In most math classes, I would assume that most students think of math as this:
There is one (or perhaps multiple) way(s) to appraoch a problem and within that approach, there is a set process to follow, and one must follow the arithmetic properties of numbers in order to get the correct answer.
Although this is partly true, most students (such as myself) get hung up on this, which is shown in this chapter when it states "these students were solely preoccupied with being walked through problem-solving steps yet again" (Buehl, 2017). Personally, I believe for this to hinder student learning because the way I see how one can effectively learn math is by practicing it. You do not and will not get better at something by watching someone else do it. Yes, math is difficult, and failure in it is inevitable. However, these small failures should be seen as learning experiences because not only does one see what he or she did wrong, but one can also see why it is wrong.
Another point I thought was interesting was how earlier in the chapter, Buehl stated how the author of any given text assumes the reader has a certain knowledge of certain topics so that a text can be effectively communicated between the two. When Buehl talks goes on to discuss math, he connects this to what he said earlier by stating "Math texts, possibly more than in any other discipline, require readers to carry over significant previously encountered concepts and certainly language" (Buehl, 2017). I think it is important he mentioned this because math concepts are so intertwined and have more than one applciation. Not only that, but these concepts also build off one another, and I believe that is why so many people have difficulty with math. A solution that I have in mind would be to have teachers teach from the textbook more often than not because students will be more "math literate." That way, they can think more mathemtically and do not have to rely on the teacher or someone else to just tell them what to do. By reading the textbook, they cna figure it out themselves so that this "authentic learning" can take place. Obviously, this would not be an effective way to approach teaching if the student has no idea what is going on, but some element of independent learning should take place.
Moving on to the fourth chapter. I did not understand too much of this chapter, since I thought it was a bit boring and dry, but one idea that struck me was when videos/media was mentioned (Buehl, 2017). Although they are useful and just overall convenient for everypone, I would say that their math literacy takes a huge toll on this because as stated previously, they would just ask to be walked thfough an example again and memorize the process. I know for me personally, Khan Academy was a phenomenal too when taking Calculus II here at UIC because my professor was not only useless, but the textbook was too hung up on all the technical math jargon to the point where I just could not follow. Sal not only made the problem solving clear, but his explanation for why he did each step in a problem made much more sense to me as well.
I mention Khan Academy because I actually had an experience with it during high school. A teacher of mine actually assigned it as homework during winter break in preparation of the final, so it was basically a study tool, but it was taken for points. Although earlier I stated that textbooks should be the way to learn math, I will make the exception of Khan Academy. I think it was a great tool, especially for the students that had no idea what was going on in class. They could go at their own pace, watch certain clips over and over again, focus on what they thought they needed the most work in, monitor their own progress, etc. In their case, this resource was able to decrease academic gaps just in time for an important exam, as well as retaining the information because as stated rpeviously, math concepts build off each other (Buehl, 2017).
Hi Daniel,
ReplyDeleteI had a similar experience with the textbook in my math classes as the one you describe. I remember thinking of the textbook as basically just something that teachers could assign problems out of. Even classes like history that did occasionally assign readings from the textbook, I just scanned through the pages so that I could fill in the right blanks on my worksheet.
Have you (for your program or for fun) encountered the book "What's Math Got to Do with It?" by Jo Boaler? It's about the benefits of a nontraditional problem-solving approach to mathematics. Boaler would say that the reason for the math illiteracy you talk about is the inaccessible and uninteresting textbooks that are currently used in most classrooms. I'd be interested to get your take as a future math educator on that.
Hi Robin,
DeleteI totally agree with you. Perhaps it is just a matter of schools getting their hands on more interesting books rather than those that are just so dry and uninteresting because in those cases, like you mentioned, students just "read" for the sake of the worksheet(s).
To answer your question, I have to even heard of such a book, but I will have to go it a go as it may even help me right now. Thank you for the suggestion!
My math experience was totally different from yours when I was in high school. Our math textbooks were not as thick as the one that you were using in the U.S.A. But I think every sentence in our math textbook was essential and important. It provided the basic math theorems and instructions on how to think on the math problems, why to think in that ways, and how to apply theorems to support the solutions. Teachers would encourage students to read the textbooks before the math classes so students could pay attention to the lectures and focus on how teachers analysis were same or different than the textbooks. We have to read the content and understand the examples it provided before we were able to do more exercise and finished the homework.
ReplyDeleteThink you for sharing Khan Academy with us. I took a quick check on it, I think it is a very good resource -- Mathematics can't do without thinking and practicing.
You are lucky enough to not have that same experience then! I genuinely cannot imagine a much younger version of myself trying to read my alegbra textbook. I would imagine that reading the textbook beforehand at such a young age would have improved my math literacy. That would had made such great use of the textbook too, since I was already carrying it aroiund everywhere.
DeleteGlad to know you think Khan Academy is a great resource!
I think it's interesting that you mention that teachers should "teach from the textbook more often than not," which, from my experiences and from what I've seen, math teachers do teach from the book. Teachers use the examples, definitions, and theorems directly from the book and implement them into their lessons. In classrooms that are one-to-one, I've seen the teachers and students screenshot and crop the definitions, examples, and theorems directly into their notes and move on from there. In my opinion, I don't think the issue lies with whether or not the teachers are teaching "from the book," but from another idea you stated: that students aren't as "math literate" as they should be. I think therein lies the problem. Many schools and teachers don't take the time to teach how to read their math textbook as often or in depth as, for instance, a literature teacher would teach their students how to read poetry. Math has become this process of memorizing the steps and this monkey-see monkey-do sort of learning that isn't effective for the long-haul. I think teaching students how to properly read their textbook as well as restructuring how we teach math could be the things that make teaching and learning math effective.
