be very useful in the real world. We are all students who have loans and want to make the most out of the loans we are taking and find the lowest rates.

"I thought that the reading was very interesting this week. I liked learning what roulette is because I hate when I watch movies and I have no idea what is going on in casino scenes. I also liked seeing the different strategies for roulette. I never have any strategies when I play games: I usually just make it up as I go. I probably won't be playing roulette any time soon, but it is still kind of cool to know different strategies."

"All in all I think this class has been very enjoyable over this past semester and I truly have learned so much in this class. I have found it to be interesting as well as informative." [this is from the weakest student in this class]

"I think the programs for ROULREP and the Martingale programs are really cool and interesting to learn about and I found the fluctuation between win and loss really interesting."

"I loved class today. I love to gamble and it was awesome to be able to 'gamble' on my calculator."

"After going through the reading, I have realized that there is no good strategy to gambling. There is no method that really leads to winning outcomes. The sample strategies are misleading at first, until you realize and see the point where you start losing your money fast."

"I thought the problem with the seating at the tables was interesting. I actually had to look that up for my psychology class once and most people say they prefer to sit at the corner because it is closer and more direct. I do see though how there also is a higher chance for the corners because there are 4 ways to sit as opposed to 2 across. I also liked the dart throwing program and how it shows us π."

"I enjoyed reading this section of the text on roulette. Aside from learning about a real life situation, I now have a better understanding of why gambling is such a scam. I have found it interesting to be able to simulate realistic trials of roulette on my calculator as this gave me a better idea of how the game is played."

"I am glad that I now have a better understanding of how stuff like interest works."

"I feel like this topic [money] will be the most useful after the semester is over. It will be the part that I look back on most as I get older."

"The debt we will have from our college loans does put a lump in my throat every time I think of it. But I know that 1. I will be able to pay it off because 2. I will have a greater chance at getting a job because I went to college. I like to think of it as an investment on my brain. It's easier to just say that you'll work right out of high school at a job that pays you minimum wage than to go into debt by going to college when you're just as uncertain if you'll be able to get a job above minimum wage that can pay it off."

"I'm happy to be going on the strong note of the money chapter."

"I really like the program you made, AMORTIZE, it is really to use and seems like it could be helpful in life even after this class ends. I like this section of the book not only because of its relevance to real life, but also because the book itself was easy to use and actually understand."

"This chapter is very interesting to me because it has to do with finance and that relates to my business major. Thank God for the programs though, because I would not be able to do that in my head. I like learning about this because we all have money and we should know how it's handled in the bank."

"In the beginning of the year I felt entirely overwhelmed by the programs we had to use for our homeworks, but as this class has progressed I have become more comfortable and capable of using my calculator properly. These programs really do make all of these questions much easier. So thank you for teaching me how to use them and potentially make my own. As a class, I started off worrying about the difficulty., I would now consider this my favorite class and the most understandable."

"So far, I think this lesson on credit cards has been the most useful subject I've learned in the Money chapter."

"Initially I didn't like the Money Matters chapter but it has begun to grow on me simply because money does matter. I believe that a lot of the concepts of this chapter could actually be handy for many people in day-to-day activities. The homework was particularly helpful in managing a credit card since many people fail to read the fine print associated with them."

"The moral of the story is to always pay off your credit card. Once again your homework has shown a very real life situation. You have scared me off of owning a credit card ever, which is probably a good thing since I would be one to end up in credit card debt. So thank you for the real life lesson. It really made an impact on me."

"So far I am really enjoying this chapter. So far all the information has been incredibly useful and I will definitely keep the information in mind for later on."

"The programs we used in this section I really enjoyed using bedause I understood how they work and how to use them. Things relating to money have always seemed so mind boggling to me. I still have to be careful about how I handle my money because I want to do a lot of things but money does seem to burn a hole in my pocket."

