Thinking about
Middle Grades Math


A MiddleWeb Listserv conversation

Also see: Literacy, Mathematics and "Connected Math"

Melba's question about math journals started a new MiddleWeb discussion string that drew out ideas of how to implement writing in math class -- and evolved into a deeper conversation that included successful strategies to prepare all students for algebra and the ongoing debate about girls and math.

Hey all, I usually don't write for help, but I need some input. My school's focus this year has been literacy. We all journal in our classes and I have just about run out of ideas for math related journal topics. I have done the "how-to" paragraphs all year long, the "how is this applicable in the real world", and topics of that nature. Can anyone give me some interesting ones, or just new ideas even if they are not interesting, please? I teach 6th grade math and Algebra preparatory (6th grade also).

Melba

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Brenda shared an assignment that requires students to reflect on their mathematical past.

Melba:

Here is a math writing assignment that I created for the beginning of the year but I think it could be very effective at the end of the year too. I call it "My Life in Math Class" (I sometimes call it "My Mathematical Past"). It's really a student autobiography pertaining to math. Students share a positive math memory, a negative math memory and several strategies that help them problem solve. It has been a real eye-opener for me at the beginning of the year- it equips me with meaningful background knowledge on each student before our year gets going.

When I introduce the assignment I always share some of my personal mathematical past. Students seem to be quite interested. If this assignment was given at the end of the year, it would serve as a fine reflective piece about their learning that year. It could even be included in the report card.

For what its worth, here is my assignment:
http://www.occdsb.on.ca/~proj1615/mathclass.htm

Brenda

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Deb suggested using children's literature alongside math.

Have you tried some silly math writing or poetry? I saw a childrens' book this year about "Sir Cumference" and it was a riot. Your students might like trying to write riddles or puns to show off their knowledge. Just a thought...

Deb

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Deb commented on Brenda's assignment and wondered how the assignment might affect at risk students.

Brenda's math autobiography assignment sounds great! I really like the way it blends math and writing with some real metacognition. I'm sure that the modeling she said she does about her own experiences is critical in this assignment.

I'm wondering how a student who hasn't experienced much success would respond. I had some students who really disliked math, had terrible anxiety about it etc.

What strategies might you use with a student like the one I just described?

Deb

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Kate shared various math journal prompts and how they can challenge one's thinking.

I have kept a math journal, both as a teacher and student. One of the types of entries I have found hardest (both scenarios) is to speculate on the foundation of an algorithm or to develop one. Simple example of a difficult algorithm, when we divide by a fraction do we invert and multiply? Are there any concrete examples of this type of division (divide a pizza into 1/2 equal sections?)? Is the answer a circumference of a circle formula?

Develop a formula for how much you would have to save from your allowance for something that costs $x if you save $y for z weeks. (Use real numbers for 6th, maybe variables for alg. prep)

Look at 11 squared. 111 squared. 1111 squared. Find a formula.

How many ways can you position non-attacking kings on a 3 x 3 chessboard? 4 x
4?

Use Mathcounts materials for ideas. Also unsolved problems in discrete math or number theory. My students loved perfect numbers.

Kate

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Chris pointed out the value of helping students recognize how math skills connect to everyday activities.

Melba: Maybe you've already done this, but how about working it in the opposite direction? Identify everyday activities that people do to carry on in their lives and have the students identify math skills needed to accomplish them. I believe this might be a valid way to focus on what's really "essential learning" as we try to unbloat the curriculum.

Chris

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Crystal took an alternative approach when using math journals.

Melba,

I used "explain what's wrong" approach in my journals this year.

Crystal

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Susie recommended using literature as a model from which to write math stories.

I had the privilege of having a wonderful, creative math teacher on my team for several years. She used such things as a "Math Autobiography" that sounds similar to Brenda's idea. I also think you could read "The Math Curse" by Scieszka and Smith to your students, and they could write their own "math curse". (By the way, by the end of the book, the main character realizes that math is more of a blessing than a curse!) I use it with my seventh graders and have them write "The Science Curse".

Susie

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Larry took this discussion in a different direction when he asked about strategies to ensure success for all students entering algebra classes.

Our state standards call for all children to be in algebra in the eighth grade. This requirement is reinforced with the fact that State assessments in mathematics next year will require that eighth grade students have an algebra program since that is what the assessment as based on our state standards is following. This is a good discussion in itself, however, that is not my question at this point.

Since all children must be prepared to take an algebra class in grade 8, and our standards lead them to that point, what kinds of teaching strategies should we be giving to kids who are not comparatively as high functioning in their arithmetic skills so that they can succeed in this 8th grade requirement.

As a former math teacher, I have my point of view, but I am looking for input that either will support my beliefs or refute them and make me think through directions that our district needs to take.

Larry

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Marsha revealed how students can meet success in pre-algebra concepts by following a well- thought out progression of skills.

Dear Larry,

I have just about finished my first year of teaching math (many years teaching science) in a brand new curriculum to our district. I would not have believed what I actually saw with my own two eyes regarding algebra. At the beginning of the year, we STRUGGLED to add, subtract, multiply and divide integers. I really couldn't see how they would ever progress to doing simple algebra.

Well, I just finished grading the end of the unit test about 15 minutes ago. They knocked me dead. The gradual progression of this curriculum gets them there without them knowing it. First by looking a comparisons, finding unit rates, building thousands (not really, but it seems like it) of rate tables; they gradually see how to use patterns to make those tables and want a shorthand way to do it --- that's algebra!

