Patricia Dickenson

Felton, CA

Interests: 21st century learning,...

  • Posted 4 Years ago
  • 2.3k

Reform in Mathematics Teaching

Mathematics instruction changes as a reflection of what society deems to be valuable in terms of the skills and knowledge needed to be successful in the workplace.  The Progressive movement of the 1920's was widely influenced by John Dewey's ideas that schooling should be  largely directed toward children's experiences and interests. Although this has good intent and justification,  in 1940's tracking in mathematics emerged as means to steer students toward mathematics courses.  As a result of tracking there was a sharp decline in the percentage of high school students taking algebra-from 57% in 1905 to about 25% in the late 1940's and early 1950s (Jones & Coxford, 1970). 

Delivery of instruction is also contingent upon the reaction of perceived shortcomings of previous movements. The "Back to Basics" (1970's)  approach which focuses upon a skill and drill approach to instruction, was in response to the failings of "New Math" (1950's)  which focused on advanced mathematics  and was often developed by mathematicians who focused on higher level mathematics.

Currently we see the focus of mathematics on higher order thinking and 21st century skills  with a focus on conceptual understanding more so than procedural. Content knowledge expectations are clarified by grade level standards and there is a spiriling of curriculum so that students have content knowledge that is in greater depth than breath.  As schools and districts move toward the Common Core standards, instruction must change too ensure the emphasis is on what students understand more so than what they can do.  And as we enter another pardigm shift in mathematics it is unknown what shortcomings await and what new challenges will emerge.

According to Philipp, (2011) "the challenge is no longer how to get mathematics into students, but instead how to get students into mathematics".  How will you address this challenge and meet the expectations of the newest reform in mathematics?

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Donoho_Donoho

29 Sep 12, 03:43 PM

It will be interesting to see how the Common Core impacts instruction and if students' performance improves with this latest shift in instruction.
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Marcus_Humphrey

29 Sep 12, 03:20 PM

This history of mathematics is quite interesting. I did not realize there was that much of a shift of mathematics in American culture. I would be very interested to find out how this sort of shift happened in other countries as well. I have done some research into English shifting some common practices (The Great Vowel Shift). This was well written and I enjoyed finding out about this topic.

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Joe_Warren

29 Sep 12, 03:16 PM

this is good to read, especially since I am thinking about taking the math CSET!
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Holly_Sinclair

01 Aug 12, 05:00 PM

Each math reform I believe has good intentions, it is finding which one actually works best that is the hard part. Because the reforms are changing so frequently it is hard to decifer if the new approach is or isn't working based on the reform or if it is do to other factors. It is hard to tell whether a group of students is suceeding based on the teachers ability to teach, that particular group of students, the functionality of the school, or the actual reform. My personal belief is that we need a combination of approaches, but the emphasis and order of the approaches is crucial. I believe that you need to get students "into" math before you get math "into" students. As teachers we need to be able to connect the abstract subject of math to the students daily and personal lives. All of math is embedded in our personal lives yet many students are under the assumption that it is completely abstact and disconnected. If we can get them to have an understanding and grounding of where the formulas come from and how they are connected then I think some form of repitition and memorization can be useful. It is important for students to be fluent in the building blocks of mathematics, but these building blocks are useless without understanding. I am a firm believer that we understanding, but it is also crucial for them to have some fluency in the basic procedures as well. With CCP I do believe we are getting closer to melding procedual with understanding in mathematics.

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Chris_Nguyen

01 Aug 12, 02:05 PM

I think the most effective way to address this challenge and mee the expectations of the newest reform in mathematics is by making the concept and lesson relatable to the students and their everyday's lives. Also, since we have technology as a resource, I think we should incorporate in into the lesson and engage the students.

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Zach_Clynne

01 Aug 12, 04:17 AM

I think that one of the most important things teachers can do to engage students is to provide them with activities that present mathematics in a new or novel way.  We need to find ways to bring their prior knowledge and experiences into the classroom and use that as a foundation upon which to teach them mathematics.  Instead of convincing students to learn a subject they think they hate, we should be telling them about all the amazing things they could be doing with their new understanding of the world.  Teachers need to remind students, and everyone really, that mathematics is everywhere and in everything we do.  Enthusiasm helps too.

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Zach_Clynne

01 Aug 12, 04:08 AM

I think that one of the most important things teachers can do to engage students is to provide them with activities that present mathematics in a new or novel way.  We need to find ways to bring their prior knowledge and experiences into the classroom and use that as a foundation upon which to teach them mathematics.  Instead of convincing students to learn a subject they think they hate, we should be telling them about all the amazing things they could be doing with their new understanding of the world.  Teachers need to remind students, and everyone really, that mathematics is everywhere and in everything we do.  Enthusiasm helps too.