"When I started to read the section about credit cards in the book, I again noticed something that I really like about this course. The way that you will use one example in class and provide us withg another in the book is very helpful to me.

The Science of Secrecy

"As we are going into the last week of classes, I really am going to miss this class."

"I liked how you summed it up with the 'Science of Secrecy' chapter because it was actually a fun chapter. My personal favorites were the Modeling chapter and the Secrecy chapter. And I must say you do have a true knowledge in your field of work and a passion for what you do, even if it means teaching at 8 in the morning."

"One of the things that I really liked about today's class and the writing of this chapter is the way that you incorporated your own experiences in the material. I really did find the story about the flags on the naval ship interesting. It also made the material more relatable because it gives real life examples of the secrecy and code aspects."

"I find the coding very interesting - it's challenging and poses the same intellectual challenge as a game of Sudoku. I like how you explained the techniques in class (particularly the mention of the Zodiak killer's use of code) but for the homework, I really grasped an understanding of binary, hexadecimal, octal and decimal through the explanation in the text. Also, in all honesty, without the help from your email, with its examples of de Vigeniere, I'm not sure if I would have reached an answer as easily."

"Deciphering messages is probably my favorite chapter this semester. It's exciting when you try to figure out a message. I feel like coding and decoding is a race between countries. That's fascinating to me."

"I loved today's lesson on secrecy and uncoding. It was the most interesting topic covered this semester, and I feel fortunate for being in this class because I'm not sure if I would have learned about this in another math class. I thought it was very good that this lesson was rich in history, as good background definitely supplemented the class. I think that I liked this lesson so much because I love word puzzles (like cryptoquip) and it was very intriguing to learn about new codes and strategies."

"I really, really, really like this unit. I think it is a very fun unit and a fun way to end the semester. I almost wish there was a class in just secrecy. I also really like that you have personal experience in secrecy. I think that the personal experiences made the reading and the class even more interesting. I grew up watching military shows on the history channel, so actually knowing somebody who has decoded messages in real life is pretty cool."

"I thought that the reading was interesting and I really liked the story about using the wrong flag. I though that the reading was pretty easy to understand but I did have to read some parts several times."

"OMG! I loved class on Tuesday. One of my favorite de-stressers is doing Sudoku and sometimes the puzzles with the crossword-like set-up and the numbers corresponding to numbers (sic!) I find it cool that going back forever people and countries used code to send secret messages and stuff? That is awesome."

"The secrecy section is really interesting. If I were better and math was not so confusing then I would definitely consider a career doing this kind of thing.

"I am very glad that you decided to make the secrecy chapter one of the last that we got through in this course. Everything that we have covered in this chapter is new to me, and it makes me want to learn more about coding and how mathematics relates to coding."

"Throughout the semester we've covered some very interesting topics. I wish we had more time to cover this instead of rushing through. I didn't think I was going to learn much in this class, but it turns out I did. I liked the way your integrated the TI-84. It's a great tool to use and I'll be keeping all of the programs for future use. Who knows, maybe I'll even program some of my own some day and use them in my classroom. It's been a pleasure, although I'm glad THIS is my last commentary."

"Modulo arithmetic is something I haven't previously dealt with in any math class. Nonetheless, I was able to understand it because I thought the text was written very clearly."

"I found the section on the RSA code very interesting, as this code is one of the most complex codes to break."

"Overall, I was very happy with this class this semester. I remember being very nervous in August and September when I learned that this course would heavily depend on my calculator, but I have come to be very grateful for my calculator. Mr. Rising was such a nice teacher and I thought that his textbook was very clear and concise. I also liked the format of this class and thought that all homework assignments were reasonable."

"As I've said before, I do really like this chapter. I'm very glad you included it because it is fun and interesting."

"Anyways: the reading about the mod stuff clicked more with the letters than it did with the clock. I understood but the letters clicked quickly."

"The RSA code was my favorite section of the two readings, only because I've always had a thing with the idea of secrecy, things that could only be understood by some and not all."

