Dear TNLI Fellows:

Believe it or not, December is right around the corner.  While we will still continue with our current TNLI national listserv conversation through November, below please find the reading information & link for you to prepare in advance of our December reading—to be hosted by our Sacramento (CA) affiliate, and moderated by Sacramento Fellow Diane Diamond.

December TNLI National Listserv Reading.  Rethinking Mathematics:  Race, retrenchment, & the reform of school mathematics (pp. 31-40), by William F. Tate.  Rethinking Schools Online.  A direct link to this article is available at:  www.rethinkingschools.org/publication/math/RM_race.shtml.   

Thanks so much—and we look forward to this December conversation, led by Diane and the Sacramento TNLI affiliate!

Ellen, Peter, and Jenn

Season's Greetings from Sacramento. My name is Diane Diamond and I am this
month's moderator for what we hope will be a lively discussion about a
provocative article, Rethinking Mathematics by William F. Tate. Dr. Tate is the
Chair of the Department of Education and the Edward Mallinckrodt Distinguished
University Professor in Arts and Sciences at Washington University in St. Louis.
He is also President-Elect of the American Educational Research Association. His research
and practice have focused on the political and social dimensions of mathematics
education and science education, as well as urban education.

Let me begin by offering some highlights and end by prompts which we hope will
inspire you to share your thoughts and experiences.

Tate begins with the premise that "Traditionally schools have provided
African-American students with few opportunities to connect mathematics to their
lives and experiences." Because the foundations of math education, mathematics
and psychology, emphasize objectivity and neutrality, little has been done to
consider cultural appropriateness in the teaching of math. However Tate feels
that "connecting the pedagogy of mathematics to the lived realities of African
American students is essential to creating equitable condition in mathematics
education."

With little effort made to build upon the realities of the African-American
student, assessments have shown growth in the acquisition of basic computational
skills but none in more advanced levels of mathematical reasoning. Currently
many advocates of reform advance the cause of better treatment for African
Americans in math classes because it is in this country's economic self-interest
to do so. Arguements to connect the experiences of African-American students (an
individual human right) lead Tate to ask the following questions? "Should school
districts support mathematics teaching built on the experiences and lives of
African American students? Should the focus of mathematics teaching be to
prepare African-American students to participate in the national economy or in
our democracy?'

Tate advocates that teachers take a "centric prespective" that would have
students' math problems and responses linked directly to their life experiences.
Tate proceeds to develop his thesis by asking if the question of what agenda is
being maximized by a given example of mathematizing should be the foundation of
classrooms discussions. He holds that all students should learn to analyze and
critique mathematical situations to understand whose agenda is being served.

I hope this has whetted your appetite to read on and share your opinion.

Two prompts to help initiate the discussion are:
1) Should mathematics instruction be built on children's life experience?
If you believe it should, how can you provide this instruction for all the
ethnic groupings in your classroom? Is this appropriate for some groups and not
others? What does the instruction look like?

2) How do African-American students in your locus of control respond to the
current methods of teaching math? What are your feelings about Tate's thoughts
about the role math should play in preparing students to participate in a
democracy?

Let me thank eveyone in advance for their consideration of the material and
participating in this discussion.

* December TNLI National Listserv Reading. Rethinking Mathematics: Race,
retrenchment, & the reform of school mathematics (pp. 31-40), by William F.
Tate. Rethinking Schools Online. A direct link to this article is available
at: www.rethinkingschools.org/publication/math/RM_race.shtml.

*Please note: if you are interested in the references for this article, look at
the menu on the right hand side of your computer screen when you access the
article. There are additional resources listed for Math Education; under the
button for the Tate article, you will see a sub-button for "resources" -- these
are the article references.

Diane Diamond
Sacramento
12/1/06

a few years ago while I was supervising student teachers I noticed an
African American fourth grader sitting at a desk in the hall after
school doing a multiplication worksheet. The following dialogue
ensued:
Me: You're doing some good work there.
He: My teacher says I need to learn these.
Me: Yes, it's important. Did she tell you why?
He: To get a good grade?
Me: That's true, but can you think of any other reason why it could
help you in your life outside school?
He: (thinking long and hard) So I can teach my kids so they'll get good grades?
Me: (laughing) That's a great reason. but isn't there aqnything else
you could use times tables for?
He: (curiously) I don't know.
Me: How about if you need to buy more than one of something and you
have to figure out how much it costs? And figuring out taxes.
He: Oh yeah!
He smiled as he went back to his work.

