From 19 June - 30 June 2006, Judy Ward agreed
to be a guest facilitator for the Women and Literacy
listserv. The focus of her discussion was numeracy
and women learners.
Thanks to Ryan Hall, a graduate student at
Georgia State University, the following represents a
compilation of the various topics discussed by
discussion list subscribers while Judy Ward facilitated
the discussion. Each topic is organized by a series of questions
followed by the responses to those questions. The questions
and discussion postings were posed by listserv members and the
guest facilitator, Judy Ward. Most of the postings were copied and
pasted verbatim, with a few words edited here and there to facilitate
reading. Also, during the discussion, several members of the
listserv suggested various websites, books, articles, and forms
related to teaching numeracy skills. A list of those resources is included at the end of the discussion. For complete postings, along with author information, go to the Women and Literacy Archives and look at postings between June 19, 2006 and June 30, 2006.
Previous to earning my doctorate in adult education, I was a seventh-grade mathematics teacher. Many of my students had experiences that manifested as mathematics anxiety. I found that by changing my teaching techniques to a more hands-on and visual approach and teaching for understanding, the anxiety level decreased drastically. About ten years ago, I stumbled into adult education and found there was a need for my expertise. I am in the second year of a two-year term as President Elect of the Adult Numeracy Network (ANN). ANN is dedicated to upgrading mathematics instruction for the adult learner.
Since this is a women and literacy listserve, I assume that all have a deep concern and interest in advancing women through a literacy perspective. Also, I assume that you all love reading and writing and would like to help others feel the same way.
To get the numeracy and math anxiety discussion going I would like to begin from a different direction. I would like to tell you a little about my "anxiety" with English class during my k-12 years. Although I never made bad grades, English class was a challenge for me. Remembering all the sentence structure rules was overwhelming and didn't make sense. Diagramming a sentence, as well as the other 10 or so that were assigned, was a painful task. The process didn't make sense to me and I wasn't able to carry the exercise over to writing.
Writing was and still is another challenge and most of the time almost a painful experience for me. You could say that my anxiety about putting words on paper is a stumbling block and I have to work extremely hard just to get started. There are times when I must write something important, like now, and my stomach gets knots in it, my mind goes blank, and I have to write and rewrite over and over. Just before I send this email, my anxiety level will increase drastically because someone will read this and find mistakes or think the writing is terrible. Where does this anxiety come from? Probably past experiences with teachers that loved and knew their subject, but didn't teach the way I learn. We know a lot more now about how learning takes place than in my k-12 years.
I believe math anxiety can be a clear barrier for some students in seeing themselves as successful at math (self-efficacy), and ultimately inhibiting their ability to make progress with math. What strategies do you use to help learners reduce math anxiety? How do you know (assess) whether or not the strategy does indeed reduce anxiety? Of course there's simply asking them what they thought of the activity, but are there also quick tools or other formative assessments you use to gauge student comfort with learning math? Are there math activities or classroom strategies, in particular, with which women as learners have experienced success? How do teachers (of any subject and any level) on this list explain the "why" to your students? Do you wait until they ask, or is it something you build your lesson plan on? What types of activities do you use to make the "why" more visible for those students who don't get it the first, second, or even third time?
2A. That "why" Judy writes about is, I believe, essential information that is often missing from instruction in all areas, not just math. Teaching anything in an unconnected, abstract manner only creates a new list of useless facts that students try to memorize for a test they have to pass in order to be able to take the next test of useless facts. It sounds very pessimistic, I know, but teachers create this attitude when they forget to make sure students understand the "why" behind the abstract principles they are teaching. What creates academic anxiety of any kind is the student's inability to learn what is being taught the way it is being taught in the short amount of time it is being taught. Not knowing the "why" only adds frustration to the already overly anxious student who, at some point, decides to quit caring at all in hopes that s/he will never have to deal with the subject matter again. For me, it's definitely math, and the only reason is because no teacher would (could?) ever tell me why I needed to know it outside the classroom- having no real-life application for this information left me without motivation to continue trying, so I didn't.
2B. I agree that the why is important. In high school, I had a very nice advance math teacher who was an ex-navy man. While reading a Tom Clancy novel, which involved submarines, it suddenly dawned upon me why he might have become a math teacher... Math might have been more meaningful to me if he'd talked with us a bit about his career and how math got him (his ship) out of some tough situations...
I teach at university level, but I think this is useful in any setting...During the first day of class, I talk about why I [became] interested in the particular topic I'm teaching. Then I ask [the students] to tell me why they are taking this particular class. Whenever I move into a new topic, I try to remember to tell the class how they will use this information. Prior to ending the class, I suggest how they might practice using the new information.
2C. If your anxiety is related to a particular concept, that's a starting point. However, working more problems from the textbook will not help because that method is probably part of the problem. Remembering the algorithms (rules and procedures) is a major anxiety stimulant. You may be a visual and or kinesthetic learner and if you are manipulatives will help. Look back in your "math history" to find where the problem began, maybe it was a particular teacher or time in your life. But, if you are a visual learner manipulatives will help and those can be found at any school supply store or website.
2D. Math anxiety is an emotional response to math based on negative or unpleasant past experiences. It can also come from not understanding one basic concept, like fractions. When I began using manipulatives with 7th graders, the importance of "why" became obvious to me. The same "why" is just as important to adults, both teachers and students. Also, most adult students are visual and hands-on learners, especially in mathematics. Math was difficult for them in school because it was taught in an abstract manner - usually the way the teacher learned. As you know, more of the same doesn't work.
My suggestion: You know what concept(s) is a stumbling block for you. Take a friend and go to the math section of a school supply store. You should see Cuisenaire Rods (fractions), color cubes (blocks for teaching/learning multiplication, area, perimeter, etc), base ten blocks (place value, decimals, and percents), AlgeBlocks (solving equations) just to name a few. Ask for a book that will go with the manipulative of your choice, go home to your kitchen table, work with it, and learn. It's better to work with a small group, but if that isn't an option, work alone.
I have used all the manipulatives listed with both adults and children. They work! I can't tell you how many tears of joy have been shed during one of my workshops because an adult educator (ABE/GED/ESOL/Literacy/Workplace) understood and could "see" the why for the first time. When you feel confident, take the manipulative to your students. Let them "see" the why.
2E. I was "tracked" in HS to the academic threads - including algebra 2 and advanced science. Of course, how serious my all girls' HS in the early 70s was about sending girls to college is open for debate. I do remember getting "scared" out of calculus and trigonometry - never took either. I can't remember if it was a phobia about those subjects that scared me off or the reality of who was teaching it! I've never really been math phobic and especially loved algebra -- something about its abstractness and solving puzzles actually appealed to me. I didn't like geometry then because it was all about memorizing the theorems (at least, that's how I was taught) -- too many abstract words for me -- I didn't want to "read" math in that way. For some reason, x + y made more sense - go figure! But I think I'd like it better now as I understand myself as a spatial/visual learner and that's in geometry, too, I think. I like anything dealing with number sense, but I have a terrible time remembering anything that has numbers in it. (I can't rattle off statistics or percents unless it's written in front of me).
My experience is not so much with ABE learners, but with teachers. I've met a number of teachers who are called upon to teach math -- though it may not be their strong suit. I've talked to a couple of teachers who experience a lack of confidence (which may or may not include phobia) in teaching math and feel they struggle along with their learners through the process. But I've also met a number of women teachers who are excited and competent about teaching math -- and finding interactive & practical/meaningful ways of teaching it. I think one of the things I've come to appreciate over this past year with the initiative is the understanding of how numeracy reaches across many topics and educational areas. We tend to want to isolate it into a 45-minute period when, in fact, teaching and learning math can happen in reading, social science, day-to-day survival skills, and workplace skills. Also, teaching and learning math -- there is more than one way to arrive at answers. We may be looking for one answer, but there will be multiple options for how we get to the answer.