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Zach_Clynne

01 Aug 12, 04:02 AM

I think that one of the most important things teachers can do to engage students is to provide them with activities that present mathematics in a new or noval way.  We need to find ways to bring their prior knowledge and experiences into the classroom and use that as a foundation upon which to teach them mathematics.  Instead of convincing students to learn a subject they think they hate, we should be telling them about all the amazing things they could be doing with their new understanding of the world.  Teachers need to remind students, and everyone really, that mathematics is everywhere and in everything we do.  Enthusiasm helps too.

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Stephen_Chen

01 Aug 12, 12:45 AM

Since we are focusing more on students achieving a better conceptual understanding on the content, teachers should be willing to try out new ways to teach the students. For example, teachers should try to give out hands-on activities to the students, so that they can have fun with the activity and learn math at the same time. Also, the students should have time to work with their peers, so that they can help each other learn. In this case, the class will not be so dry because the class will not  just be lectures, but the class will have hands-on activities, group work, and etc. That way, the students are more likely to be interested in mathematics and willing to learn mathematics.


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Chris_Nguyen

01 Aug 12, 02:07 PM

I think it is a good idea to use hand-on activities to engage the students and enhance their brain activity to inspire them to discovery and understand mathematical concepts. But I think that we should use other methods, such as powerpoint presentations and game activity.
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Mariah_Vega

31 Jul 12, 10:09 PM

The newest reform in mathematics expects teachers to use students' experiences and inclinations to their benefit. As a teacher I would try to relate new mathematical concepts to the everyday lives of the students. I would have to give them opportunities to "meaningfully communicate about [math] and form connections between important mathematical concepts and ideas." Students should be active in their learning and be giving the opportunity to express their thought process. This reminds me of the "Stand and Deliver" clip Dr. Dickenson showed in class. The class worked as a collective group, adding and sharing their own methods of solving a problem. The teacher even tried to make the word problem relatable by including "gigolo girlfriends." The teacher was able to provide an enironment that was funny, open and non-judgemental that brought many students to participate. Granted this was a movie, but I believe the teacher has the most power in setting the mood for the class and that type of classroom environment can be attainable. If I want to bore my students I'll talk in a monotone voice and read straight from the book. As a teacher I would never want to do that. So, what I could do to keep the class excited and energetic is bring in outside materials, video clips, maybe even sound effects just to change up the routine. I'd want my classroom environment to be silly and relatable to students so that they discover the importance of learning math. Getting "students into mathematics," in terms of getting them excited about it, may take a lot of creativity and enthusiasm on the my part, but I believe it can be done.
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Erin_Caldwell1

31 Jul 12, 09:50 PM

I think one of the easiest ways to address this statement is to try and garner excitement and enthusiam in your students for the material you are teaching. If you design your classes to be repetetive and routine, or entirely procedural, your students are going to get bored, disinterested and lose interest in math. I think it is important to not stick to one method of teaching for the entire year. Change it up every now and then. This will keep things exciting and can generate interest in students. If as a teacher you can find different ways of approaching a particular lesson, students are less likely to get disengaged and are given an opportunity to gain interest in the subject through a different approach. (This is particularly nice if they weren't too thrilled about a previous way it was taught.) I think this idea of multiple approaches also addresses the newer ideas of teaching for conceptual understanding rather than procedural fluency.

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Mariah_Vega

31 Jul 12, 10:13 PM

I definitely agree that changing up the routine would be best for the students and probably for the teacher (teaching the same way every day would be a boring job). In order to grab the attention of multiple students it only makes sense to teach with multiple approaches in mind.
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Holly_Sinclair

01 Aug 12, 05:07 PM

Multiple approaches to math is crucial to create understanding and enthusiasm across a broad spectrum of learners. I think as teacher we need to present concepts and ideas in 2 or more ways so that they can make connections and also so that students can see that their is creativity to math. Many students believe that in math their is only one right way and one right answer, but in my experience you can solve almost any problem with any number of methods, there is infinite room for creativity for your personal approach to solving a problem.
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Cera_Wong

31 Jul 12, 09:13 PM

The new mathematics reform seems to suggest that as Teachers, we need to start thinking about mathematics differently and also strengthen our own understanding.  We need to see ourselves as perpetual learners and take risks by trying new activities in the classroom not done before.

I agree with John Dewey's emphasis on the need to implement learning activities that can relate to students' interests and experiences.  Instead of working on algorirthmic exercises, students need to be able to participate in activities where they have the authority to explore a concept and find their own solutions.  They should also be able to see how other students find solutions so that they are able to see different representations of a concept.