Final remarks:

"Thank you for teaching this course. I can honestly say I thoroughly enjoyed it. I was scared at first because my math skills are a bit rusty, but this class you learned as we went along so it didn't rely too much on previous math knowledge, which was nice. It was cool how this math was a more in-depth discussion of __how__ and __where__ the procedures were developed. I really enjoyed taking this class, by far my favorite honors class yet."

"I think this class would be a nice elective, especially for math ed majors. I am going to miss these commentaries. It helped me stay engaged in the class."

"Dear Mr. Rising, this is my final commentary for your class I'm sad to say! But this class has been very interesting."

"This being my last commentary for this course, I would like to take the opportunity to say that I enjoyed it. Coming from someone who does not enjoy math whatsoever, this class has been very informative and possible for me to follow and stay engaged in. I am very happy I took this course. thank you for all your efforts and understanding. Best wishes."

"I thought the programs you created on the calculator were really impressive, fun to use and interesting to learn about."

"Going in, this class was not what I expected at all, in fact I was quite worried about it. But now at the end of the semester I can truly say that it is my favorite class. You are a great professor. Thank you for all your help and kindness."

"I'm sad to see that this class is coming to an end. I really enjoyed it! Thank you for such a great semester, Mr. Rising! You did a great job -- I learned a lot."

"I hope that you make the rest of the textbook available so that I can see what other sections you focused on. This is the first math textbook that I have been able to read without wanting to pull my hair out. I know that it is important to read the textbooks in order to better understand the concepts, but I just don't find them that interesting. That's not how I felt about your book however. I think that it is really interesting, and I would be interested to see what type of course this book could be applied to."

"I have really enjoyed this class. I liked how we learned a little bit of everything. I think that this class would be perfect for non-math majors or as an introductory course in math. I also loved learning so much about my calculator."

"All and all I am very sad that this class is ending so quickly. I really learned a lot and I can definitely say I have never taken a class like this before, but I wish all of my classes were like this."

"I have learned a lot in this class and I am really glad I took it. The programs in my calculator I will probably end up using later on."

"I found the homework to be quite easy and fun. I feel like I learned a great deal. Thank you for your time and support when I found things to be hard or confusing."

"I pretty much wrapped up what I thought was the final commentary in the last commentary I wrote, but I'll summarize everything up again. So, at the beginning of the semester I was hesitant to accept the class when I found it was a mathematics based class. I've never been a big fan of math and I was already taking a statistics which would give me enough of the math-related grief I needed for the semester. In the end of it all, I am happy that I gave the class a chance because I did enjoy it quite a bit. Waking up at 7 in the morning to get to class (most often late anyway) was not my cup of tea, but the various lessons was pretty enjoyable itself. I really liked the "Modeling" chapter with the lessons on probability and the calculator programs were pretty fun itself. I also liked "The Science of Secrecy" chapter even though we got to do one class session on it so far. Wasn't too fond of "Getting Started" chapter since I had a difficult time with the calculator programs although I got it after a while. Other than that, it was a pleasure to be in the class. I would prefer this class other than physics or chemistry for a natural science class. And I must say that you're a good professor, your knowledge and experience showed which I appreciate. So now I'll always take as a basic sense of knowledge from this class is to always fold the raffle ticket for a better chance of winning."

"Mr. Rising, I just wanted to say thank you for a very interesting semester. I really did enjoy your class, even though it was not what I had expected initially! Thanks again and have a merry Christmas!"

"I really appreciated your class. You're a great professor! Thank you!"

From course evaluations:

I liked the course materials and the text was nice to read and easy to follow.

I would rate the quality of the course materials very high.

A+ Text was easy to understand

The course was a nice course and had good quality

Course materials were very much tailored to our needs

I would rate the quality of the course materials as superior

On a scale of 1-10 I would give this course a 9.5. The course material was mostly new to me touching base with things I already knew.