2F. On National Public Radio Weekend Edition Sunday, in the Will Shortz "Puzzle Master" segment, the Public Radio host, Liane Hansen, often asks the contestant, "Are you a puzzle person?" How would you answer this question? For me, it's complicated. If I knew I wouldn't have to compete on the radio, and if I had as much time as I needed, I might say "sometimes," depending on the kind of puzzle.
Those who would without waffling say yes, do not have "puzzle anxiety." They confidently dive into the deepest, coldest puzzle knowing that even if they thrash about they won't sink, and that they also know several strokes (strategies) in addition to treading water. Those who hesitate, qualify their "yes", or answer "no" have probably gulped water a few times, and it wasn't fun. They may be thinking that these waters are dangerous.
So here's my question. How do you as a teacher help those who are not "puzzle people," or "math people," become more confident? Is it best for them to learn a few strokes first in shallow water? Or to dive right in to the deep parts with a buddy who can swim? What is the teacher's role as lifeguard? What are some strategies to help the most anxious to put their toes in the water? How do you help a mature fish to not feel foolish learning to swim next to all these smart fry swimming circles around them? How do you help a cautious swimmer become a strong swimmer?
And since overcoming any anxiety is tough work, what do you tell your students is the reward? What's so great about swimming when you can enjoy sitting on a sunny beach or walking on the shore?
And do you have any good stories? Let's hear about one of your students who was "aqua phobic" and who now loves to dive and to play water polo, or who at least can enjoy an occasional swim. How,
exactly did that transformation happen? What was your role?
2G. What I can contribute is personal experience, but why not, it probably shows what numbers can do. Soon after I separated from my husband, income tax time came around. I knew I couldn't do the math, but even assembling the documents was overwhelming. I ended up on the rug of my rented apartment crying and picking fuzz off the rug.
A couple of years later, I had mastered the assemblage of documents, but I neglected to send in the completed forms until I got a letter from the IRS. Now, because I am a small business, I have to divide my expenses into 4ths and multiply by 3. I was so put together this year that I have even put the little coupons in their envelopes -- stamped -- and written down the reminders of tax time on my calendar.
Turns out I am POWERFULLY MOTIVATED to save money, so I put in the extra time to NOT SPEND on checks to the IRS.
The above reasons are why I feel it is REALLY IMPORTANT for women to know the ins and outs of managing money. I had to go out and get the knowledge, and I sure wish I had had a helping hand, so I am really STRONGLY in favor of emphasizing the practical uses of math.
Planning what to do with money can give a person control and motivation. Unless a person is planning to go into theoretical physics or math, money has daily practical consequences.
2H. [The previous] description of her personal numeracy development is so real and rich. Once, a math professor of mine started the class with the question: "How can a boring, heartless subject like math evoke so much emotion?" I often think about that remark and maybe the answer is more complex than we had bad math instruction. However, since I am a math teacher, people do tend to share with me some horror stories about school math experiences that caused them to "check out" big time.
When I read that story, I was interested in why one has to divide by 4 and then multiply by 3. Does the division by 4 get the quarterly expenses? What does the multiplication by 3 do? I think the answer to alleviating math anxiety/avoidance is to keep asking why -to keep sticking with the meaning behind the rules- if I know WHY you divide by 4, and then multiply by 3, and can picture it in my mind, I tend not to forget. It's memorizing rules that I don't "get" that makes me feel anxious.
Anyway, this morning I am finally getting it together to go to a financial advisor for post divorce advice. The meeting is in 2 hours and writing back to you is one way to avoid stuff- hmm, have to go - there's so much lint on my rugs and I would rather pick that than face the REAL math music. I have noticed that many people who say they are bad at math are great handling their money and a lot of math types are not so great (case in point). I think the two types could learn a lot from one another.
2I. We usually think about emotion/feelings/affect related to math as "math anxiety" -- that fear of engaging with anything that has to do with numbers. But [the] description of mathematical exploration addresses another kind of math related emotion that is rarely addressed -- frustration.
Many people seem to believe that when others try to solve math problems (whether "typical" word problems or more complex, real problems) they immediately know what to do and how to do it. Maybe this comes from years of teachers standing at the board presenting problems from beginning to end, never showing students a process that may include false starts, selecting a strategy that is non-productive, having to start over, having to work backwards, etc. And watching the students who get or "see" those particular answers right away just emphasizes the notion that the answer or methodology should just pop into your head. But what really happens often is a feeling of frustration when you hit a wall, or at least a stumbling block. And this, for absolutely everyone, even research mathematicians studying arcane theoretical math, leads to feelings of frustration. The issue is what to do with that frustration? Learners, and everyone for that matter, need to realize that there are alternative responses to that feeling of frustration. Some people cut and run, and then say, "I can't do this and never will be able to." Others might say, "I will just start again and try something different this time." Others might really get fired up in response to the frustration, and say, "I will figure this out if it's the last thing I do!" Talking about frustration and alternative responses to it is probably at least as important as talking about "math anxiety."
2J. When frustration occurs in problem solving, the student goes back to the concrete, and works up again to competence. So, any problem solving can be charted/graphed, and what will come out is a series of ups and downs and eventually a stable up. Also, performance depends on context. That is, how the skill is to be displayed/ used. Think bicycle riding on a road and bicycle riding on a dirt path. Competence is constructed.
2K. Frustration is an impediment to solving any problem and going back to the concrete may or may not help. It depends on the individual. I have a tendency to perseverate on whatever is frustrating me. Discussing the problem or situation with someone is just about the only way I can get around the frustration and the wall. If it is a math/numeracy problem, working with a group is best for me.
I am wondering if there are others on this listserv who have experience using manipulatives, such as Cuisenaire Rods, color cubes, base ten blocks, AlgeBlocks, or anything else either for themselves when they were/are learning math, or when they were/are teaching math. Can you share with us your experiences? Also, I wonder whether typical adult literacy programs that include math instruction have budgets for these manipulatives? I have only visited a few math classes for adult learners, but have never seen manipulatives in use. I am trying to figure out if this was just coincidence or representative of adult literacy and math instruction. Does the suggestion to use manipulatives correspond to women's learning theory, or does it have more to do with multiple intelligences contexts for learning?
3A. As a 7th grade math teacher, I became tired of students coming to me still not understanding fractions, decimals, and percents. So, I changed my teaching methods to include manipulatives and other visual methods. Once I began teaching for understanding by using manipulatives such as the Cuisenaire rods, the "light bulb" came on for everyone, and they were much happier (as was I).
When I stumbled into adult education, it became obvious that the same problems existed. Not only did the adult students not understand fractions, decimals, and percents, but neither did the instructors. During the workshops I have given, there have been many occasions the "light bulb" moment has occurred with an adult educator. Sometimes even tears were shed.
3B. My research of GED programs in Arkansas showed the following: 95% of the instructors utilized a textbook/workbook curriculum (algorithm based instruction), 99% used paper-and-pencil- repeated practice as the instructional practice of choice (algorithm based), 95% used individual instruction as their instruction method of choice, and 99% reported repeated practice as their most effective instructional method. The instructors were teaching the way they were taught and had no idea there were other methods. If you visited 100 sites, you might come close to the same results.
Literacy programs are in a great position to teach basic math concepts because basic math instruction can be easily integrated into the reading curriculum. Although literacy providers understand and accept alternative math instructional methods, they seem to have difficulty integrating it into their programs. What about implementing a small group math/reading/discussion program?
3C. The research supporting the use of manipulatives is the concrete to semi-concrete (or representation) to abstract sequence. All of that research was done with children and, to my knowledge, none has been done using adults in ABE/GED/Literacy programs. There were a couple of studies completed during the late 1990s with community college algebra students.
