Response to "A Linguistic and Narrative View of Word Problems in Mathematics Education"

In Susan’s article titled “A Linguistic and Narrative View of Word Problems in Mathematics Education”, she looks at the pragmatic structure of word problems to try to find the “unspoken assumptions underlying its use and nature as a medium of instruction”.  She writes how word problems are typically structured using three components: the set-up component to establish the characters and location of the story, an information component that lists the needed information to solve the problem, and lastly, the question component.  This part was very interesting to me because this is how I actually make up word problems, and yet if someone were to ask me to describe the process I take in making word problems I probably would not describe it this way.  I would say that I use real-life scenarios that ask students to use the mathematics we just learned to problem solve.

This brings me to the next interesting part from Susan’s article about looking at word problems using linguistic and metalinguistic verb tense.  While I don’t quite understand what these terms mean (there are definitions of them within the article), an example she gave really brought home to me the point about word problems not really making sense at times.  The example is “A truck leaves town at 10:00am travelling at 90km/h.  A car leaves town at 11:00am travelling at 110km/h in the same direction as the truck.  At about what time will the car pass the truck?”  She goes on to explain how “a truck leaves” and “a car leaves” are linguistic present tense and “the car will pass the truck” is linguistic future tense.  She explains how the tenses used in word problems are often self-contradictory and how this takes away from the truth-value in word problems, which is the last thing I will discuss.

Susan gives a word problem and then rewords it with the information in parentheses added.  The word problem is this: Every year (but it has never happened), Stella (there is no Stella) rents a craft table at a local fun fair (which does not exist).  She has a deal for anyone who buys more than one sweater (we know this to be false).  She reduces the price of each additional sweater (and there are no sweaters) … The problem continues on in this same way.  She makes note how the truth value of the word problem doesn’t actually change when this extra information is added in. 

I personally have never really struggled with solving word problems, but this article brought to my attention how flawed word problems are.  It is no wonder people struggle with solving word problems.  Their tenses are contradictory and there is no truth in their statements.  This made me question the purpose of word problems.  I understand that we use them to try to make the math seem more realistic and to show students where they can use the learned material in everyday life, but if the word problems are bogus, are we really benefiting our students?

Response to "Psychology and Mathematics Education"

The article I read this week titled “Psychology and Mathematics Education” discusses the difference between cognitive psychology and the psychology of mathematics education.  The author says that Piaget’s idea of psychology does not match up with the psychology of math education because it was not interested in the effects of instruction on the development of mathematical reasoning and because he believed that intellectual development is essentially a logical one.  He states, “The "psychology of mathematics education" is not produced by applying psychology to mathematics education. Rather, it is achieved by identifying genuine psychological problems in mathematical activities” and proceeding from there.

This idea is very true about different curriculums and/or concepts in general.  For example, there have been some articles we have read in our education programs about a teacher in a math classroom performing a certain task that sounds great, but applying it to our specific classroom might not turn out in the same way it did for the teacher in the article.  Just like what might work for one student might not work for another student in terms of learning style or organization or amount of practice problems to be completed or…the list could go on forever.  In fact the author makes note that psychology may be very helpful in math education, but only as a general theoretical framework.  This concept applies to Beth’s articles we read last week about color-blindness, the voice of the textbook, and revoicing students’ words or ideas.  I think all of her articles were very insightful, but at the same time a bit one-sided.  I think that any concept in life may be related to another concept or provide a “general” description, but will never be the exact same thing.  Just how all textbooks do not have the same, unfriendly kind of language, not all of psychology can be applied to each subject area and work perfectly.

Response to "Strong is the Silence: Challenging Interlocking Systems of Privilege and Oppression in Mathematics Teacher Education"

The article I read titled, “Strong is the Silence: Challenging Interlocking Systems of

Privilege and Oppression in Mathematics Teacher Education” states that “it is time to consider math teacher educators’ (MTE) knowledge and practice—their preparation and their research agendas, frameworks, approaches, and strategies for action toward equity in relation to the interlocking systems of privilege and oppression within which they (we) operate.”  The authors propose that MTEs should do this by 1.) looking at diverse schools and relatively homogeneous teaching populations, 2.) focusing also on mathematics teacher educators to create systems of equitable work, and 3.) understanding oppression and privilege as interlocking systems.

This article mentioned how schools in the United States are 90% White and that 43% of K-12 students are of color.  It said that White teachers state that they claim a color-blindness approach.  This bit of information made me really question myself.  If I were to answer honestly, I would claim that I too take the color-blindness approach.  But what is the alternative to this?  Is it to say that we see color or that we acknowledge that we have a diverse classroom?  As a white female, I do not know the alternative route to take in terms of a color-blindness approach or noncolor-blindness approach. 

The article also stated “it is well-documented that teachers hold lower expectations for students of color and those from poor families than they do for White middle class students”.  I do not believe that I am a teacher that has lower expectations for students of color and from poor families, but is this too something that I am unaware of doing?  I felt like the article was trying to say that White teachers are unaware of doing this, and yet it happens.  So am I one of the teachers who fall into this category?  And how do you fix the problem of holding lower expectations for different groups of students if you are unaware of doing it?

Response to "The Reasonable Ineffectiveness of Research in Mathematics Education"

In the opening paragraph, Kilpatrick says that the title of his article is a play on the title of a different article called "The Unreasonable Effectiveness of Mathematics".  I have not read "The Unreasonable Effectiveness of Mathematics", but I am assuming Kilpatrick chose to name his article about research in math education in a similar way because the effectiveness of mathematics is not necessarily because the research in mathematics education in effective itself.

The article was about how research in math education is ineffective for several reasons.  The ways to improve research in math education are to create more of a community that includes practicing teachers, a theoretical construct for viewing the work, and the ability to recognize the limits and complexities of the researchers' domain. 

The article mentioned how using research to solve a math problem is like a technology problem whereas using research to solve a math education problem is quite the opposite since it now becomes about dealing with people.  This differentiation between humans versus technologies is so interesting to me when thinking of teaching math or of just the school system in general.  There are so many things going on in a mathematics classroom when considering just the teacher, but add the students in there and the school environment, and the picture becomes even more complex.  It is nice to read research articles on math education because they can be very insightful, but what may work for one teacher in a certain school may not even come close to working for a different teacher in even the same school. 

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