In my fifth grade class I took a check from my account, made it out
for $1,000,000 and copied it for each my students (deleting the bank
information, of course). I brought in catalogues, newspapers, and
magazines and put them at a center. Each child had a spending log and
they had to figure out tax. They found out that 1 mil won't buy a lot
of real estate in San Francisco but it will cover the essentials quite
nicely. Kids went joyously to the math center to spend. In that same
class we looked at salaries for entry level jobs in S.F. versus living
expenses. Then we looked at entry level salaries for college
graduates. The light went on.

Time and time again I've seen students soak up learning when teachers
have provided a connection to their own lives.

Susan Gold
San Francisco
12/5/06

I am sorry to announce that most of us will never use trigonometry again in our lives. Nor will we solve equations or find the log of 248. And I'm beginning to suspect that we will never have to prove that two triangles are congruent. But the fact that what we once learned will never pass our way again should not diminish what we learned nor it eloquence.

I loved math. (Still do)  I taught it for 35 years in a Brooklyn High School. I loved it when it was based in reality and I loved it when for most kids its was a total abstraction. My job, I thought, was to teach specific concepts and at the same time to pass my love of the subject onto my students. "Math is special",  I would tell them. "You can debate forever the true nature of Hamlet or the causes of the Civil War, but in math you can come up with the exact right answer and not only that. You can check it."

I remember teaching and invariably I would see that hand go up that was not interested in answering the question, but out of frustration wanted to know, "How this was going to help them in later life?" I would tell this person that in all honesty it probably wasn't, but that I happened to know that to get into heaven you had to pass a test and 20% of that test was math. And I also knew for certain that the test went up to trig.

I like reality, but I often grow tired of ridiculous attempts to link math to the "real" world. I remember in particular one attempt to teach that multiplying a negative times a negative is a positive by relating it to running a film upsidedown backwards. It was silly. Sometimes math is just math. There is nothing more magical in math than when a student reaches an "Aha!" moment and the light of understanding goes on. It's a special moment shared between student and teacher and nothing to do with the outside world.

There is a beauty mathematics and sometimes its enough for that beauty to just exist in your room. I always felt comfortable just linking what my students know to what they didn't know. It was my job to build the right bridge that would bring my entire class from one side to the other. At the end of the day I just wanted my students to leave my class loving math. For me that was enough.

And finally one word on reality. When all is said and done and every concept of math is finally linked to the "real" world, it should be remembered. Sometimes reality sucks.

Mark Grashow
Brooklyn, NY
12/6/06

I agree with Mark.  Sometimes Math is just Math.  But there has been another concept that I put out there to students and that in learning math they learn how to think a problem through.  So many times in life, we run into a situation that doesn’t have an easily identifiable answer.  We have to think through the answer, math and science teaches us to do that.  It’s that analytic, logical side that brings clarity to situations and problems. 

Catherine Young
Delaware
12/6/06

I have no argument with Mark's view that math is a fabulously constructed system and beautiful in and of itself. However, as a middle school teacher I see my sixth graders in the throes of transitioning from concrete to abstract thinking. Some have already made the leap (maybe they were born that way), many haven't. I am lucky enough to see some of them again in my eighth grade class and note their progress. I hope we don't throw out the Piaget baby with the cultural bathwater. In elementary school most students are not ready for abstraction, but far too many classes I have observed give them just that, as my story illustrated. I want my students to go to high school math appreciating the role math plays in their lives and what it can do for them. When they get to the age of abstraction I want them to know how to apply math when they need to. By forcing them into abstracting too early they are turned off to numbers and never arrive at that sense of appreciation. I think that's the issue Tate was addressing. And believe me, students ask the same application question about history!

Susan Gold
San Francisco
12/6/06

Well that was a very interesting article! I am still processing what I think. On the one hand I get where the author is coming from, providing culturally appropriate instruction. I support that. But, on the other hand I think some of his examples are insulting. Can you figure out what 2 humdums plus 2 humdums is? It is four humdums ...even though I don't know what that is. The example of not being able to do a simple adding problem in second grade because you eat a different kind of pie at Thanksgiving is suspect. His first grade teacher did not do the job of teaching him the basic skills to solve an addition problem no matter what you are adding. On the other hand the example of using bus fare was a fantastic example of how eurocentrism dominates...how smart and undervalued the kids explanation of the problem! I heard another example a long time ago about how a teacher was marking an EL child as incorrect on the speaking part of an EL exam because he answered that he had rice for breakfast. The teacher assumed that he did not understand the questions, when really, he DID have rice for breakfast, but that was not the norm in the teacher's culture. I think this is a really important conversation. Here are some questions.