What they perceived as impossible at the beginning of the intro algebra book was "simple" by the end. And I must tell you that our sixth graders did the book with the same results. (Next year this book will only be taught in sixth grade, but this is part of a transition plan.)

Larry asked: "Since all children must be prepared to take an algebra class in grade 8, and our standards lead them to that point, what kinds of teaching strategies should we be giving to kids who are not comparatively as high functioning in their arithmetic skills so that they can succeed in this 8th grade requirement."

Over and over and over again I have reinforced the reading part. Understanding the problem before you begin. I use a visual aid of a giant magnet to suck out all the info. (Corny, but the message comes across). Most of my struggling students will tell you that it's usually a reading problem, not a math problem. Knowing what's holding you back is a big part of the battle. My kids ALWAYS have access to the graphing calculator. No one has to grind everything by hand. I do encourage them to try and do mental math and certainly to check the reasonableness of their answers.

Last, but certainly not least, I offer tutoring during lunch on Tuesday and Thursday. About 8-10 of my strugglers come in to eat and work on math. I also have about 3 -5 faithful early morning students that I tutor. I preview problems, work the hardest homework problems with them, and give notes for them to review. The extra help is essential.

I also modify in great detail the tests. Often, I color code the problems. Especially where they have a multi step question where the results of one part must be transferred to another part---I color code it so the transfer is easier and they can concentrate on the math. I have also been known to break down the problem into component steps while I enlarge the font size. Sounds dumb, but bigger font with numbered steps helps them enough to get over the hump.

Marsha Ratzel

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Marsha continued by discussing how mental models, and scaffolding help students meet their potential in her math class.

My biggest thing is that I need more help to do this. Our parents don't understand this method because it wasn't the way we learned. Constructivist math is not the way we learned and it makes them extremely uncomfortable to leave their child in the lurch. That happens frequently at the beginning of a new book until they get enough experience under their belt.

Now my classes just say, "OH Mrs. Ratzel, this is the beginning of the book and we're suppose to be confused. Don't worry. We'll know everything before the end." If nothing else, they are a confident bunch. But the students have learned they'll get it if they hang in there and hypothesize, test, reformulate their thinking, hypothesize, retest, and so on.

I send home parent helppages and lots of supporting voicemail with hints on how to help their child with that night's homework. I also keep up an e-board site with copies of all class notes, the working class glossary, and digital pictures of the overheads that we used to work through the problems in class that day. A whole lot of work and I wish I had an assistant to help me.

The district had once a month meetings for everyone in the grade level to come to. But the nitty gritty stuff wasn't discussed much because in the first year of implementation there's too much other stuff to talk about. I'm hoping we can work collaboratively to build some of these supporting resources---"jigsaw" if you will because it's inefficient for each teacher to do what I've done alone this year.

I hope that helps. Again, I'm a new math teacher, and I've really approached math from the scientific method perspective. I know they can learn algebra if the incremental steps are small enough and there's enough practice. I've seen it with my own two eyes---they not only can do it, but they understand the whys behind it. Wow!!! I wish I'd had that chance as a middle-schooler.

Marsha

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Larry asked for further explanation concerning Marsha's math program.

Marsha,

Thank you for the response. The more information that I gain, the better able to help schools make a comfortable change I can be.

I wish that every teacher had your dedication and tried to break down our profession into the science of teaching. We need to all learn from the best practices of others.

How will your school be preparing kids for algebra in the future? Are you the only person who has taken on this challenge in such a positive way in your school? Do you have peers to share and interact positively with? Why did you decide to teach with this approach, and how much of your teaching fit the textbook?

Are you a California teacher?

Thanks for sharing, that is the best part of this listserv.

Larry

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Marsha addressed each one of Larry's questions.

The new math curriculum is k-8 this year and extending all the way into 10th grade next year. So everyone has the tools and hopefully the desire to implement it.

The kids should have finished Algebra I by the end of 8th grade once we are fully implemented. They will go into Geometry as freshmen. We are also hoping that the emphasis on writing will improve the district's AP scores in later years. Students do very well now on the AP tests, but could do better with an improved ability to communicate in writing.

The Reflection pieces of this curriculum really force insightful thinking---especially when the students know they will have to do and redo until they reach a point of mastery with explaining what they've learned. As they've looked back in their portfolios, they are amazed at what they've learned. And how much they remember.

Are you the only person who has taken on this challenge in such a positive way in your school?

No. There are many different perspectives, but my building has been mostly positive (we are one out of seven middle schools). Some buildings hate it. Some teachers teach the "old" way with the new curriculum. But I think the majority of teachers are trying to adopt most of the new methods.

Do you have peers to share and interact positively with?

Yes. Every month, the district coordinating teacher for math holds meetings for k-8 teachers by grade level. We talk about stuff for the better part of 2 hours. In my building, the district has contracted with a teacher leader to have a sub once a month. She comes into our rooms to demo teach or watch us teach or co-teach. Whatever we want, she tries to do to help. Also, my principal required a weekly grade level math meeting. We tried to stick together in where we were in the lessons, although I know the three of us approached it very differently. I really appreciated that because I had no idea how to pace this material and I relied on the 20-year plus vet that teaches across the hall for pacing.

Why did you decide to teach with this approach, and how much of your teaching fit the textbook?

I didn't know what to do as a math teacher. So I just taught math as if it were science. Questions and real life problems were the basis for all the problems---so a problem solving perspective was most appropriate. We have had wonderful class discussions about temperature rising/falling, comparing population and sample data, profit/loss statements, credit card bills, how to pay tips, calculate tax rates, etc. I really did the book pretty cookbook like. I wouldn't presume to know better lessons, better scope and sequence, better problem sets. It was just the style of teaching and support that was mine. So everything I did fits into the text.