ReplyDeleteI totally agree with you! Math is a difficult subject to be properly understand, and I think teaching students how to read these sorts of textbooks at such a young age has great benefits in the long run.
DeleteAs for your comment on students memorizing steps, again, I am with you there. There is no real thought process here, and perhaps some students do not even see the logic or reasoning behind the steps. They just want to know what they have to do to get the right answer.
I do agree that many math books are just used to assign the problems in them. I had many times my teacher would lecture and do some example problems in class but when it came to do my homework later I would get stuck. There would be a different problem from what was talked about in class and I had to go back through the instruction part of my math books to figure out how to approach the problem. Granted, I enjoy math so it didn't bother me but, for other people the not knowing how to even approach a new problem could be devastating to their motivation to learn the material and finish the problem. This is where sites like Khan academy are useful and teachers should make sure that their students know about different resources out there that could help them.
ReplyDeleteI have had similar experiences as well. It seems as if the examples one does in class are always super easy, but when time comes for the homework or exams, the problems do not resemble anything like previously encountered examples. Again, perhaps if there were actual assigned readings from the textbook, then students would encounter these situations less often.
DeleteDaniel,
ReplyDeleteI love math but I have always been that person who takes 10X longer to solve a problem. I do not think that the only issue are the way it is taught or what is in the books, but also that teachers do not make any of this applicable to us, as students. I think educators should also put effort in teaching students how to apply the concepts that they are teaching so that it can make more sense to them. They shouldn't be content with the students memorizing formulas or steps, but help students understand the reason behind each step.
You make a very good point. Way too often we are taught something in math, and when students ask the question on why we need to use it, that question usually goes unasnwered. Perhaps is teachers were able to better answer these questions, that may spark more interest within the students, and so students may perform better in math as a result.
DeleteHello Daniel,
ReplyDeleteI think that you bring up really interesting points and that your discussion of traditional math textbooks and kahn academy recreates the tension facing in service math teachers. Often times curricula require that teachers utilize a textbook, precisely for the reasons that you mention here - students need a resource that they can utilize to support their learning, students need to increase their math literacy - however there is a dearth of high quality texts. In my experience, both as a teacher and student, instructors feel the need to augment or substitute the official text - maybe because the content of the text is not culturally relevant, maybe it sustains stereotypes, maybe as you described it relies on dense jargon and is not helpful to students.
Why, like your highschool teacher did, can't we consider resources like Kahn Academy texts? they too require math literacy. I agree that it is the teacher's responsibility to make the textbook a useful resource, but I do not think that we should passively accept the content provided by publishing houses - we should not adapt our instruction to the text, but rather adapt the text to our instruction.
I have never really thought of it that way. Throughout my experience, it was either the teacher focuses his or her curriculm entirely off the book, or the teacher completely disregards the book. Perhaps there is a "sweet spot" that can be found for optimal learning that will fit the needs of the teacher and the student.
DeleteI like the quote you chose to use about students simply waiting for the process to find a solution being given to them. I was recently working with a 7th grade student on a math problem that did not have one specific way to solve it. He had the same exact attitude and told me that I was just going to tell him he was wrong and show him the right way so what's the point in trying. While I think as teachers we can avoid creating this type of attitude, I personally was having a hard time working with that student. How do you change that attitude from the get-go? How do we help these students that are stuck in their ways with what you are given? -Kiley
ReplyDeleteAnswering his or her questions with a question may be an answer because that way, students are forced to think at least a little bit and are forced to give you some sort of answer. That way, you can "assess" or analyze their understanding of the material.
DeleteI can relate to the students who cannot comprehend math; I am definitely not a math person. However, I do agree that math is a certain text that many do not understand and its the teacher's job to teach the students on how to read a math book text. Math text is extremely different than literacy text in english so teacher cannot make the assumption that students already know how to read a math text. Its hard for students to ask question because they don't even know what they don't know; this is how I always felt in math classes.
ReplyDeleteI sympathize with your experience, as I have had similar experiences as well. Perhaps the teacher has to dedicate more time to a specific topic than expected so students can better understand it. However, a classroom is a two way relationship so students also have to put forth effort on their side and if that means studying more, then so be it. A teacher should not solely be seen as a dumpster of information.
DeleteThank you for sharing your personal experience. I had a similar experience as you, with all my math classes. I am actually going through the same thing now with my proofs class, but it is kinda the opposite. I read a chapter and I always don't understand what I just read. Even sometimes if I read it numerous times I still have trouble applying the content. I think it is important to teach students to read from textbooks at a young age because not doing so, is literally setting them up for failure. Especially, for higher level math classes.
ReplyDeleteYes of course. Although the math jargon can be boring and difficult, it is important to teach because higher leveled mathematics require these reading and thinking skills.
DeleteI do agree with you. I remember that when I was in high school, my math teacher often asked us to preview before class, then she would teach with the assumption that all of us had known about the knew lesson. However, in fact, the math text book was difficult for us to read and understand, thus, the preview was always unhelpful but easily to cause me to lose confidence and interest in math. I agree that it is necessary for teachers to teach students how to read the math text and lead them to solve the problems by themselves. If so, when they meet the difficult problems and cannot get the answers right away, they may find the solutions through reading the text books by themselves. If they solve a difficult problem by themselves, they will tend to be more confident about math. Teachers cannot teach their students all, so it is important to teach them learn by themselves.
ReplyDeleteI completely agree with you. Perhaos what your teacher should had done was still have you read the text, but come to class the next day with questions they may have. Assuming everyone did the reading can be seen as preparing them for a post secondary education, but at that point in time, it seems to be doing more harm than good.
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