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Today on the Diane Rehm show, she interviewed Andrew Hacker, the author of a New York Times (28 July 12) op-ed piece called "Is Algebra Necessary". In addition to Mr. Hacker, she also included Ed Nolan, Jacob Vigdor, and Juldy Bolton-Fasman in the discussion and debate. As a counter point, Ms. Bolton-Fasman authored an opposing viewpoint article called In Defense of Algebra and Other Difficult Subjects.
The basic premise of the discussion and debate was whether or not Algebra should be required for American students. As a science teacher, I fully support teaching Algebra to all students. I feel the problem solving skills and understanding of math concepts that students learn through algebraic thinking are critical skills for all Americans. With the recent focus on STEM and looking for ways to bolster our students critical thinking skills, I'm curious to hear other educators' opinions on this subject.
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This is an excellent topic. Math is the language of science. E=mc (squared) is a simple equation that most people have heard if not understood. Starting in grades in middle school we teach that density is mass over volume. This simple mathematical algebraic equation explains so much about the world around us. I couldn't image not having it in school. In fact, I strongly believe that they (algebra and physical science) should be taught together. Teach the math in context with the science to make both more meaningful.
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Every student in my middle school would be screaming, “No, absolutely not,” as an answer to this question. In fact, I probably would have had the same response as my students 30 plus years ago. Over time however, I have found Algebra to be the language of thinking and problem solving. Most of the time, there are more than one way to solve a given problem. I am forced to stop and think, which would be the most efficient method to arrive at the correct answer. I have come to respect Algebra is more like a puzzle than anything else.
As a Science teacher, I agree with Maureen and see its value. What I am not sold on is the fact we are pushing 7th and 8th graders to take Algebra too soon, before they are developmentally ready to really grasp the concepts and their applications. So often they are able to manipulate the formulas or algorithms, arrive at an answer,, but have no idea whether or not the answer is reasonable or what it represents. Granted, there are some students that have an exceptionality for Math and we shouldn’t hold them back. But I am really questioning the rush to get through Algebra and Geometry before ever setting foot in high school.
I am left to wonder how many of those students that have taken Algebra and Geometry as middle school students and then have to remember and apply it for their upper level Science courses in a meaningful manner. I would love to hear from some of the high school teachers whether or not these students have continued to do well in their understanding and application of Algebra in the Science classes.
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You are so on the mark.
Great thread! I felt my stomach turn a little when I saw the title though. I am an algebra 1 teacher and I am a huge supporter of the subject and its contributions to our understandings of science and many other things. Like stated above, algebraic equations helps us to both describe and understand many things in our world. E=mc^2, D=m/v, D=rt are just a few algebraic equations but they can be used in so many different situations. When working on the Rock SciPack, I kept thinking about how the density equation can be used to help identify what the rock was made of. So, my stance on the issue is that ALGEBRA IS ABSOLUTELY NECESSARY! :)
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I think the biggest problem with math (and science) education right now is that we teach them so separately. In Hawaii, 8th grade science is Earth and Space science. And, people at my school really struggle with putting 'real math' into our lessons and labs. Everyone just defaults to graphing. Yes, graphing is math, and it's very important math, but it's not all the math there is in science, and it's certainly not all the math that kids need to know to do Earth and Space science.
So, I had my kids figure out the density of ocean water, and then figure out how much table salt they would need to make a similarly dense solution of salt water. Then, we made more concentrations of salt water to create a water column of 'ocean' water. It was fun, and messy, but the kids could handle that level of algebra (d= mass/volume, with percents thrown in for fun).
Anyways, my point is, I think that we need to be far more explicit with our inclusion of math in science courses. Maybe even teach the math we want before the math teachers for things that aren't too complicated. My team has played with this idea over time and come up with a few notions. I teach scientific notation and attempt to teach the dreaded significant figures. My team has split graphing so that the different content areas teach the graphs they use the most (I do scatter, bar, and line). I also teach differential analysis for unit conversion, and crystalline structure, which helps my math teacher when they cover the different prisms and other solids in math class.