Are you a California teacher?

No. I'm from Kansas.

I think the sharing is the best part, too. I'm glad we are having a conversation that I can add to. I'm anxious to see what others post.

Marsha

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Larry discussed whether arithmetic skills are key to higher level thinking skills.

Each post gets sent to the people in my district that are most responsible for implementing the new State requirements in math. I love math education, I have my masters in it, but I am awed by what excellent teachers do and what they can do for any child. Many of the teachers don't believe that kids can learn without arithmetic skills. I know that those are necessary, but arithmetic skills don't have to keep kids from learning higher-level thinking.

I appreciate your responses very much. This last response I am sending to my middle school principals.

Sincerely,
Larry

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Deb asked Marsha for some examples:

Marsha,

This program sounds great! What series are you using? Also could you share an example of a problem where you switched fonts to help the kids process the steps?

Thanks,
Deb

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And Mary Anne asked about the textbook Marsha used in her class.

Marsha -- What book are you using? We are using the Discovering Algebra book with our seventh and eighth graders and the teachers agree that the kids are really getting a lot out of it.

Mary Anne

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Marsha provided information about her classroom resources:

We use the Connected Math Program. Specifically we have used Accentuate the Negative (integers), Samples and Populations, What Do You Expect (probability), Comparing and Scaling (ratios, rates), Variables and Patterns (algebra) and Filling and Wrapping (geometry) in the 7th grade. There are lots more books that the 6th and 8th grade use. We share and trade between grade levels.

Marsha

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Marsha walked MiddleWeb readers through the individual steps she used when approaching a problem with a group of students.

Dear Deb,
When I enlarge the font, I meant literally that I used the copy machine. All the tests and problems are from the book. Then I just use a highlighter in different colors to show how the pieces fall together. As best I can with email here's a sample from the Unit Test.
Dee bought a compact disc player with the money he earned working during his vacation. He checked CD costs at two stores.

Taylor's Department Store sells CDs for $15.49. each.

Buyer's Warehouse has a $25.00 membership fee, then each CD costs $12.00.

Using this information you have to make a table and graph that shows the cost of purchasing several different quantities of CDs at each store. You want to figure out what is the best deal in town so you can make your money go as far as possible and get as many CDs as possible. The membership fee is something you pay to the store only one time at the beginning.

(The question the test asked was "Make a Table and a graph that show the cost of purchasing several different quantities of CDs at each store.")
Step 1: Make a table. What will you compare to see where the best deal is?

Step 2: You have to pick two things---what two things would you want to know?

Step 3: Use a T-chart for your table. Start at 0 CDs. Continue until you think you have enough data from which to make your decision. What other piece of information would you want to know?

Step 4: Create a graph using the two things you used in your table. Think about how you can use these for your labels on each axis.

Step 5: Which one is the dependent variable?

Step 6: Which one is the independent variable?

Step 7: How do these variables tie into the Title?

I think you probably have the idea now. I just try to breakdown the question into steps, use highlighting to help them track and expand information to stimulate thinking. I know not all the colors are the same, but I'm having terrible mouse problems this morning. And remember I use a good old fashion highlighter with the copy machine. Cut and paste at its finest. I learned all these techniques from our learning center teachers over the years. They are wonderful and so clever.

Marsha

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Principal Betsy Burch shared how tracking students into an ability-level groups as early as Grade 7 has become more of a reality in middle school and wondered how this may affect the mathematical "late bloomer".

As we prepare for this move to include all students in Algebra, the following courses will be in place at the middle school level beginning in the 2001-02 school year: 1:

-Pre-Algebra I, which will use a 6th grade standards-based math text
-Pre-Algebra II, which will use a 7th grade standards-based math text
-Algebra I, which will use a combination of CPM I and an 8th grade math standards-based text.

Our highest achieving 7th graders will be placed in Pre-Alg II and will begin the Alg. I course during the 4th quarter of their 7th grade year; our lower achieving 7th will be placed in Pre-Alg. I; our highest achieving 8th will be placed in Alg. I, and the lower achieving 8th will be in Pre-Alg. II. Each year we are expected to reduce the number of Pre-Alg. I courses for 7th graders to meet the state standard of all 7th graders taking the Pre-Alg. II course and all 8th in Alg. I.

Our high schools are phasing out all math courses except Pre-Alg, Alg. I, etc. No more "Math for Living", etc. Therefore, a student could take 3 years of Pre-Alg. at this point (2 in middle school and one in high school). Our school board adopted a policy that requires that all high school students not only take the Alg. I course but pass it as part of their high school grad. requirements.

One of the biggest concerns is the obvious tracking of students into ability level groups, which this approach requires. So, my math teachers are very concerned that the math levels which students achieve in 6th grade appear at this point to be the determinant of the math track on which they are placed at the beginning of 7th. My math teachers are planning to observe all of their students' progress carefully throughout the year and make class changes between the levels if students appear to need a different level. The other big question is one of access to the highest levels of math for all students - we have not solved this yet!

We plan to continue to offer before and after-school tutoring in math to support those students for whom these requirements are a real challenge. I will keep you all posted about this math program as we progress next year!

On a personal note, when I look back at my own math achievement at the middle school level, I am concerned about this approach. I was a late-bloomer in math and would never have been allowed to take the higher-level math classes in high school given this program. I am very interested in each of your personal math experiences and the effect such a program would have had on your own math education.

Betsy

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LeeAnn contributed her perspective on ability-level grouping.