The CSA sequence begins with the concrete (blocks, fraction rods, etc.) so the concept can be seen and handled. Using beans or chips for counting is an example. The semi-concrete or representation is the use of a drawing of the concept or problem to find an answer (drawing sticks for counting). The abstract is the step taken when the student can perform the operation or solve the problem without the first two steps. Adult students tend to go back and forth between the first and second steps and then "leap" to the third.
Adult students have gaps in their knowledge of mathematics. Those gaps can be concepts like place value, multiplication, fractions, etc. The use of manipulatives can help the adult student "see the why" and fill in those gaps. There are many success stories told by instructors who took the knowledge of how to use manipulatives back to their students. Those students became more confident in their math ability by "seeing the why".
3D. [It was] pointed out that manipulatives can be made out of construction paper and other items found around the home and school. The cutting and tearing of construction paper, paper plates, rulers, etc. are wonderful activities from which the student learns many things, and [these activities] can be used as an assessment technique. But, if you think differently and look closely, there are things all around you that can be used.
I looked in many $1 stores in small Arkansas towns, as well as WalMart for geometry "things". Guess what? Look in the cosmetic section of WalMart, Walgreens, Kmart, Target and most grocery stores and you will find cosmetic sponges that are very inexpensive and are great for teaching geometry concepts. They come in circles, rectangles, and wedges (some of them are very nice prisms) of different sizes that can be cut, stacked, and colored.
The manipulatives that are "store bought" are not expensive because only one set is usually all that's required. The Cuisenaire Rods come in sets for 1 to 4 people and cost around $10. There are several reasons why I like using the CR:
1. the student learns that "1" can be anything. When using fraction circles one is always 360 degrees.
2. the student can see immediately what an equivalent fraction is and it makes sense.
3. that "reducing" a fraction, which doesn't make sense, is actually "exchanging for fewer parts".
3E. I didn't know what [math manipulatives] were. A computer science colleague kept talking about them, but never explained what they were because she assumed I knew. My daughter just completed 9th grade math with a much better teacher who knew the subject matter and so spent more time explaining the material. However, I'm fairly certain she didn't have manipulatives. The reason is cost. And, I would imagine the same is true in adult education. You've all inspired me to visit the math education specialist at the University where I work. I'd like to engage them in a discussion of how they are using manipulatives in their teaching.
3F. I can't recall if it the same in the US, but in New Zealand we have little plastic discs on the bread bags, which record dates and are in different colours. I collect these and use them as manipulatives.
They are useful for sorting activities, for explaining abbreviations (months), the concept of Best Before and Use By dates (we use both in New Zealand - I seem to recall you only use one in the US), they are durable and they are free.
Otherwise, the laminator is a great friend in the resource-making department.
Australian numeracy experts Beth Marr, Dave Tout and Sue Helme have written a lot about math anxiety in their publications - Breaking the Maths Barrier and Strength in Numbers.
One of the simplest things we do in professional development (taken from Marr and others) is to get participants to fill in a page called "Maths in My Day." This makes people recognise all the "maths" they do that happens under the radar so to speak and which they never think of as being maths, but just part of running a household and being a parent.
3G. hmmm... about manipulatives...though some commercial products were named, and the suggestion that "cost" was a reason for why they are not used in ABE.... I think the point of manipulatives is to make numeracy-related concepts both visual and kinesthetic. So, once we have a sense of what a specific manipulative might be used for, I think we could be creative about how to acquire them....perhaps learners could help make them (to explain the why) and they could be left in the classroom for future use...colored paper cut in shapes, clean leftover plastic food containers of all sizes, children's building blocks, deck of cards, various grains and beans of differing shapes and sizes -- heck, even a bag of M&Ms or different kinds of cookies could be used. In this regard, I think we're only limited by our imagination! As this conversation progresses, though, I find myself asking what it has to specifically do with women and literacy? Several suggestions seem fairly generic, not particularly gender-specific to women.
[One suggestion offered was that] women have typically not been encouraged to consider financial or money management issues in the way that men might be. The overwhelming (or assumed?) sense that math anxiety is typical among women (more so than among men) could be another connection.
I wonder if women use numeracy more than we identify it, and may not fear it as much if we could get to more holistic, relational, and creative ways of teaching/learning and experiencing it throughout the fabric of our lives (how we cook, clean, garden, apply medications, shop for bargains, sew or do fabric arts, figure better gas mileage, estimate time, use public transportation, maintain a budget, decide what phone plan to use, decide which job is better to take in terms if income, distance, child care, etc. etc. etc.)? I am curious to hear from other folks about their experiences teaching data literacy to adults? Any suggestions for resources that define data literacy, and discuss how to teach it to adults (adults who have a range of education levels from GED/HS diploma to Master's degrees, but mostly all experience some level of math anxiety, and certainly the overwhelming majority of who are women).
4A. Many think that math is computation only, and it is taught as an isolated subject. However, as we all know, in today's world more is needed. Also, most people use math in everyday life but don't consider it math because math is what they did in school. This is where numeracy comes into play. Math becomes part of reading, literature, social studies, everyday problem solving, and science. We must remember that everyone does not learn the same, especially when it comes to math. Literacy instructors know there is more than one way to teach reading, but when it comes to math, the tendency is to be stuck on computation only.
4B. [The] realization that "data literacy is a set of skills called numeracy skills and that there are folks out there thinking about numeracy and teaching them to adults" is very important. My main purpose for participating in this discussion is to inform others about numeracy and that there is a group of individuals dedicated to the cause. That group is the Adult Numeracy Network (ANN).
4C. My job is as a community-based researcher in the field of early care and education. My work is about responding to research questions posed by the community, working with the community to gather the data to answer the questions, and then giving the data back to the community so that action can be taken. As I have produced more and more reports, it has started to trickle back to me that folks need help understanding how to read data. How do you look at a graph and understand what it's telling you? How do you critically read a statistic? How do you read data that is displayed on a map? How do you take data and use it in key decisions? These skills are all second nature to me, but I have begun to think of them as a type of "data literacy" -- data literacy in the manner of skills for how to read and gain meaning from numbers. This current conversation has me intrigued because I am realizing that perhaps this set of skills is also called numeracy skills, and perhaps there are a lot of other folks already out there thinking about numeracy skills and teaching them to adults.
4D. People don't know how to read graphs and understand the information or data that creates a "picture" of the story. As you have discovered, others should but don't have the skills you so aptly call data literacy. This set of skills is a very important part of numeracy. While doing workshops and presentations, I quickly discovered the participants did not have a clue as to how to take data and put it into a graph or how to read one critically. Just describing or giving handouts on different types of graphs to a group doesn't get the information over to them. Only gathering data, putting that data into a graph, and explaining the information helps them understand. This is an extremely important skill in today's society.
I belong to the Adult Numeracy Network (ANN) which is THE organization dedicated to recognizing the importance of numeracy and placing it on the same level as literacy. The website is www.literacynet.org/ann and there are links to other important sites. Also, there is an adult-based curriculum called EmPower that has a set of lessons on using data. It is also listed on the website.
4E. [These posts are] making me realize actually how much I have always been comfortable with numbers and that I did have good experiences in school with math. I think I knew somewhere that this was not common, but this is making me actually process and realize that. More importantly, though, this is making me think more about how I can use these skills to help others who are not as comfortable with numbers- use a strength I hadn't realized was a strength.