By including more of the equations and graphs and math analysis in my class I'm showing my kids that it really is used everywhere, especially science. And, I'm making the math more fun because they have to know it to be able to do the super-fun lab we're doing in class.
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I am taking a Math methods class for elementary school teachers this semester and I have found that a lot of students are not getting the kind of math background that they need to understand some mathematical concepts. I did not even learn half of the things that I am learning now about math theory (which I should have) and, if I did, it would have made my life so much easier as a child learning math. I feel if they get this instruction that they would be ready to learn algebra and geometry in middle school. They are doing it in other parts of the world (and certain schools in America) so why can't we?
Other things aside, I do agree that math should be more integrated in the science curriculum because they do go hand and hand. For example, chemistry and physics are highly math based and, without math background, it would be impossible to understand what is going on when trying to solve problems. If students are introduced more to how intertwined these two subjects are in the earlier grades, they might have more confidence when tackling harder problems in the upper grades, because they are more familiar with the process.
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I totally agree! If you build certain algebra concepts early on, they can really master it at the end.
I believe algebraic thinking is fundamental in science. I teach 5th grade math and science but I am very conscientious of what students are learning math in K-4 before they get to me, and what they are expected to know from grades 6-12. Our K-2 teachers are using a new math curriculum which emphasizes algebraic thinking. Students in grade 1 are using circles and squares to represent numbers in finding sums of numbers. Even at this early age, algebraic thinking is used. The whole idea of finding an unknown value is very important. Finding unknowns is relates to what we are doing when we are trying to identify variables in science. This is, perhaps, the "thinking" part that we need to foster and I believe that it's through algebraic thinking that we can help students make the connection to the world around us in science.
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I found an excellent resource that is free and on the Internet. It is called Mathematics and Science Classrooms: Building a Community of Learners:It’s Just Good Teaching This 52 page document is produced by Northwest Regional Educational Laboratory. It is not just a document that talks about the need to do both, it actually provides ways to accomplish this.
The pdf file can be found at the following location:
In an 8th grade STEM class I am always looking for ways to get them to listen with interest so I developed a series of short presentations. The big idea is "Math makes life easier." The presentations explain how the specific math lessons have an impact on a career. I started with a chef and discussed the distributive property. I used recipes so kids could understand why the concept was important when cooking for 200. I moved to car design and manufacturing discussing how the Porche manufacturers use the distributive property as well as how they can predict their costs using variable expressions. I am a work-in-progress but with some fun 2 minute films and pictures, I have noticed a change in their discussions about math. Food for thought.
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Allow me to play devil's advocate. Is it really necessary for *all* students? If the student plans to attend college, absolutely, Algebra is a necessary evil.
But what if the student has no plans to go to college? (gasp!) What if he or she plans to go into the family business or is only interested in a vocational track? What then? Do we force them through classes that they not only have no interest in, but no real need for in their life? I'm thinking of a member of my own family right now, so perhaps I have a slightly different perspective.
We can argue that education in and of itself is the end goal, and I completely agree. To a point. I also argue that we should value all members and vocations within our society, whether they require advanced math or not.
Looking forward to reading your comments,
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The problem is not the Algebra, the problem is how math is taught. I have seen a large range of ability students engage in algebraic thought. But, if we continue to follow textbooks and teach our students one way, then we will continue with the same results. The practice of counting off points without providing reasons or feedback to students leaves them confused. I have sat with countless students to hear them say, "I can't do math". I will watch the student (young and old, sometimes older than I am) do the problem and see that they can do it. They only make a small mistake. But years of red marks and no feedback just leaves them feeling as if they cannot do it.
My suggestion is to do the tough thing, admit that some previous methods of teaching math are not effective. Let's not spend time discussing what concepts need to be taught, but instead discuss methods of teaching math that are effective. How about we provide students good feedback in ALL math classes that provides the student a clearer picture of what they are doing right (usually quite a bit) and what they are doing wrong.
Thinking skills are what is important. Math really emphasizes good thinking skills that are applicable everywhere, if taught correctly. I say, as science teachers, we go an talk to the math teachers and start figuring out ways that we can work together to effectively teach all students.