That was the one thing that stood out to me in your post. We started the Connected Math this year and while I am not a math teacher, I absolutely love the groupings I get now for my lang. arts classes because we are not ability tracking for math. I went through middle school in a program like yours and I was in the high group so I loved it. I was grouped with my friends, but I also had the idealistic notion that all students were like my friends and me. Whew, student teaching and my first year was certainly eye opening!

LeeAnn

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The topic of streaming and "late bloomers" caused Brenda (a Canadian teacher) to reflect on her own mathematical learning.

In response to Betty's question about how we (as math students) would have fared in a streaming approach:
I have mixed feelings about streaming in Middle School as well. As a student, I struggled in math from Grade 4 up. Each year it got worse.

On one hand, I know I would have benefited from being grouped in a way that addressed the root problems found (or not found...) in my mathematical understanding. Since the root issues didn't get sorted out, I was destined to continue in the cycle of math confusion. I did work quite hard up until Grade 11 and then fell apart in Grade 12 (mostly because I chose to stop working as hard).

On the other hand, if I had been buttonholed in Grade 7 as a struggling math student, I'm not sure I would have gotten to university and where I am now. One of the skills that I bring to the math classroom (as a teacher- yes, I do teach math!) is my understanding about what trips students up as they learn mathematical concepts. I understand, anticipate and plan for what confuses kids and often share the challenges I experienced as a math student with my students (kind of like a reformed alcoholic does...).

I wonder if being streamed permanently at this age gives the student a lasting perception of what type of learner they are (high, low). Does this cause them to settle for less in terms of future academic pursuits? Although I did view myself as mathematically challenged I still was determined to plow ahead in hopes that next year would be different. My grade 10 math teacher promised to give me a 50% grade (I think I had a 45%) if I promised not to go onto Grade 11 math ( he wanted me to go into an easier Grade 11 program in math). In the end it made me more determined to work my butt off to prove I could do it so I did register for the Grade 11 class anyway. I worked really hard and finished Math 11 with a 65%. I was thrilled.

One question I have is:

Once a students is moved into a certain stream (low, for example), can they redeem themselves or is it in cement? As Betty said, this has serious implications for the late bloomer. I would hate to have my future sealed at the age of 13!

Mathematically functional and teaching:
Brenda

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The topic of "late bloomers" prompted Ellen to share her own experiences as a math student.

Betsy,

I, too, was a "late-bloomer in math," and this approach hurt me tremendously. In seventh grade we took an assessment at the beginning of the year, and in the middle of the assessment I was pulled to have my ID picture taken. Because of that, I was unable to finish the test, yet I missed being placed in pre-algebra by only two points! Though my parents protested and pointed out the fact that I probably would have tested high enough if I had not been pulled out of class, the decision was final.

So, what happened? For years I believed I was a poor math student, though every achievement test I ever took said otherwise. Furthermore, once you are tracked, there are some courses, like Calculus, which are just not available to you. I took the minimum number of math courses to get the advanced diploma at my high school and filled my schedule with extra literature courses instead.

I actually enjoy math a lot despite being a LA teacher. When I was working as a permanent sub at a high school, I actually taught pre-calculus though I had never had the class myself...I was working about a chapter ahead of the kids, but I taught it to myself by reading the textbook and pestering the math dept. chair.

Being tracked had a huge effect on my attitude towards math...I'm not a huge fan.

Ellen

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Michelle Pedigo noted some research pertaining to ability grouping in math.

Ability grouping in math groups everyone. Also, the only research I know about grouping in math says that it is effective with stretching the highest group only, so we only have one ability grouped math per team...one class of Advanced math. The rest are heterogeneously grouped for the rest of the day.

Michelle

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Keith explored the notion that people who are experts don't always make the best teachers.

I think we CAN do a tremendous disservice to our field when we INSIST that only people with endorsements can teach content, or college majors in the field. Brenda's admission to her "struggling" math past points out that sometimes people who are "experts" don't often make the best teachers. The fact that a great teacher understands the difficulties and pitfalls (and how to work through them) will strengthen the learning, not the fact that the teacher is content proficient. (I know there are logic holes in this, but bear with me?)

In the world of professional sports do we see many great players become great coaches? Those of us who are not experts can often use our own difficulties to help us break down and better instruct content. Our notion of good teachers still has at its pinnacle the concept that the teacher must rate as an expert on content knowledge. Extreme content knowledge might be needed for some of the higher end science/math, BUT in our state bright and motivated students can go to community colleges for these subjects.

I sat on a hiring committee a couple years ago and the principal would only interview those with "outstanding" GPA (translated to "4.0"). Anyone who flunked a class on a transcript could not get in the door for an interview. His logic - "We want our teachers to show the highest academic quality." So we interviewed a bunch of straight "A" (for Anal retentive?) candidates that were a total waste of time.

This administrator hired three different, 4.0 GPA math teachers for the same assignment in three straight years. Two of them were miserable failures. The third is still around, but the kids don't go to him for help, because "he can't explain things so I can understand it." I sometimes wonder how many of our best teachers failed a subject or two along the way and learned from it.

Tracking, streaming, high math, low math, manipulatives, textbooks ­p; they all have their supporters. The only thing that will have a great effect on learning in math or any other subject is a great teacher. Traditionally knowledge of content is the most focused and prized indicator of a teacher. It's way over-rated in my book. Great teaching doesn't come from knowing restrictive appositives, how to figure the volume of a sphere, or the Pythagorean theorem. It comes from having a creative mind and a caring heart. And last time I checked they don't put much emphasis on this aspect when training (or evaluating?) teachers.