It seems to be that the daily relevance is certainly financial. Actually, figuring out what my budget is and learning how to live within it so that I can meet my priorities and goals has been incredibly empowering. Also, although I see math as being very important in terms of advocacy, policymakers listen to numbers. Being able to walk in to your legislator's office and say "83% of early education teachers will need X type of support to enter and succeed in higher education" is powerful. It moves [you] from allowing a policymaker to dismiss you because they think "oh well maybe there's just 6 teachers out there who need that support, and everyone is just repeating the story of those 6 teachers", to "wow 83% that's a lot of teachers". Stories are also helpful, but I have found numbers to be effective. This is what connects for me through to data literacy because you have to be able to pick out and understand the statistic in order to use it effectively.
And related to teaching fractions- When I was growing up, I would help my Mom cook dinner. She would decide some night that we needed 5/8 or 3/4 of the recipe, just to make me do the math :)
4F. It is simply ESSENTIAL that women learn how to manage money. This is a life-time topic. I speak from experience on this one. Nobody gave me advice. I had to hammer on people to get basic information. People DO NOT want to talk about the ins and outs of taking care of money.
Fortunately, I picked up enough [advice] to survive, but knowledge on this topic goes FAR beyond a checking account. In my experience, women, when given good information, are fabulous strategic planners. I think that what helped me MOST were money success stories from women who had been very clever with their money. I picked up tips. Another thing that helped me was [having] 2 groups of close friends who increased exponentially my connections to information. War stories help here. I know this is me talking about my experiences, but my experiences will have some linkages to adult students -- I think of myself sometimes like an adult student, anyway.
4G. There is not one accepted definition of numeracy, but for our purpose I would like to establish that numeracy includes more than computation and school mathematics.
[It was asked], "how can we understand women's relationship to numeracy/math, especially in ABE?" Also, [it was pointed] out that "all women use math in their everyday lives" although some do more than others. It is very possible that the family culture in which a woman is raised can determine her aptitude for handling money.
The ABE classroom is the perfect setting for involving women in activities that include handling money in their everyday life. One of the ABE instructors that participated in my Arkansas program led a group of 5 women and 1 man in a special project. They figured out how much they were spending at the laundry each week over a period of a month (the total amount surprised them). They then went to Sears, during class, and found out they could buy a washer and dryer for what they were paying at the laundry. The project helped them realize that they can do "math" in the context of a real life situation and that math is more than "school math". During the process, calculators and problem solving skills were used. Many activities based on real life situations such as this one, can be developed that will provide women with opportunities for learning how to handle money.
Developing an activity on the interest charged when buying any household item would be good. An activity teaching them to read the fine print at the end of an ad that advertises no interest for ___ years would be very useful. Such knowledge really gives women self-confidence and power over their lives.
[Many others] discussed the importance of financial knowledge. During my divorce I was very thankful that I had knowledge of my financial situation and had played an active roll in the process. That made a huge difference in my financial situation.
Numeracy is also an empowerment issue for women. It is more than school math, computation, or solving the word problems at the end of the chapter. Is it knowing how to function in society? What do you think?
Sure, there may only be one answer -- but exploring all the ways to get to that answer can help with learners' ability to "know what they know" -- help to create a confidence in experimentation, critical thinking, multiple solutions, and problem-solving. Now there may be times when using some options may get the wrong answer -- but this can be an important part of the process as well. And some options may be more complicated (convoluted) or more time consuming than others -- but the answer will still be the same. Isn't that sometimes the way life is?
5A. I often wonder -- Are there keys in women's learning theory or specific gender-based concerns that can help us to understand women's relationship to numeracy/math, especially in ABE? I wonder if it has to do more with socialization and structures of power than anything to do directly with math. Why do I say that? Well, here's my own theory (for what it's worth):
Think about what has been considered to be "typically" women's work....and how math-related they all are... cooking (need to understand relationships of amounts, volumes, measurements -- how much of what to use, when, to feed how many....etc.), fabric arts (counting stitches, how much thread, yards, how big is the person being sewn for...etc.), gardening (how much space will something take in relation to other plants, how much water, food, length of growing time, astrology), farming, childcare, transportation, home repair, food storage, bargain shopping, bartering (how much is something worth really). So much of common "women's work" and everyday survival DOES depend on a certain familiarity with "figuring."
I think that as math became more associated with money management (class / power) and abstract theoretical "higher" problem-solving, the more it became removed from women's hands -- "closed" and made "mysterious," even frightening for women. And, I do believe it has to do with power and access- basically, women's self-sustainability and self-sufficiency. That's my rant for the day. Also, I'd venture to guess that math may be a great "equalizer" for women ABE learners as well as ABE teachers -- in this subject area, we may be most like our students in comfort and expertise, than not!
5B. One of the things I've learned through my colleagues at TERC & SABES and through the EmPower program is that there is more than one right way to arrive at an answer. Sure, there may only be one answer, but exploring all the ways to get to that answer can help with learners' ability to "know what they know," help to create a confidence in experimentation, critical thinking, multiple solutions, and problem-solving. Now, there may be times when using some options may get the wrong answer, but this can be an important part of the process as well. And some options may be more complicated (convoluted) or more time consuming than others, but the answer will still be the same. Isn't that sometimes the way life is??
We all learn and do differently, and I think being able to do this through numeracy can help us to not be so anxious about math. Sometimes I think the pressure about math is that we have been made to believe that there is only one right answer and only one way to get to it...so if you don't do it right, then you fail. And, I think that's how women's lives get presented to us as times as well. Having the assertiveness and confidence (and the "permission" to make mistakes and start over) helps us all to function in our various contexts. I think "literacy" has tended to show how this can happen through reading and writing, but pursuing these "life lessons" through numeracy, especially for women, can lead to some very powerful results.
5C. Lynda described a measurement activity she uses that involves critical thinking, problem solving, communication, decision-making and many more skills and concepts all while working with measurement in the context of a real-life experience. With this activity, some explanation in the beginning from the teacher may be required, but the students can work together on a solution of the problem. The teacher becomes a facilitator rather than an expert dispensing knowledge. Meanwhile the students, "by exploring all the ways to get to that answer can help with learner's ability to 'know what they know' - help to create a confidence in experimentation..." This activity is an example of "numeracy" and allows the students to achieve power over their own learning and success.
There is a time and place for paper and pencil drill and practice, but using it as the main teaching and learning tool does not provide an environment that allows for the student to "know what they know". Most do math everyday, but since it isn't "school math," they don't consider that what they do everyday is math and, therefore, don't have the confidence to do math.
5D. Money matters (math) have everything to do with money and power, and absolutely nothing to do with gender, except in human societies, where gender matters a lot. One of my teachers, Don Warwick, worked in what were then called "developing nations," and reported that in Pakistan women excelled in math. He thought it was a matter of training, and so do I. The comment about Pakistan shows that there was, indeed, a time of optimism.
My mother remarked to me once, "I should have taught you about money." This was woman to woman, too. So, I had to learn about money on my own.
In my senior year at school, we were given an assignment to use the newspaper and find an apartment to rent and look at ads to find out about food to buy -- a truly great assignment. A family member turned out to know A LOT about money. He is a lawyer who specializes in land deals and is a crook -- or at least was when I knew him. He learned very well.
About Cuisenaire rods -- I have used them, and I think they are terrific. I don't know how much they cost. They are beautiful to look at and to use, so buy them. I would use coins etc. with them for fractions, multiplying. I would also use items like grocery slips, tax bills, insert every piece of paper that comes with numbers into math lessons.
By the way, math knowledge, indeed knowledge in any field, is built from the bottom up, in discernable stages. Start with the concrete. Take students to city hall where they live, look at tax valuations (publicly available), get to know all the ordinary lessons about money. I learned to ask, "Where does money come into this?" about everything.
5E. What a fabulous insight; yes, math takes assertion.
Can you talk a little bit about how you move these women from quiet observers of your instruction to active participants who actually take initiative and offer suggestions for solving math problems? Also, do you have any suggestions for dealing with their wrong answers- ways that will not return them to their silence?