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@Kendra and @Susan. I think both of you have hit the nail on the head. Math, in general, is taught as a bunch of facts and trivia. They're problems to be solved, with some anecdotal references to how they're used in real life, but there isn't any actual application of the math. There's no connection to real life by having the students just do math for math's sake in a math class. It becomes pure trivia. We lose most of our kids, especially the struggling students, because they don't see how the a^2 + b^2 = c^2 relates to the wold around them. Word problems and streams of problems don't teach kids to appreciate math or use math outside of class. That's what the 'non college track' kids need. Heck, that's what all of our kids need. Even the Gifted kids who are going to go to college have a hard time applying math
I think one of the things that I went through in math that contributed to my disconnect with math was the fact that I was never really taught the logic behind the concepts. I was just taught how to do it and these rules only applied because they just simply worked. Now that I am learning the logic behind the math in my class, I understand it a whole lot better, which helps me connect to why we get the answers we do in math.
In response to what Kendra said, yes, I believe that even students that want to go to a trade school or inherit their family business should learn mathematical thinking. It really helps someone think through a problem. If taught properly, math could even boost a student's confidence because they were able to solve the problem. This is especially true if a student is able to work through a difficult problem. It helps improve their problem solving skills in and outside the context of math. This problem solving is transferred into the science classroom when students are asked to think critically about what is being presented to them. It might not have the math behind it in this case, but it surely requires the same through process which is to solve the task at hand.
This web seminar being offered tomorrow and I believe several other times throughout the year certainly speaks to the importance of algebra....check it out --students need to understand how to apply the variables in a formula (learning to think abstractly and less concretely) and then how to solve for unknown or desired factors. Although the Pythagorean Theorem may appear in geometry prior to algebra, math really may not be separated into discrete entities so that students take one and not the other. I believe cognitive research has linked algebra to those higher order thinking skills that all science teachers aim for; as applications, not as memorized statements.
Pythagorean Theorem: Exploring Space Through Math--Lunar Rover, October 24, 2012
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*nod* math is so vital to science, but it's even more vital to just plain thinking. I've heard that a lot of law schools like having former math majors enter their ranks (or at least, they like students who were good at math) because they had really excelled at critical thinking and thinking logically. So, that kind of thinking is really powerful to teach our kids. Plus, it's how we set up a budget, build a house, plan a wedding, cook food, etc. Sure, doing a matrix might be a bit outside of the norm, but the basic concepts of algebra (abstract concepts, solving for unknown quantities, etc) those are pretty ingrained in real life.
Wow. No one ever asked me whether I really needed to master the mundane and arcane structure of the English language! For some reason, we all assume we need to understand prepositions and participles, even though most of us will never need to write professionally. Most of us also had to take courses in fine arts and music - it is part of the process of becoming an educated human! No, I didn't like English - especially not poetry and thick books of fiction written by dead white guys, but we never really questioned the need to learn the language.
Personally, I love math. I consider mathematics to be a language. Just as we learn to express ourselves with words, we can express certain ideas with mathematics much more effectively and concisely than with words. Imagine expressing the quantitative relationships found in chemistry or even the natural environment without the use of algebra and geometry!
I think what we fail at is introducing mathematical concepts with any rigor until our students are in high school. Instead of simple cause-and-effect, purely qualitative, observation-driven science curriculum, how about more integration of math in the elementary grades. Amazingly, fourth and fifth graders did a great job of "measuring" the distance to the "moon" by using ratios and intuitively understand much more than we often think they are capable of. (I know, it's a dangling participle). By protecting them from math we make it much more difficult to introduce it later.
The other thing that I think is critical is for us to limit the access to calculators in elementary and middle schools. I know this is radical, and there are some places where they are useful, students who are able to "speak math" as natives before they use a "translator" (calculator) tend to understand the concepts much better than students who are calculator-dependent. Imagine going to a foreign country and pulling out an electronic translator to have a conversation!