Keith

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Keith's experience on the hiring committee that would only consider teachers with high GPAs struck a nerve with Nancy.

There you have it! How can a teacher relate to struggling students if he/she never had to struggle with a subject? One of the main things that makes a teacher effective is their ability to identify when a student is stuck and then show him/her how to get un-stuck.

Cris Tovani (I Read It but I Don't Get It) explained it so well in the area of reading comprehension, but it applies to all subject areas. We learn through our own struggles how to help others with the same difficulties.

Nancy Long

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Nancy asked readers to consider the impact gender issues may have in a math classroom.

Has anyone else noticed that girls, especially, often suffer from math anxiety starting at about the time fractions are introduced? There is certainly a good body of research on the topic, but many of us (like Brenda) could write about it from our own experience.

The GESA (Gender-Ethnic Expectations, Student Achievement) training from back in the 80s pinpoints the fact that our math teachers treated many times us differently. While male students were challenged and pushed to keep trying until they got it right, we female students were often patted on the head and told, "Nice try." We may have been subtly programmed to think that girls weren't supposed to be good at math.

I consider this circumstance of my education a blessing, for while I was never the brightest penny in my higher math classes, it has given me a profound understanding of what struggling math students are going through. In my science classes I take every opportunity to practice math skills and demonstrate math "tricks" to help students overcome their fear or mental block in math. I occasionally tutor the ones who are not doing well in math class after school for a few minutes just to get them over some sticking point, like exponential notation or such.

It does the students good to see that people other than math teachers understand and use math, and if you can tell them honestly that you know how they feel because you were just as confused when you were their age, it gives them hope that they will catch on too.

Nancy

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Sharing your own struggles as a learner helps math teachers connect with their students. Hearing a teacher say, "If I did it, you can too" will only encourage students to try and work harder. Melba's posting supported this belief.

I agree with Nancy, students do appreciate personal stories from teachers. I always tell my students the following story: I never understood word problems. Sixth grade was the worst for me. Since I was promoted from first to second grade, I figured I missed the lessons on clue words. In elementary, junior high, high school, and even college algebra after numerous hours of tutoring and repetitious "review" all of my teachers would ALWAYS say, "Don't worry, there will only be 2 on the test." Indeed, there were always only 2 word problems on the tests.

Once I tell my students this story, the ongoing joke is "there will only be 2 on the test". Students can relate to these types of stories. I always tell them personal stories. They like to hear them. Of course, they are also forced to listen to my Grandma stories.

Melba

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Avis asked for some direction from teachers who are familiar with Connected Math.

It sounds like our 6th grade is going to use Connected Math. Can any of the Grade 6 teachers on this list share which ones they are using in Connected Math?

-Avis

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Laurie responded to Avis' query.

Hi Avis,
Although I am a special education math teacher, another Special Education colleague and I have adopted the CMP Math Program for our learning-disabled 6th graders. We have only done CMP this year and have covered:

-Bits & Pieces I
-Shapes and Designs
-Prime Time

We did not cover How Likely Is It, which our regular ed. colleagues did; we will definitely cover it next year and feel it is important because there are a lot of probability questions on the MCAS, our state's standardized test for all Gr. 6 students. (We teach in Massachusetts).

Laurie

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Naomi provided further information regarding the "Connected Math" program.

Generally Our 6th grade starts with "Data About Us". It is a great way for the kids to get to know each other. Make sure you have a bunch of post-its on hand. We even created a huge graph of all the 6th graders in the hall.

We utilize CMP with our inclusion class (12 spec ed, 18 general ed,) and since they have been together for 3 years, 6,7 &8, they have actually moved ahead of any other 8th grade class.

We never get to "Bits & Pieces II" in 6th grade, but use it at the beginning of 7th. It is basically impossible to do all the grades books in one year.

Naomi

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Deb told MiddleWeb readers about her mathematical past.

I was fine with fractions. My difficulties began in high school. I went to an all-girls high school and had only female teachers, but the expectation that you should just soak up the info without any concrete application was in full force.

Because I had always been a "good" student nobody really took my difficulty seriously. I was patted on the head and my confusion and shame deepened. I skipped math in 11th grade, taking two languages instead. I finally convinced my teachers to put me in track two as a senior, but my first teacher was awful and the damage was done. As an adult I returned to a Community College where I had a wonderful teacher, who made everything concrete and I breezed through the class. However, I still get pangs, go blank etc. when people try to race through math acting like "anybody with half a brain would know these answers."

My problems definitely helped me to understand my students as a math teacher, but I did always worry that they might benefit from having someone who had more confidence in their math ability.

Deb

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Michelle explained how perceptions about math teaching methods can interfere with teaching and learning.

My perception is that a lot of math teachers bring this attitude to their students, and many times, to other teachers. "Well, you don't understand how to teach math" was conveyed to me often as their principal, because I had been a lang. arts teacher, or "math is different" could often be heard.

With persistence, though, I think math folks can understand that, in math, concrete examples work best, as well as utilizing the multiple intelligences to teach it, like in all other subjects!

Michelle

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Micheala introduced the idea that brain development may have a great deal to do with the success rate of students concerning their understanding of mathematical concepts.

My past as a student of math was mixed. I always placed in the advanced classes in middle school (jr.
high at the time), but my performance was mediocre at best. I just didn't 'get' it. I had a mix of excellent and poor teachers so I can't put the blame for my lack of understanding on anyone but myself. I struggled with advanced math (pre-algebra, algebra, and geometry) until 10th grade.