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Erin_Caldwell1

31 Jul 12, 09:53 PM

I agree that trying new things is really important in teaching, especially in math. It is so easy for a math teacher to just make all of their lessons about just teaching a formula, having students memorize it, then quizzing students to see if the memorized it. Activities are also a great way to make math more fun! I think that is a good way to get more students interested in math by having them see math in a different viewpoint then a bunch of numbers and formulas
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Zach_Clynne

01 Aug 12, 04:06 AM

Group activities also give students an opportunity to use peer resources. These activities can be used to help struggling students understand the concepts of a lesson when individual instruction from the teacher is not available for all the students. Collaboration can also promote diversity of thought as students consider and critique each others ideas.
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Cera_Wong

31 Jul 12, 09:11 PM

The new mathematics reform seems to suggest that as Teachers, we need to start thinking about mathematics differently and also strengthen our own understanding.  We need to see ourselves as perpetual learners and take risks by trying new activities in the classroom not done before.

I agree with John Dewey's emphasis on the need to implement learning activities that can relate to students' interests and experiences.  Students need to be able to participate in activities where they have the authority to explore a concept and find their own solutions.  They should also be able to see how other students find solutions so that they are able to see different representations of a concept.

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Jacki_Jung

30 Jul 12, 05:28 AM

During my undergrad, I was fortunate enough to take a class that focused on diversity and equity in the classroom and emphasized improving access to mathematics. I was introduced to this idea of a “pedagogy of questioning,” which challenges teachers to allow an open dialogue to form. Mathematics is thus learned under the context that each student is a valued member of the classroom, and that in order to participate in the world, we must first understand it. 

In this way students are not only engaged in the material, because it pertains to them and their lived experiences, they are also required to support their claims based on the mathematical concepts at work. This requires students to not only understand the material, but to be able to analyze situations, and appropriately apply these mathematical concepts. A pedagogy of questioning thus follows the newest reform in mathematics, while also empowering students to understand and interpret the world around them, and then be moved to action by participating in a mathematical dialogue. 

Getting students “into mathematics” isn’t difficult, as they already have an innate drive to understand the world in which they live. We are simply charged with the task of relating these lived experiences to a mathematics curriculum and challenging our students to also think critically about the ways in which we can view our world through the lens of mathematics. This can be a challenge in and of itself as our student populations grow more diverse, yet as teachers we are responsible to meet all of the needs of our students, including those relating to their cultural and linguistic backgrounds. To be honest, that is the real challenge I am sure I will face as I try to meet the expectations of my students…

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Cera_Wong

31 Jul 12, 09:21 PM

I agree with you on this topic, Jacki. I think it is important for student to explore concepts so that they are able to analyze situations and apply mathematical concepts. I also agree that one of the toughest challenges will be trying to accommodate the diverse students in the classroom.
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Lane_Bacchi

29 Jul 12, 10:13 PM

The newest reform in mathematics means that there is another paradigm shift in mathematics. However, this is not necessarily a bad thing. Especially in a subject like mathematics when there are so many ways to teach a single lesson it is important to know what has worked in the past and learn from our mistakes. As we continue to move forward into this new reform of mathematics we intend to give the greatest opportunity for students to learn. As we move forward it is crucial that teachers understand the ideas of new reform and how they can interest students in mathematics.

We need to continue to make the classroom enviroment one which is comfortable and one where ideas from all students are welcome. This new reform focuses more on conceptual understanding rather than that so much of procedural fluency.  Because of this it will be crucial to allow students to devlop understanding on math topics by allowing time for them to create their own algorithms for solving certain types of problems. This way they are not doing 25 algebra problems but instead understanding the problems at hand more deeply.

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Stephen_Chen

01 Aug 12, 12:56 AM

Yes, I agree that students need to develop conceptual understanding in order to achieve a better understanding in the content. Just procedural fluency is not enough in a classroom because students need to have conceptual understanding in the material in order to learn better.
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Nichole_Caiocca