6A. In my observation, some women who have survived violence in their past or are dealing with it in their present, have learned not to express an opinion, because they have not been allowed to have opinions, or have had dire consequences to expressing an opinion.
Yet, you cannot do math without expressing an opinion. "I think ________ would be the best way to tackle this problem." "I'm going to move the decimal two places to the right." "The answer is ___."
Such women are caught -- if they are to do math, they must jettison a survival tactic that has served them well. As an instructor, I have to take this into consideration as I teach math -- I cannot just expect women to jump in.
6B. I notice out loud that sitting back is a strategy that works in some places, but is usually less fruitful in math classes. I acknowledge that I am asking them to do something difficult ( i.e., be more active), but that I am confident that they can do it and I am confident it will make a difference in their ability to learn math. I notice and encourage very small steps they take, and get them to talk about how/why/what they are feeling as they work in math. I teach math in a group, so they can encourage each other and follow each other's lead. I work with them on learning styles and multiple intelligences, so they know themselves better, and then invite them to make some choices about what kind of assignments or studying they will do.
6C. Primarily, I like to use manipulatives, because it is hard to get the wrong answers when you use manipulatives. For example, 3/8 plus 1/4 never turns out to be 4/12 when you use manipulatives.
6D. [It was observed that], "some women who have survived violence in their past or are dealing with it in their present, have learned not to express an opinion, because they have not been allowed to have opinions, or have had dire consequences to expressing an opinion."
As a seventh grade teacher, I worked with children who were from homes where violence and abuse existed. Unfortunately, it is too common. Also, I have known women who experienced and survived violence and I know that violence destroys their self-confidence and inhibits their ability for social interaction. The fear and mistrust inherent in a situation such as this is a block for learning and it is very difficult to overcome. Including her in a group discussion will probably not work at first, but might over time.
I hope that this discussion helped many of you become more familiar with the term "numeracy". As literacy providers you are in a unique position for providing basic math instruction. And remember that just as literacy is more than reading, numeracy is more than computation.
Change is difficult and thinking differently about math is extremely difficult because, generally, we were taught math by using drill and practice methods. Several years ago a workshop participant commented that using an activity based curriculum takes longer. My comment to her was that it is like driving to a location where you have never been and on a road you have never driven. It seems like the drive to the location takes forever but the return journey passes very quickly. A second trip to the same location goes much faster and you can pay more attention to the scenery. Just try one simple activity. Once you see the results your second journey will be quicker and better.
If you google the term numeracy, you will find thousands of results, but look closely because the large majority of the numeracy sites are in other parts of the world. The US is behind in recognizing the importance of numeracy. Cheryl Keenan, during her presentation at COABE in Houston last April, talked about the importance of numeracy and that it should be elevated to the same level of literacy. ANN's membership is dedicated to the numeracy cause and we hope you will join us at COABE in Philadelphia next spring.
Here is some information about ANN:
In April 1990, a group of Adult Basic Education teachers addressed the National Council of Teachers of Mathematics (NCTM) General Meeting in Salt Lake City, asking NCTM to "extend its agenda to adults". As a result, in 1992 NCTM agreed to co-sponsor a conference with Adult Education Organizations. In 1994, NCTM, The National Center on Adult Literacy (NCAL) and OVAE co-sponsored "The Working Conference on Adult Mathematical Literacy". The Adult Numeracy Practitioners Network (ANPN) was formed at that meeting. The Math Practitioner, a quarterly newsletter, and the NUMERACY listserv were established.
In 1995, a planning grant was awarded to ANPN by NIFL to begin developing Content Standards and a reform plan for the ABE system. This was an early phase of the Equipped for the Future initiative. ANPN submitted the report to NIFL in 1996. The title of the report was "A Framework for Adult Numeracy Standards: The Mathematical Skills and Abilities Adult Need to be Equipped for the Future".
In 1998, ANPN changed the name to Adult Numeracy Network (ANN). ANN is an affiliate of both the NCTM and the Commission on Adult Basic Education (COABE). ANN members are active in both state and national organizations by giving presentations and workshops to increase awareness of the need for numeracy instruction in adult education.
During the last year, ANN developed teaching and learning principles that address both the curriculum and learning environment for teaching mathematics to the adult learner. In addition, professional development principles were developed that address both the design and content of mathematics professional development.
Last April, ANN presented a Pre Conference session at the COABE meeting in Houston where practitioners from 21 different states attended the day long session. The newly developed teaching and learning principles were successfully integrated into the session. All participants agreed that the activities, along with the new principles, made for a great day!
Next spring, ANN will be in Philadelphia for COABE. Plan to be there for our Pre Conference session and presentations during the regular session. Our website is http://literacynet.org/ann. A membership form can be downloaded from the website. Membership provides a newsletter, The Math Practitioner, 3 times a year. The newsletter includes numeracy activities that can be used with your students, as well as general news for the adult practitioner. Also, as a member you will be part of a group dedicated to increasing awareness of the importance of numeracy.
On behalf of the subscribers, I would like to thank Judy Ward for facilitating an interesting and thought-provoking discussion on numeracy. I also want to thank all of the members who contributed by writing, reading, and/or thinking about the posts.
Women and Literacy List Facilitator
Throughout the discussion, several members of the listserv suggested various websites, books, articles, and forms related to teaching numeracy skills. Below is a list of those resources.
8A. The website for the Adult Numeracy Network (ANN) is: http://literacynet.org/ann.
8B. As you may know, the president of the United States has created a National Mathematics Advisory Panel. According to the Executive Order, the Panel is to "foster greater knowledge of and improved performance in mathematics among American students." More information about the panel, its charge, and its members is available at: http://www.ed.gov/about/bdscomm/list/mathpanel/index.html.
8D. The National Center for Family Literacy has been exploring and creating strategies for basic intergenerational financial literacy. You can explore some of the online resources we have used with adult learners and their children. There are some interactive materials for adults here that are very helpful and fun! www.literacycampus.org/campus/library.asp
8E. To subscribe to the Numeracy list, write to majordomo at world.std.com. In the message area, type: subscribe numeracy
8F. Numeracy Research and Practice topic section on the ALE Wiki: http://wiki.literacytent.org/index.php/Numeracy_Research_and_Practice
8G. Information about the EMPower curriculum can be found at http://adultnumeracy.terc.edu/
8I. National Institute for Literacy's Special Collection on Science and Numeracy
8J. This September, the Adult Literacy Media Alliance is releasing a new multimedia financial literacy curriculum TV411 Save Smart developed with a generous grant from the NASD Investor Education Foundation. TV411 Save Smart features TV411's math-minded Calculating Woman and highlights key literacy and math concepts behind saving and investing. The curriculum, designed for ABE students, is made up of four units: Planning for Retirement; Tax-Deferred Savings and Investing; Tracking Mutual Funds; and Reading the Fine Print.
To learn more about it go to: http://www.tv411.org/index.shtml
Many thanks to Andrea Wilder for sharing the following financial forms!
I have sent in an almost complete copy of the forms I mentioned. They are designed to cover every financial eventuality you can think of, I think. This means that someone with a minute income can use them as well as a person with a gigantic income.
I think the expenses side is very useful, also the places where it is possible to prioritize what you want and what you feel comfortable with. Still, the best idea is to itemize everything and write it down. As for making a will, you can actually get forms from the web. Just be sure to write everything out in your own hand.
A form for Income would include the following:
- Earned Income (e.g., salary and wages, self-employment, pension/retirement)
- Unearned income (e.g., interest and dividends, income from annuities/trusts, partnership or S Corp
- Other income (e.g., social security benefits, disability, other sources of income)
A form for Housing Expenses would include the following:
- mortgage -- second home
- PMI (private mortgage insurance)
- condo fees
- real estate taxes
- real estate taxes, second home
- utilities: electricity/gas/oil/water/sewer
- telephone: base and long distance
- cell phone
- cable/Satellite TV
- Internet access
- home security system
- maintenance and repairs
- home improvements
- grounds maintenance
- cleaning/domestic help
- household supplies
- other: parking fees/swimming pool, etc.