Something happened as I entered 10th grade. I understood what the teacher was talking about. I could suddenly take the awful theorems that I had painstakingly memorized the previous 3 years and apply them in a logical manner. Was it the teacher? I don't think so. She taught in the same manner as most of my previous teachers.

Now years later as an educator, I am reading about brain development and its impact on education. I think that this has a great deal to do with my understanding of math. I only regret that I lost so much information with my years of math confusion.

Michaela

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Robbyn's experience supported the belief that ones' ability to learn mathematical concepts may have more to do with developmental issues than ability.

My mathematical past was much like many of yours. I struggled for years to get through my math classes. I can remember sitting for hours with my father pouring over word problems that I just didn't "get". As a freshman, I took Algebra and was given (given, not earned) a "D", only because the teacher knew I had worked hard and I just couldn't grasp the concepts. As a sophomore, I took Geometry. I was able to get through that due to (this is embarrassing but honest) cheating. I was so thankful to be finished with math. I only needed 2 math credits to graduate. I swore I would never take another math class, EVER! For some reason or another, I decided I needed to try again and as a senior took Algebra II. I aced it, even without cheating!

My only explanation is something in my brain clicked and it finally began to make sense. This is why I have always put stock in the theory of brain development. And guess what type of teacher I became, that's right...a math teacher!

I truly love math and am so glad I gave it a second chance. My students love to hear about how I struggled and how I still struggle with memorizing the 6, 7 and 8 multiplication facts (we had this discussion earlier on the list). I want my students to do their very best, but I also want them to understand if they don't "get it" now, don't give up. I am living proof that a "D" in math as a young person is not an indicator of math skills for life.

Robbyn

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Keith offered some observations about teaching and learning math.

I'm not a math teacher (OK you may have guessed this). BUT, in keeping an eye on this thread, it seems that most (all) of the people posting on struggling math pasts are female. How many of us EVER had a woman for a math teacher and what is the mix of male/female math teachers in secondary?

From my experience men dominate this field in education. I think perhaps a number of reasons for this (as noted in threads) - brain development, 4.0 teachers (esp. men?), stereotypes...

Of all the disciplines, I'm concerned about math the most especially at middle level. Seems we can often do more harm than good in the interest of "more (and faster) is better"?

Keith

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Bill explored the idea of "stereotyping" in math.

Answering Keith's question about how many women math teachers we had:

From 7th-12th grade, I had women teachers five out of the six years, plus my mom (a physics teacher) was my at-home tutor. This shows the importance of role models for boys as well as girls: when I first realized some people thought boys were inherently better at math than girls, I was simply perplexed that anyone could conceive of such a notion since it went completely against my own experiences.

Additionally, I grew up in Amherst, Massachusetts, a town which very deliberately fought gender stereotyping. Indeed, I first learned of the existence of gender prejudice by inference: if so many people were telling me girls were just as capable as boys, were we supposed to have been thinking boys were more capable? I chose to remain as gender neutral in my thinking as possible, but it is fair warning that we walk a fine line, for boys as well as girls, when we proclaim a certain point of view.

When I was working at an all-girls school, I found that within a general context of positive woman role models and positive messages about women, those who truly understood girls' learning styles and enabled the girls to bring about their own success carried some of the most inspirational teaching out. Rachel Rinaldo's article in John's excellent posting on resources for girls and math reinforces that point.

What I find surprising and frustrating this year, my first in a coed classroom since I was a Teaching Assistant, is the girls' insistence on taking a back seat to the boys (or at least to a boyfriend), plus my own ignorance of what boys' dominant learning styles are. I plan to devote part of the summer to working on ways to improve my knowledge of boys' learning styles, plus add to ideas on how to promote equal participation by girls in a coed context. Any ideas people have for sources I could turn to are most welcome.

Bill

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John comments on some of his own mental models concerning math.

Ditto, Bill:

I attended a small rural Southern high school and had the same math teacher for four years... algebra through pre-calc. Mrs. Eady - a math whiz if there ever was one. When I fell behind, as I often did, I went to my classmate and next-door neighbor's house, where my classmate (she!) patiently coached me. I finished high school under the (mistaken?) assumption that women were BETTER at math than guys.

I'll admit that when my right-brained, literary daughter hit calculus, I began to develop a more balanced view....

John

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Melba shared some observations based on her experiences as a math teacher.

Girls are definitely better in math these days. Last week I was asked to submit the name of my highest averages for each of the two courses I teach (Algebra Preparatory (pre-algebra) and math 6 (regular 6th grade math). Guess what? I have 2 girls in the Alg. Prep class that blew everyone else out of the running, and 6 girls that were hundredths of a point from each other. The boys didn't even come close!

I have always been pretty good in math. I am an all-level music major (piano and clarinet) -- yes, a band director, teaching math to 6th grade students! I have an elementary endorsement with no special certification in mathematics. I might also add that 86% of my students passed their state test this year.
That is only because I had to include 2 students who checked in 3 weeks prior to the test, 2 students who were removed from our school and took the test elsewhere, and one moderately autistic student.
Otherwise my passing rate would have been 93%.

There are many teachers who may not have a certification in math, but who can teach it and reach the students. Like Nancy said, it's knowing how the students think and planning our strategies from it that breeds success.

Our school district began the "Algebra for All" through the 8th grade program a few years ago with Brian
Enright. Each campus' math offerings vary according to student needs. At my campus, we offer regular 6th grade math to our 6th graders and algebra preparatory. We use the Glencoe Course 1 book for the math 6 and Course 2 for the Algebra Prep classes. The 7th grade offers Algebra Prep and Algebra IA. The 8th grade team teach Algebra Prep, Algebra IB, IA and Algebra I (high school honors course). Algebra IA and IB is what used to be called paced Algebra.