29 Jul 12, 01:55 AM

It seems that through the material we have examined thus far that many of the legal initiatives that have been put into place to make education better actually had unintended negative consequences. If we truly believe that “mathematics instruction changes as a reflection of what society deems to be valuable in terms of the skills and knowledge needed to be successful in the workplace (reform in mathematics teaching),” then I am not sure that we really need to teach the average student more than how to access and use a calculator or math program. Although oversimplified and probably taken too literally, I think that only having a successful workforce is not the ultimate goal; our school system should aspire to achieve successful members of society. Therefore, I find it crucial that the members of our society have a deeper understanding of mathematics. We must thus appeal to the other discourses we have been examining. We need to stimulate students’ curiosity and therefore allow them to learn through providing a safe classroom forum. In the past it seems that mathematics education has been seen as a rigid and sequential system but there must be a way to steer away from this way of thinking. My own mathematical success stemmed from a more liberal program in which many hands on activities and visuals were used to try and establish a deeper understanding. I think that the more ways you can depict something the better chances you have of getting through to more students. The new challenge we will face is trying to be inventive and new while still falling within the constraints of the new standards in teaching.
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Benjamin_Pang

29 Jul 12, 10:11 PM

I do agree that mathematics should steer away from a systemic sequential standard. The thing that i do not know about is how to do so because in order to further someone's mathematical knowledge, they must have a decent understanding of previous mathematics courses. For example, in order to understand geometry, that student needs have an understanding for algebra.
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Jacki_Jung

30 Jul 12, 05:40 AM

Nichole, I really enjoy what you wrote. Often times I would be frustrated while working in a classroom because the kids really did have a point, "Why are we learning how to do this if we can just plug it into the calculator?" My response was always, "Trust me, you need this." It's just so hard because we have been teaching it for soooo long this way. We now must switch over from preparing students for the work force, and shift to preparing them for the world. This leads in to the second part of your post about curiosity, a classroom forum, and a deep understanding through activities, visuals and multiple representations. The world to me is one, big, multiple representation of all kinds of math. And to the students, the world is intriguing, something to be talked about, and ultimately understood. I think we strive to understand the world we live in (and NOT a world where Suzy and Tim are going to the store to buy milk at $3.50 plus tax) and as teachers should challenge our students to think critically about this world through the lens of mathematics.
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Benjamin_Pang

27 Jul 12, 09:33 PM

It is funny to know that throughout the 20th century, mathematical educators influenced education based off Dewey's ideas. Then they switched math education to a tracking system. Next, educators moved onto the idea of "New Math." Then, we shifted to an era of "Back to Basics." Finally, it seems that we are shifting back to the 1920s movement of looking at education from Dewey's perspective. United states education has gone through a lot of reforms and revisions. We have been trying out a lot of different stuff to see what works and what does not. What i am suggesting is that we should reflect upon our educational history and look for mistakes. The next step is to learn from these mistakes and create reforms that will not repeat history's mistakes.
        I understand that there are a lot of ideas out there for reform and views of thinking about the measures that improve our educational system. My second suggestion is to ask that we stick to one kind of reform. We need to be consistent and work together to create a better educational system for our future generation.

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Nichole_Caiocca

29 Jul 12, 01:54 AM

It seems that through the material we have examined thus far that many of the legal initiatives that have been put into place to make education better actually had unintended negative consequences. If we truly believe that “mathematics instruction changes as a reflection of what society deems to be valuable in terms of the skills and knowledge needed to be successful in the workplace (reform in mathematics teaching),” then I am not sure that we really need to teach the average student more than how to access and use a calculator or math program. Although oversimplified and probably taken too literally, I think that only having a successful workforce is not the ultimate goal; our school system should aspire to achieve successful members of society. Therefore, I find it crucial that the members of our society have a deeper understanding of mathematics. We must thus appeal to the other discourses we have been examining. We need to stimulate students’ curiosity and therefore allow them to learn through providing a safe classroom forum. In the past it seems that mathematics education has been seen as a rigid and sequential system but there must be a way to steer away from this way of thinking. My own mathematical success stemmed from a more liberal program in which many hands on activities and visuals were used to try and establish a deeper understanding. I think that the more ways you can depict something the better chances you have of getting through to more students. The new challenge we will face is trying to be inventive and new while still falling within the constraints of the new standards in teaching.
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Lane_Bacchi

29 Jul 12, 09:06 PM

Ben I most definitely agree with the points you have brought up. The United States has gone through a tremendous amount of reforms and changes over the past 100 years. I believe the United States has seen its mistakes and is learning from them which can be seen by the amount of reforms and changes to the educational system recently. I also agree that consistency and the ability for all schools to work together can create a better educational system for our future students.
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Nichole_Caiocca

29 Jul 12, 10:34 PM

It is amazing to me that although positive change and progress were the goal of math education reform, that in actuality math education basically came full circle from the descriptions of 1890 and then 1974 (The paradigm shift in mathematical education 10). Although all of this change and reform occurred, what portion of it was positive and what happened to the students whose education was based on testing these various failing systems? I agree that there now needs to be some sort of consistent, at least framework that teachers operate under so that we have a better educational system for the future.
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