It was good and I am glad I took it.

A COURSE FOR SCHOOL MATHEMATICS TEACHERS

During summer 2011 I taught a University at Buffalo course for school classroom teachers of mathematics. The aims of this course were quite different from those of the undergraduate course. These students were undergraduate majors in mathematics and so part of their responsibility was to react to how the content was being interpreted. But, as the commentaries show, they found much new in the text. They too wrote daily commentaries and the following represent brief excerpts. The complete file of commentaries is available for inspection.

Chapters

Calculus

"In the calculus chapter for sure the language that is used is more of a novel than a mathematical textbook. I was able to read and reason more so than I ever done before simply because the emphasis was not on calculations and problems. A lot of the diagrams and charts used to show the slope at a point in time are very beneficial to whoever is reading and for my point of view helped me deepen my understanding of the derivative and more importantly the relationship between velocity and time. I feel that many calculus teachers jump right into the derivative and the rote memorizations of the tools used to find it and often overlook the meaning behind it. That was my experience throughout college and this book helped close the gap between the rules I have memorized with the meaning of the concept behind them."

Reconsidering Arithmetic

"Even though an elementary teacher may be teaching basic arithmetic operators like addition, subtraction, multiplication, and division; these foundational operators as you see in the unit on “reconsidering Arithmetic” have alternative methods and uses. If the elementary school teacher only knows one way of explaining how to teach the concept, he or she may hinder the student’s thinking for their future mathematical explorations. By reading this book and having the wide range of concepts thrown at you, you are forced to gain new perspectives of traditional mathematics that most people never experience."

The Science of Secrecy

"Each of the arithmetic units and secrecy units was all bonus material from my perspective. I have had experience with different mods but never in the shape of code breaking and deciphering. I really feel that these two chapters was truly a learning experience for me that I enjoyed. Yes at times I was confused, but the larger picture was the exposure that I gained to an area of mathematics that I never really have seen before. I am certainly not a master and would not feel comfortable teaching the unit without formal hands on teaching experience, but seeing this new type of information has opened more doors and expanded my knowledge base in mathematics. Those were my two favorite units by the way!"

Final Remarks and Evaluation

"I absolutely loved this textbook and feel that I have grown so much in my own mathematical understanding throughout the course."

"The first couple of chapters started off very basic with an upper level high school feel to them. I feel that seeing certain topics again really helped me refresh my thinking and possible alternative methods or approaches I could use in my mathematical classes."

"In the later chapters of the text is where I benefitted the most from a mathematical point of view."

"I feel that this is one of the most user friendly text’s I have ever come across so far in my mathematical career. The main reason I can say that is because this book does not emphasize the typical rote memorization of formulas, rules, and procedures. This book allows students to explore the background meaning of several advanced topics, but through the use of the calculator allows them to not get hung up on the technical calculations that most other books emphasize."

"I feel this book would serve any type of teacher preparation program ranging from elementary education throughout secondary education and across all concentrations. This is a very bold statement that I made but I feel this book is written in a way that the most advanced topics are written in a way that all audiences would be able to learn them."

"This book has opened my perspectives on a lot of mathematical concepts. Even as a mathematics teacher as I was reading this book I was learning new concepts, or alternative approaches to the concepts that I already knew. I feel this is very important for a mathematics teacher to constantly explore new concepts or even improve/look into the current concepts that he or she understands. If a teacher can expand his or her own thought process through alternative methods, imagine what how he or she can inspire that gifted student and challenge them as well."

"I enjoyed how this book was more words and took the time to tell applicable stories to students about how mathematics is involved in their everyday life. I enjoyed thinking through the exercises that forced me to think versus compute a problem from a process I learned. Most of all I enjoyed and appreciated the way this book was written; to teach mathematics that are used in everyday life with appropriate exercise and examples that highlight this. Students should learn to like mathematics and this is one step towards pushing them in that direction."