A form for Transportation Expenses would include the following:
- loan or lease payments
- gas and oil
- excise taxes
- maintenance and repairs
- parking fees/tolls
- auto club ex: AAA
- train and bus fares
A form for Medical Expenses would include the following:
- drugs, prescriptions/medications
- insurance deductibles (but not insurance premiums)
A form for Entertainment and Recreation would include the following:
- lunches/dining out
- theater/movies/sporting events
- membership and club dues
- videos/DVD rentals
- weekend trips
A form for Professional Expenses would include the following:
- financial planner
- investment advisor
- dues, books, periodicals
- business organizations
A form for Living Expenses would include the following:
- child care
- child support/dependent care support
- dry cleaning/laundry
- tailor/shoe repair
- personal care/grooming
- pet care
- charitable contributions
- safe deposit box
A form for Income Taxes would include the following:
- federal tax withholding
- state tax withholding
- social security tax withholding
- Medicare tax withholding
- federal estimated tax payments
- state estimated tax payments
A form for Savings would include the following:
- bank/credit union savings
- non-retirement savings
- retirement savings
- deferred compensation
- education savings
A form for Planned Giving would include the following:
A form for Personal Information would include the following:
- Personal and family information (e.g., name, place of birth, social security number, date of birth)
- home address
- home phone/fax number
- work phone, you and spouse
- mobile number
- us citizen?
- spouse US citizen?
- date of marriage
- prior marriages
- significant health problems?
- financial support to parents?
- Does anyone other than your children or your parents depend on you or spouse?
- Other advisors (e.g., investment, attorney, banker, insurance agent, accountant)
- current employment for you and your spouse (e.g., company, position, years employed)
- Are you or your spouse engaged in any professional activities, paid or unpaid, outside of your
main employment (ex: board memberships, volunteer work, professional association memberships,
- Financial planning goals- indicate specific financial planning goals and indicate their relative
importance to you and to your spouse
- personal objectives- indicate relative importance of each of the following personal objectives to
you and your spouse
- saving regularly
- making a major purchase
- home renovations
- taking a dream vacation
- minimizing personal income taxes
- developing or revising your investment strategy
- investing for a comfortable retirement income
- providing for your children's education
- providing for your grandchildren's education
- making gifts to relatives
- making gifts to charity
- minimizing estate taxes
- determining how your estate assets will be distributed
- avoiding probate costs
- minimizing the burden of health care costs
- providing for your family in the event of your/spouse's death
- providing for your family in the event of your/your spouse's disability
- changing or modifying careers
- Investment objectives- rank the relative importance of each of the following objectives to you and
- current income -- dividends or interest to spend
- liquidity -- ability to quickly convert investments into cash
- safety -- little or no danger of losing the investment
- capital appreciation -- possibility to original investment gaining in value over time
- tax shelter -- current and/or long-term tax advantages
- Please describe any significant investments planned in the near future
- Indicate if the following statements summarize your and your spouse's financial attitudes/beliefs
- optimistic about financial future
- comfortable with aggressive investments
- rather work longer than reduce my standard of living in retirement
- concerned about protecting my assets than about growth
- I feel I can reduce my current living expenses to save money for retirement
- my immediate concern is for income rather than growth
- I prefer a predictable steady return on my investments, even if the return is low
Part III (Assets)
- Cash Accounts
- type: checking account, saving accounts, money market funds, CD's, treasury securities, US
savings bonds, other
- who controls? you, your spouse, together?
- type: checking account, saving accounts, money market funds, CD's, treasury securities, US
- Brokerage/Investment Accounts (non-retirement)
- name of institution/ownership/ current market value
- Stocks, Bonds, mutual funds
- direct ownership with company name of security/ ownership/number of shares/current
- direct ownership with company name of security/ ownership/number of shares/current
- Retirement Accounts
- Employer Stock Purchase Plans
- amount each pay period
- Stock Options
- company/ownership/date and type of grant/ # of options granted, number of options vested,
stock price, current market value
- company/ownership/date and type of grant/ # of options granted, number of options vested,
- Real Estate -- personal use
- ownership/cost/market value/outstanding mortgages and home equity
- loans/interest rate/term of loan/ years left/monthly payment
- institution/ownership/contract date/type (fixed variable)
- basis/current market value
- description/loan amounts/interest rate/payments/maturity date
- Real Estate -- investment
- ownership/cost/market value/outstanding mortgages and home equity
- loans/interest rate/term of loan/ years left/monthly payment
- Limited Partnership Interest
- description/ownership/date acquired/capital contribution
- Closely Held Business Interests
- description/date acquired/percent owned/estimated fair market value
10A. I love to use manipulatives when I teach math. I think one of the reasons they are not used by more instructors is that students resist using them, and it is hard to keep saying "yes" when the learners are saying "no." Over the years, I have developed some ways of honouring student resistance, and reducing it -- and I'll refer you to my article Working with Student Resistance to Math Tools at http://www.literacyjournal.ca/Forumpages/forum4_s05readings.htm
10B. I would recommend Managing the Mean Math Blues by Cheryl Ooten: a friendly book that combines a framework for understanding math anxiety with a variety of strategies for developing math skills.
10C. As I read the list this week, I am compelled to share a resource which has intrigued and helped me overcome financial challenges and some of my math anxiety (I believe both are linked). I think many of you might enjoy it and benefit from the practical advice within its pages. The Nine Steps to Financial Freedom by Suze Orman. (ISBN 0-609-80186-4) This book explores how your past holds the key to your financial future and helps you take charge of what to do now.
10D. I use a great paperback book with the CR titled "Everything's Coming Up Fractions". The adult instructors and students that I have worked with love manipulatives. They work and they make sense!
10E. I just received the following article from the Washington Post that has bearing on boys potentially falling behind in math (and other school subjects). I found it really interesting. It might be worth looking at the actual NAEP study, too. For a few years, I have been worrying quite a lot about whether boys were hitting some significant barriers in school and post-secondary education, and as the mother and grandmother of two sons and a grandson, this has been of particular concern to me. After reading this article, I continue to think that boys are experiencing social problems and difficulties in entering the workforce and society, as well as performing in school, that are worth looking into very seriously. But it's interesting to learn that perhaps girls are just doing better than before, with some significant obstacles having been reduced or removed for them, rather than males doing worse.
Study Casts Doubt On the 'Boy Crisis'
Improving Test Scores Cut Into Girls' Lead
By Jay Mathews
Washington Post Staff Writer
Monday, June 26, 2006; A01
A study to be released today looking at long-term trends in test scores and academic success argues that widespread reports of U.S. boys being in crisis are greatly overstated and that young males in school are in many ways doing better than ever.
Using data compiled from the National Assessment of Educational Progress, a federally funded accounting of student achievement since 1971, the Washington-based think tank Education Sector found that, over the past three decades, boys' test scores are mostly up, more boys are going to college and more are getting bachelor's degrees.
Although low-income boys, like low-income girls, are lagging behind middle-class students, boys are scoring significant gains in elementary and middle school and are much better prepared for college, the report says. It concludes that much of the pessimism about young males seems to derive from inadequate research, sloppy analysis and discomfort with the fact that although the average boy is doing better, the average girl has gotten ahead of him.
"The real story is not bad news about boys doing worse," the report says, "it's good news about girls doing better.
A number of articles have been written over the past year lamenting how boys have fallen behind. The new report, "The Truth About Boys and Girls," explains why some educators think this emphasis is misplaced and why some fear a focus on sex differences could sidetrack federal, state and private efforts to put more resources into inner-city and rural schools, where both boys and girls need better instruction.