How do we make our instruction culturally revlent within the confines of our day to day instruction/curriculum/standards/expectations?
What about Latino students and Hmong students? If, as the author supports, Afrcian Amercian students need their own math curriculum, then what about the other groups of students? Is it possible to meet all these needs simultaneously? I ask this because in my school we do not have homogeneous classrooms. How do teachers become culturally proficient, to the level of being able to modify curriculum, in all the cultures represented in their classroom?  


Respectfully submitted,
Alison Merlo
Sacramento, TNLI
12/7/06

A question I struggle with is the thought that each time I make material culturally relevant for one group, am I excluding another?  In addition, another question haunts me.  In making a decision that a student needs culturally relevant material for a math lesson, am I being elitist?  If someone tried to teach me fractions by using the example of a cutting up a pastrami sandwich, I'm not sure how comfortable I would be.
Diane Diamond
Sacramento
12/8/06

In order to make "experiences" relevant. I try to "create" the experience in class. Whether a website, film, story, or experiment – if we do it and talk about it in class, then those who are present, can answer the questions. It isn't always possible, but it is one reason I
enjoy teaching the IMP math curriculum.

Shelley Klein
Santa Maria High School
Santa Maria, CA
12/8/06

I think that whatever we do, there will always be someone that is left out, culturally, socio-economically, or otherwise.  In my opinion, as long as we hit the same standards in various ways and in many different modalities with not one, but several contexts (3-4 different stories or types of writing in examining a certain theme, for example) we can hope to reach as many students as we can. 

Of course, I speak from the standpoint of teaching language arts and in that venue, finding multiple ways of connecting students may be less of a struggle than with math.  Math, however, has more universal application than say "Antigone" and many students will tune themselves in to learn how the numbers they have learned as grade schoolers can apply to making buildings or going to the moon.  In this aspect of universality, I think math has a cross-cultural construct.  However, how you reach the students to apply it in a universal way may be difficult.  I know that word problems are a fundamental part of math and that, depending on the vocabulary and syntax used, changes how a student may connect with the problem.  In this case, I think vocabulary lessons in math would benefit students by connecting them to the text. 
James Leu
12/11/06

I have enjoyed reading the many responses to the article, particularly since I have taught math at both the pre-school and high school levels. I agree with the idea that when math (or any subject) is linked with a student's life, the student may become more motivated/engaged in the subject matter.  Particularly in the early years, it makes sense to relate mathematics to play and their everyday life.  However, I also agree with the idea that not all mathematics that is taught needs to be tied to "real life."   I liked the parallel that was brought up between mathematics and the arts, and the need for learning skills and discipline to attain greater proficiency in the subject.  Creating an artificial "real life" situation will not engage students.  The article refers to an example of a child that is not engaged in the math problem about pie.  Perhaps the child was not interested in the "real life" problem about pie, or maybe the child had not found success in solving previous problems.  A major factor in a child being successful in a subject is a child's previous success and their prior knowledge. 

The article did make me think about mathematics, race, gender, ethnicity, economic status, etc.
While these things need to thought about when curricula and standards are developed, a major link between these things is language and literacy.  There is an interesting book - Radical Equations by Robert P. Moses about this topic.  The book ties together civil rights, language, and mathematics; also, the Algebra Project curriculum is based on this link between teaching language/literacy and mathematical language and literacy.  If you have never heard of the Algebra Project or Robert Moses - check it out!
www.algebra.org

From the webpage:
__,_.F_,_

The Algebra Project seeks to build the demand for math literacy in local sites across the country. Its leadership views this focus as a continuation of the Civil Rights struggle in which transforming math education in our schools is as urgent in today’s world as was winning the right to vote in the Jim Crow South in the early 60s. Its goal is to address the lack of economic access that face children from communities of poor people and people of color. It aims at bringing about a sea change in the attitude of teachers and young people toward math learning and math achievement. One example of this is happening today at Jackson, Mississippi’s Lanier High School where large numbers of students are taking trigonometry and introductory engineering.
 
This is the context in which we do our work:

• According to the Urban Institute, 50% of black ninth graders, 49% of Native Americans and 47% of Latinos/as do not graduate in four years.
• In some poor urban and rural schools drop out rates approach 80%.
• According to the National Assessment of Education Progress, 43% of black 12th graders and 58% of Latinos/as are testing at “below basic.”

 
- Has anyone in the group been a part of the Algebra Project? 

Tara Redican
New York City
12/12/06