Just as in learning a language, there are things I will never use in algebra and geometry, but we learn them to understand the structnre and foundations of the discipline. Otherwise, we would read "Dick and Jane" books, and speak English in a manner equivalent to the Spanish taught in a first-year class. Saying we really don't need to understand that much algebra and geometry is a little like that. Algebra and geometry are very basic, fist steps beyond addition, subtraction, multiplication, and division. Even artists I know need to understand more math than that!
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This is very dynamic discussion! Like many, I have trouble bridging the use of math (algebra) in my robotics class. It seems to me that students are use to compartmentalized lessons and they tend not to use their skills outside of the math classroom. So it feels like that a whole lesson plan must be developed and implemented to cover a specific type of math; algebra, graphing, analysis, or geometry, but you know for sure that the students are already exposed to this topics because the evidence is everywhere in the math class. Maybe the difficulty is students are applying thier math to different context and not use to applied math, therefore tend to "forget" their math.
Any and all ideas for successfully bridging math and technology will be greatly appreciated.
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While all of us await results from the election, we might sign up for one or both of these webinars to fuel our side of the equation about the necessity of algebra
Preparing for NGSS: Using Mathematics and Computational Thinking, November 6, 2012
Algebraic Equations: Calculator Controlled Robots, November 7, 2012
Both look interesting!
Personally I am prepared to support the statement that critical thinking grows deeper and sharper with algebraic manipulations of variables and with explaining situations through mathematical statements. And just think, during international Olympiads, students easily converse with one another via mathematical equations and graphical analysis even if they collectively speak 20-30 languages. Mathematics, after all, is the language of science.
I totally agree! Most math is taught as these discrete nuggets in a single room and there's no bleed-over into other classes. Some of this is because of content. I really have a hard time finding an authentic and purposeful place for math in a language arts class. Poems about numbers seem puerile to me; and, while people can read Alice in Wonderland for its mathematical problems, I don't think it justifies including it in the curriculum. Most of the other subjects, however, can integrate math seamlessly and effectively.
PE and Health classes can graph growth, track nutrition, calculate Calories, and determine stats for the unit they're working on. The goal could even be to create a 'dream team' a la Fantasy Football. Art can analyze the importance of scale and proportion and really get into the geometry of art. Music can discuss beats per minute, the difference between octaves, what 'sharp' and 'flat' mean mathematically, and how those all contribute to different styles of music. As for History/Social Studies, well the recent election proved that math is a vital part of truly understanding the socio-economic political issues our country faces. Algebra is there in the world, we just don't think of it as 'math' because it's either fun, or so imbedded in the other content that it doesn't seem like a new or different thing. It's our job as educators to point out these areas where they bleed.
Angelo, thank you for reminding us that math is used across the curriculum and is fundamental to all learning! It's a great post:}
I think this is a great discussion! First, I feel that I need to qualify myself for this discussion as an AP science teacher and remedial math teacher (on the same day!). I feel that Algebra is necessary for some/most learners, as they will move on to develop concepts that involve variables and abstract concepts. For my weak students who aspire to enter technician-type careers, I feel that Algebra is not *necessary* and definitely should not be forced. Math is necessary. Concrete operational skills are necessary. Abstract computation and estimation is not necessary. Our learners need to feel uplifted and supported. I truthfully have difficulty explaining to my remedial students when they will need to factor quadratic equations in their life after this class, if not to help their children when they are in high school. But, they will need to calculate tax on goods purchased, and tip in a restaurant. Calculators make that easier, not possible.
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I feel Algebra is one of the most important math classes middle/high school students take. Other than basic math, I feel like it is the math I've used the most as an adult. The ability to problem solve is critical.
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Here is a pdf summarizing the research done on the importance of algebraic 'thinking' as a means of developing critical thinking skills as well as establishing logical thought processes at all levels of learning. The research goes beyond what a traditionalist connotes when hearing the word algebra and the research upholds how vital sequential thinking is. It ladders learning across the curriculum and supports abstract reasoning.
Here is the site for the article:
And I will attach it below for interested readers.
Research and Implications of Learning Algebra (External Website)
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