"There's no doubt that some groups of boys -- particularly Hispanic and black boys and boys from low-income homes -- are in real trouble," Education Sector senior policy analyst Sara Mead says in the report. "But the predominant issues for them are race and class, not gender."
Black and Hispanic boys test far below white boys, the report notes. The difference between white and black boys in fourth-grade reading last year was 10 times as great as the improvement for all boys on that test since 1992. Still, the report notes, the performance of black and Hispanic boys is not getting worse. The average fourth-grade reading scores for black boys improved more than those of whites and Hispanics of both sexes.
Craig Jerald, an educational consultant who has analyzed trends for the federal government and the newspaper Education Week, said that "Ed Sector is right to call foul on all the crisis rhetoric, and we should stop using that word, though there are a few troubling statistics and trends that deserve further investigation." He noted a huge gap in writing skills between girls and boys, bad results in reading among older boys, and a sharp drop in high school seniors' positive feelings toward school that is worse among girls than boys.
Michael Gurian, a best-selling author who says boys are in trouble, said in reaction to the report: "I truly don't mind if everyone took the word 'crisis' out of the dialogue." But he said he thought the report "missed the cumulative nature of the problems boys face." The federal education data it cites, he said, are "just a small piece of the puzzle."
According to the report, reading achievement by 9-year-old boys increased 15 points on a 500-point scale between 1971 and 2004, and girls that age increased seven points, remaining five points ahead of boys. Reading achievement for 13-year-olds improved four points for boys and three points for girls, with girls 10 points ahead. Among 17-year-olds, there was almost no change in reading achievement, with girls up one point, boys down one point and girls 14 points ahead.
In mathematics achievement between 1973 and 2004, 9-year-old boys gained 25 points and girls gained 20 points, with boys ending up three points ahead. Thirteen-year-old boys increased 18 points and girls 12 points, with boys three points ahead. Among 17-year-olds, boys lost one point, girls gained four and boys were three points ahead.
The report notes that boys are far more likely to be diagnosed with learning disabilities. Two-thirds of students in special education classes are male. But, it notes, "the number of girls with disabilities has also grown rapidly in recent decades, meaning this is not just a boy issue."
To some, however, it's all about the boys. "At every level of education, they're falling behind," Newsweek reported.
Esquire proclaimed: "We're faced with the accrual of a significant population of boys who aren't well prepared for either school or work."
The Detroit News said that "every year, women increase their presence on campuses nationwide, while men do not."
Some of today's focus on boys might be backlash to legal remedies such as the 1972 Title IX law set up to ensure equality in education for girls, critics say. For several decades, school systems have worked to steer girls into more skilled math and science classes. Now girls in high school appear to be better prepared for college than boys, the report said. But, it adds, both sexes are taking more college-level courses, such as calculus, than ever.
More men are enrolling in college, and the share of men ages 25 to 29 with a college degree, 22 percent, is significantly higher than that of older men. The study did note that women are enrolling and graduating from college at higher rates than men.
The "boy crisis," the report says, has been used by conservative authors who accuse "misguided feminists" of lavishing resources on female students at the expense of males and by liberal authors who say schools are "forcing all children into a teacher-led pedagogical box that is particularly ill-suited to boys' interests and learning styles."
"Yet there is not sufficient evidence -- or the right kind of evidence -- available to draw firm conclusions," the report says. "As a result, there is a sort of free market for theories about why boys are underperforming girls in school, with parents, educators, media, and the public choosing to give credence to the explanations that are the best marketed and that most appeal to their pre-existing preferences."
10F. The Vice-chair of the [National Mathematics Advisory Panel] is Camilla Benbow, who is best known for the hypothesis that there are intrinsic gender differences in favor of males at the highest level of mathematical performance. The Association for Women in Mathematics has urged the removal of Dr. Benbow from the Panel in order to avoid actual or perceived bias against women and girls in the Panel's recommendations. If you are interested in reading a rather lengthy paper about this, here it is:
1980, 1983, 1988 Work:
In 1980, Camilla Benbow and Julian Stanley published an article in Science reporting large gender differences in "mathematical reasoning ability."(1) Their evidence was scores on the SAT taken by seventh graders as part of a talent search for a program at Johns Hopkins University. In their conclusion
Benbow and Stanley explicitly favored (their word) "the hypothesis that sex differences in achievement in and attitude towards mathematics result from superior male mathematical ability . . . [which] is probably an expression of a combination of both endogenous and exogenous variables."(1) In 1983, Benbow and Stanley reported that the male to female ratio of Hopkins talent search participants with scores over 700 was 13 to 1.(2) In 1988, Benbow reported, "the ratio is 12.9 to 1 for the 278 cases reported in Benbow and Stanley (1983b). When in November 1983 SMPY had temporarily completed its national search . . . the ratio remained around 12 to 1." On page 219, she states, "From 1980, the [talent search] samples, have indeed been selected by the same criteria. During this time period there is no evidence for a decrease [in sex difference], rather the opposite." She concluded, "it is clear after the testing of several hundred thousand intellectually talented 12- to 13-year-old students nationwide over a 15-year period that there are consistent [emphasis added] sex differences favoring males in mathematical reasoning ability (or more specifically in SAT-M scores). These differences are pronounced at the highest levels of that ability."(3)
The male to female ratio for students scoring over 700 during the 15-year period was not given explicitly. However, some have interpreted this article as stating that the ratio has remained unchanged for fifteen years.(4), (5)
Critiques of Methodology Used in 1980s Work:
Benbow's 14-page article in Behavioral and Brain Sciences is followed by 34 pages of commentary, mainly from psychologists, that includes critiques of methodology.(6) Eccles and Jacobs discuss Benbow and Stanley's assumptions about students' formal mathematical experiences in light of empirical studies of SAT performance and course taking.(7) Ruskai notes also that the Hopkins Center practice of sending students brochures stating that boys outperform girls on the mathematics SAT could bias results.(8)
New Findings Since 1983: Changes in Talent Search Ratios and Other Measures
Researchers at the Hopkins Center reported that between 1984 and 1991 the average for this ratio was 5.7 to 1.(9) The Hopkins Center brochures for 1988 and 1989 reported ratios of 4 to 1 and 8 to 1 respectively.(4) In 1997, Julian Stanley wrote that the ratio was 4 to 1.(10) In 2005, the Chronicle of Higher Education reported this ratio was 2.8 to 1.(11) The Duke University Talent Identification Program (TIP) is a talent search that follows the Hopkins model. TIP was established in 1980. Its regional talent search covers sixteen states in the southeastern, midwestern, and southwestern United States. TIP talent search ratios are shown in the table below. The TIP researchers wrote in 1994, "These findings clearly indicate that the gender gap in mathematical ability is markedly smaller than the data from Benbow's recent articles would suggest."(12) The decline in talent search ratios is consistent with changes in other measures: 48% of the undergraduate mathematics degrees in the U.S. now go to women, up from 40% in the 1970s;(13) about one third of the PhDs in mathematics going to U.S. citizens go to women (this percentage has more than doubled since the 1970s);(14) women have even begun to make inroads into the rarified air of the prestigious Putman competition: for decades no woman placed in the top fifteen, but in 2004 there were four women in this exceptional group.(15)
Recent Talent Search Ratios Not Cited By Benbow and Colleagues
In 1992, Lubinski and Benbow gave the 13 to 1 ratio. Part of an endnote says that "In American samples, these ratios have been fluctuating over the past decade at least partly as a function of increasing numbers of Asian students entering talent searches. For example, in Asian samples, the proportion of males/females with SAT-M = 700 is 4/1 (this ratio has also been observed in China); in Caucasian samples, the ratio is closer to 16/1."(16) In 2000, although Stanley had stated the ratio was 4 to 1 three years earlier,(8) Benbow et al. cited the 1983 ratio of 13 to 1 without mention of later changes.(17)
Recent Talent Search Ratios Not Cited By Psychologists:
Psychologists and others have used the 13 to 1 ratio. In his 1998 book, Male, Female: The
Evolution of Human Sex Differences, the psychologist David Geary wrote, "The consequences of the sex differences in intrasexual variability are more dramatic for mathematics than for reading and are most extreme in samples of highly gifted people" and gave the 13 to 1 ratio without discussion of any fluctuations.(18) (Geary is a member of the National Mathematics Advisory Panel.) In 2002, psychologist Steven Pinker's 2002 prize-winning book,(19) The Blank Slate, also gave the 13 to 1 ratio -- again, without discussion of later changes.(20) Pinker wrote, "At the right tail, one finds that in a sample of talented students who score above 700 (out of 800) on the mathematics section of the Scholastic Assessment Test, boys outnumber girls by thirteen to one, even though the scores of boys and girls are similar within the bulk of the curve." Pinker cites Lubinski and Benbow's 1992 article but apparently did not read the endnote that accompanied the 13 to 1 ratio.