There is a lot of pressure to move to the more accelerated math courses, and it makes the students who are not yet ready for algebra feel like "losers or dummies" as they call themselves. I have had to run interference with several of my former math students just trying to make them understand that sometimes we are not ready for algebra at the same time. We avoid tracking by just assigning the top third to the algebra prep classes in the 6th grade and place the remainder 2/3 in the math 6 course. The same holds true for the upper grades.

We also have the flexibility to move the students up or down as the need arises. Our parents have been pretty wonderful about this. Most of them accept our opinions. The 7th and 8th grade teachers use the University of Chicago book for the paced and the Algebra I courses.

Melba

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Satinder points MiddleWeb readers to a book that explores reasons why girls may not do well in math.

There is an interesting book entitled Failing at Fairness by Sadker and Sadker that discusses the issue of girls not doing well in math. It is a research study, and although at times it's a little over the top (girls as victims, ad nauseum) there are some valid points. One of these is the way that teachers encourage boys and girls differently. Boys are intellectually stretched and challenged by many of their teachers, while girls are given praise for merely trying, and more often given the right answer.

This is something for all of us to think about as we teach.

Satinder

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MaryAnne identified research on the subject of differences between how boys and girls learn.

Bill:
For articles on the learning styles of "gifted" boys check out the work of Thomas Hebert. He is a researcher for the University of Alabama [Note: now an assistant professor in educational psychology at the UGA College of Education] and has done some interesting work on the differences between the ways boys and girls learn.

Mary Anne


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MaryAnne shared some additional information about gender issues in math.

This Math thread is really interesting. I was never a "good" math student. I had Scarlet Fever in third grade and "missed" multiplication. Ever since then, the language of math has eluded me. I did finally learn the multiplication tables when I had to teach them! The work of Marilyn Burns really inspired me to help kids learn the concepts of math--as well as the computation.

But, that isn't why I started this...those of you who have begun to think about the difference in the way boys and girls learn math will find lots of information in a program called EQUALS. It isn't new, but they have done an incredible amount of work on the topic. They are the organization that promoted single gender math classes at the middle level several years ago.

The girl scouts have also taken on the cry. Their program "Bridging the Gap" which has its own website, is a program both for girls and their leaders. They found that the leaders of the junior troops were choosing not to teach the math and science badges because they were "afraid" they wouldn't be able to teach the girls the content.

Interesting stuff!
Mary Anne

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Finally, John provided a number of articles relating gender issues to math aptitude.

Maybe some of the gender problem has to do with the messages we've sent girls about math aptitude. We seem to be doing something about that now. I see a LOT of stories these days from newspapers around the country about programs to convince girls that they are just as capable in math as boys (and the research and current test data is backing that up). Here are some examples from past MiddleWeb news lists. See esp. the complete Raleigh N&O story.

2-28-01 San Francisco Chronicle
"Girls Now Outnumber Boys in Math, Science Classes"
[More girls enrolled in middle school technical classes.]
http://www.sfgate.com/cgi-bin/article.cgi?file=/chronicle/archive/2001/02/28/MN134360.DTL
**ALSO SEE**
The California Counts report "Who's Lagging Now?" (Vol. 2, No. 3):
http://www.ppic.org/publications/CalCounts2/calcounts.page.html

3-21-01 Lowell (MA) Sun
"Today's Lesson: You Can Do It"
[Middle school girls investigate math, science, and technology careers.]
http://www.middleweb.com/MGNEWS1/MGN0323.html#anchor1174384

3-20-01 Boston Herald
"Free to Learn"
[Catholic middle school nurtures hopes of girls from low-income homes.]
http://www.bostonherald.com/lifestyle/lifestyle_trends/skul03202001.htm

2-23-01 Raleigh News & Observer
"Not Your Father's Computer Science"
[IBM female volunteers reach out to middle school girls.]
http://www.middleweb.com/MGNEWS1/MGN0302.html#anchor15722427

2-27-01 The Oregonian
"Girls Urged to Take Road Less Traveled"
[Flight attendant or pilot? Workshops help middle school girls review options.]
http://www.oregonlive.com/news/oregonian/index.ssf?/news/oregonian/01/02/lc_32girls27.frame

2-9-01 Techweb
"Program Targets Girls for Tech Careers"
[Women engineers reach out to middle school girls.]
http://www.techweb.com/wire/story/TWB20010208S0015

12-19-00 Seattle Times
"Bringing Together Math, Girls"
[All-girl middle school will cost $12,500 a year.]
http://seattletimes.nwsource.com/cgi-bin/WebObjects/SeattleTimes.woa/w
a/gotoArticle?zsection_id=268448411&text_only=1&slug=girls19m&document
_id=134254707

7-5-00 Christian Science Monitor
"A Camp Teaches Girls How to Manage Money"
[Middle schoolers camp in Boston's financial district.]
http://www.csmonitor.com/durable/2000/07/05/fp14s1-csm.shtml

6-6-00 Detroit Free Press
"MEAP Evidence of Math Gap Between Boys and Girls"
[Girls fare worse as they enter middle school.]
http://www.freep.com/news/health/meap6_20000606.htm

7-14-00

Raleigh News & Observer

Program builds middle-school girls' interest in math

RACHEL RINALDO
STAFF WRITER

'I thought it was going to be a little bit boring, but I've learned PowerPoint and Excel," said Jill Bailey, a soon-to-be eighth-grader at Martin Middle School in Raleigh. Then she went back to throwing water balloons. It was fun and games, but it was also an algebra lesson. Sports
algebra, that is.