Also in 2002, psychologist Doreen Kimura wrote in Scientific American, "Benbow and her colleagues have reported consistent [emphasis added] sex differences in mathematical reasoning ability that favor males. In mathematically talented youth, the differences were especially sharp at the upper end of the distribution, where males vastly outnumbered females. The same has been found for the Putnam competition, a very demanding mathematics examination. Benbow argues that these differences are not readily explained by socialization."(21) (Two years after Kimura's article was published, as noted previously, four women were among the top fifteen Putnam competitors.)
Recent Talent Search Ratios Not Cited in National Media
In 2005, during discussion of the remarks of Lawrence Summers, the 13 to 1 ratio, as well as Benbow's subsequent work, were cited in the national media, e.g., U.S. News and World Report(22) and Commentary.(23) The Harvard Crimson said, "Summers said the evidence for his speculative hypothesis that biological differences may partially account for this gender gap comes instead from scholars cited in Johnstone Family Professor of Psychology Steven Pinker's bestselling 2002 book The Blank Slate: The Modern Denial of Human Nature."(24)
1. C. P. Benbow and J. Stanley, "Sex Differences in Mathematical Ability: Fact or Artifact?," Science, 210, no. 12 (1980): 1262-1264, http://www.vanderbilt.edu/Peabody/SMPY/ScienceFactOrArtifact.pdf
2. C. P. Benbow and J. Stanley, "Sex Differences in Mathematical Reasoning Ability: More Facts, Science, 222 (1983): 1029-1031, http://www.vanderbilt.edu/Peabody/SMPY/ScienceMoreFacts.pdf
3. C. P. Benbow, "Sex Differences in Mathematical Reasoning Ability Intellectually Talented Preadolescents: Their Nature, Effects, and Possible Causes," Behavioral and Brain Sciences, 11 (1988): 169-232, http://www.vanderbilt.edu/Peabody/SMPY/BBSBenbow.pdf . See pp. 172, 182.
4. D. Halpern, J. Wai, and A. Saw, "A Psychobiosocial Model: Why Females Are Sometimes Greater Than and Sometimes Less Than Males in Math Achievement," in Gender Differences in Mathematics: An Integrative Psychological Approach, ed. A. M. Gallagher and J. C. Kaufman (Cambridge: Cambridge University Press), p. 66. Halpern et al. write that the ratio is 17:1, probably a typographical error and 13 is meant.
5. M. B. Ruskai, "Guest Comment: Are There Innate Cognitive Gender Differences? Some Comments on the Evidence in Response to a Letter from M. Levin," American Journal of Physics, 59, no. 1 (1991): 11-14, http://www.aps.org/educ/cswp/gender.pdf. See p. 11.
6. C. P. Benbow, "Sex Differences in Mathematical Reasoning Ability Intellectually Talented Preadolescents: Their Nature, Effects, and Possible Causes," Behavioral and Brain Sciences, 11 (1988): 169-232, http://www.vanderbilt.edu/Peabody/SMPY/BBSBenbow.pdf
7. J. Eccles and J. Jacobs, "Social Forces Shape Math Attitudes and Performance," Signs, 11, no. 2 (1986): 367-380.
8. M. B. Ruskai, "Guest Comment: Are There Innate Cognitive Gender Differences? Some Comments on the Evidence in Response to a Letter from M. Levin," American Journal of Physics, 59, no. 1 (1991): 11-14, http://www.aps.org/educ/cswp/gender.pdf.
9. L. E. Brody, L. B. Barnett, and C. J. Mills, "Gender Differences Among Talented Adolescents: Research Studies by SMPY and CTY at Johns Hopkins," in Competence and Responsibility: The Third European Conference of the European Council for High Ability, ed. K. A. Heller and E. A. Hany (Seattle: Hogrefe & Huber, 1994).
12. D. Goldstein and V. Stocking, "TIP Studies of Gender Differences in Talented Adolescents," in Competence and Responsibility: The Third European Conference of the European Council for High Ability, ed. K. A. Heller and E. A. Hany (Seattle: Hogrefe & Huber, 1994).
14. "Annual Survey of the Mathematical Sciences (AMS-ASA-IMS-MAA), Report On The 2004-2005 New Doctoral Recipients," Notices of the American Mathematical Society (2006), http://www.ams.org/employment/2005Survey-DG.pdf. See p. 236.
15. S. Olson, "Nurturing Mathematical Talent: Views from the Top Finishers in the William Lowell Putnam Mathematical Competition," http://www.msri.org/activities/pastprojects/jir/Summary_report.pdf. See p. 5.
16. Lubinski and Benbow, "Gender Differences in Abilities and Preferences Among the Gifted: Implications for the Math-Science Pipeline," Current Directions in Psychological Science, 1(1992): 61-66, http://www.vanderbilt.edu/Peabody/SMPY/CurrentDirections.pdf
17. C. P. Benbow, D. Lubinski, D. Shea, and H. Eftekhari-Sanjani, "Sex Differences in Mathematical Ability at Age 13: Their Status 20 Years Later," Psychological Scientist, 11, no. 6 (2000): 474-487, p. 474, http://www.vanderbilt.edu/Peabody/SMPY/SexDiffs.pdf
18. D. Geary, Male, Female: The Evolution of Human Sex Differences (Washington, DC: American Psychological Association), pp. 314-315 cites Benbow, 1988, Benbow & Stanley, 1980; Stanley, 1993.
19. See list of prizes at http://pinker.wjh.harvard.edu/books/tbs/prizes.html
20. S. Pinker, The Blank Slate: The Modern Denial of Human Nature (New York: Viking, 2002), pp. 344-345. The citations for this statement are: Hedges and Nowell, "Sex Differences in Mental Test Scores, Variability, and Numbers of High-scoring Individuals," Science, 269 (1995): 41-45; Lubinski and Benbow, "Gender Differences in Abilities and Preferences Among the Gifted: Implications for the Math-Science Pipeline," Current Directions in Psychological Science, 1(1992): 61-66, http://www.vanderbilt.edu/Peabody/SMPY/CurrentDirections.pdf.)
21. D. Kimura, "Sex Differences in the Brain," Scientific American, May 13, 2002,
http://www.sciam.com/article.cfm?articleID=00018E9D-879D-1D06-8E49809EC588EEDF&pageNumber=3&catID=9 The article does not give a reference for this statement.
22. J. Leo, "What Larry Summers Meant to Say," U.S. News and World Report, February 14, 2005,
23. C. Murray, "The Inequality Taboo," Commentary, September 2005,