Jill is one of about 80 middle-school girls from the Triangle who have spent two weeks of their summer at "Girls on Track," a math and computer camp running from July 3 through today at Meredith College.

Now in its second year, the camp is designed to boost girls' interest in math and to encourage them to consider math- and computer-related careers.

Virginia Knight, a camp director and the head of the math and computer science department at Meredith College, said that studies show girls receive different treatment in math classes and are falling behind in technology. "Everything said that the middle schools were the places where girls started to lose interest," Knight said.

The American Association of University Women recently found that although the gender gap in math has largely closed, some women are staying away from math- and science-related career areas. Fewer
female college students are majoring in computer science than 15 years ago, possibly because computers have a geeky image.

"Girls get out of the pipeline starting in high school. It's really even more pronounced at the college level and at the post-graduate level," said Pamela Haag, research director for the education foundation of AAUW.

Girls on Track is part of a larger project to increase enthusiasm for math among young girls, attempting to reach them before they get turned off. The project involves Meredith College, N.C. State
University, the Wake County Public School System and the state Department of Public Instruction.

The campers, all of whom will be entering Algebra I next year, use computer analysis to examine major issues facing the Triangle. "Some of the studies showed that girls were more interested in real-life issues," Knight said.

So, they investigate things such as recycling, traffic and trash. One project involved trying to predict Wake County's population in 2020. Some of the participants studied how much trash they and their families generate and how it will affect local landfills.

"These are issues that will affect them if they stay in Wake County," said Nancy Smith, who teaches sports algebra at the camp.

Moreover, Knight said, the hands-on training "lets them know how many careers depend on a strong math background and on technology."

The so-called sports algebra games are also a big component of Girls on Track because they help teach basic algebra concepts.

"The purpose is for them to see that math can be fun and can be useful in situations other than crunching numbers," Smith said.

Take the water-balloon toss.

Each time a girl solved an equation, she joined a life-size "graph" on the lawn outside and took part in a water-balloon toss. Then those on the graph took turns catching water balloons.

The girls, most wearing sneakers and jean shorts, were quick to scream when the balloons smashed in front of them.

Afterward, one asked, only half-joking, for a hair dryer.

Several of the girls readily admitted that their mothers sent them to the camp but said that they were having a good time. "The first day you get nervous, and then you relax and get to know people and it's cool," said tall, self-confident Kora Burner, who will be in the eighth grade at West Cary Middle School this fall.

It was nice to be around girls who were interested in the same things, other participants said. Jill Bailey, the Martin Middle School student, explained that girls are sometimes turned off by math because "it seems like the guys run it," and girls are embarrassed to get questions wrong.

The participants also have opportunities to meet women in math and computer fields. This summer, they talked with the three women who run WomenGamers.com, a Web site that comments on computer games and advocates for games tailored toward women.

Next year, according to Knight, girls will be matched in groups of two or three with female Triangle professionals who use math, and they will shadow the women at their jobs for several days.

Knight and the counselors are very pleased with the results of the camp so far. "Last summer, some girls started to think, 'You know, I have more options,' " said Smith. "I think it just opened their eyes
to the opportunities that are there."

-------------------------

8-4-00

Los Angeles Times

SIMI GIRLS EXPLORE SCIENCE

SIMI VALLEY - For students Frances Kim and Lauren Faerber, this summer's Tech Trek 2000 was an opportunity to explore their interest in science and math and meet other girls with similar interests.

The Simi Valley middle-schoolers participated in the annual weeklong program that offers girls a chance to explore a range of subjects from marine biology to robotics in a college campus setting.

``I thought it was a good educational opportunity, and it was really fun being with other girls who had the same interests that I do,'' said Lauren, 12. ``I really liked staying in the dorms and being part
of campus life.''

Frances, 13, said, ``I've always been interested in math. I enjoy the subject and I've always been good at it. I'm also interested in biology. I don't know if I want to make it a career but there are a lot of opportunities in the field.''

Tech Trek, sponsored by the American Association of University Women, drew more than 100 seventh-graders from throughout Southern California to the seminar at the University of San Diego.

Students took classes in the mornings, participated in programs during the day and lived on campus.

``We're trying to get across the idea that math and science are just as interesting to girls as they are to boys,'' said Ginger Miller, co-president of the AAUW's Simi Valley branch.

Earlier this year, the association interviewed students who applied to the program from local schools before selecting Frances and Lauren.

``We were looking for students who could express themselves and have shown an interest in the subjects in elementary school,'' Miller said. ``I wish we could have sent all the applicants but funding was the limitation.''

Frances and Lauren took core classes in the morning and participated in a variety of activities during they day. Students were introduced to a range of subjects from robotics to women in history. There were also demonstrations of DNA scanning equipment, a tour of the harbor and a visit from a trainer at Sea World to study marine life.

Lauren entered the eighth grade at Sinaloa Middle School this fall, and plays soccer, draws and is involved with activities at Trinity Lutheran Church. She is the daughter of Dale and Belia Faerber of
Simi Valley and has two sisters, Kristen, 11, and Erin, 9.

Frances, an eighth grader at Valley View Middle School, pursues her interests in science and math, spends time reading and surfing the Net. She is the daughter of Charles and Theresa Kim of Simi Valley
and has an 8-year-old sister, Clara.

Going to Tech Trek made me want to go to college even more,'' said Lauren. ``I was anxious to start school again this fall. I like the challenge of taking tests and learning.''

For information on American Association of University Women, Simi Valley branch, call (805) 527-4466.

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