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Guest Discussion with Myrna Manly on Assessment in Mathematics

Full Discussion Thread

### Discussion Introduction and Summary

Dear Everyone,

I would like to welcome Myrna Manly to our List this week. A reminder that Myrna will be responding to our posts once per day.

I am very interested in hearing what you all, as well as Myrna, have to say about the following prep question that Myrna provided:

- Computation skills are easy to assess. How can we assess other important aspects of mathematics like strategic problem solving, conceptual understanding, and reasoning?

How do folks approach assessing these skills? Do you use any existing tests or assessments to do this? Which ones? Do you develop your own? What do they look like?

What are some of the things you do in the classroom to try and gauge a person’s knowledge and abilities of the more abstract concepts in math?

Thanks!

Marie Cora

Assessment Discussion List Moderator

Hi, I have one for Mrs. Manley:

My student has a learning disability with math. He is in his thirties, made 500's on all his GED tests except writing which was a 420. HE Passed. But he cannot get passed 400 on math. He does not respond with logical methods when doing problems. He cannot make change so he cannot pass a math test for employment either. This is sad. This has been going on for two years.

I have started giving him worksheets with the answers and he has to set it up and find how I got it. Do you think this reversal will help him? what more can I do??? He and

I are both frustrated! What seems so easy to me is impossible for him. What he knows yesterday he cannot do today.

I teach at Halifax Community College (NC) FT and at SVCC in Emporia (VA) PT.

Brenda Cousins

Brenda,

You describe a very difficult situation. I really have no particular expertise in dealing with math learning disabilities. The GEDTS does allow some accommodations for those with documented disabilities - Have you tried to qualify him for that?

Are there others who can give Brenda some advice?

Myrna

Brenda and others,

Regarding LD and adult math learning, there is a very helpful book chapter titled, "Teaching mathematics to adults with specific learning difficulties." It is in the book, "Adult Numeracy Development" (2000) edited by Iddo Gal and published by Hampton Press. The authors, Martha Sacks and Dorothy Cebula, are two individuals with special education/disability credentials and a particular interest in adults.

The authors describe a number of different types of learning difficulties relating to numeracy learning, provide suggestions for identifying them (informally, not using validated assessment instruments) and suggest appropriate strategies.

Lynda Ginsburg

Senior Research Associate, MetroMath

Rutgers University

Brenda, et al.---

In the situation you describe, I would recommend starting the GED Math instruction with learning the GED math notation (how the test asks you to add, subtract, multiply, and divide) and the Order of Operations. This will start to use your student's high literacy level to "get into" the math test. Then I would give only set-up problems, which necessitate the thinking through of the problems but do not require calculations. Meanwhile, I would have the student officially diagnosed with a math learning disability so that a calculator could be used on both parts of the GED Math test. (Go onto our website, www.doe.mass.edu/ged, then click on the link, "Applicants with Disabilities." From that you can print the appropriate Accommodations Request form, which will give you a good idea of what kind of documentation is needed.) Hopefully your student can then go from the proper set-up of the problem to the answer using the calculator to do the calculations.

In any case, if you have any further questions, please feel free to e-mail me directly: rmechem at doe.mass.edu.

Good luck in your quest.

Tom Mechem

GED State Chief Examiner

Massachusetts Department of Education

"GED to Ph.D."

Hello Myrna and All ~

Myrna, thanks for joining us for this discussion! Sounds like it will be a good week ahead. I have a question for you and the group.

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?

I’ve asked a similar question on the Women and Literacy List. I’d be glad to collect any strategies or resources posted to either list (pertaining to math anxiety), and share them with the group when the discussion is over.

Best, Jackie

Jackie Taylor, Adult Literacy Professional Development List Moderator

Hi Jackie,

I had a similar student in my GED class who would understand algebra, and then would forget percentages. Then she would relearn percentages and forget algebra, for example. She continued taking the GED test and getting 380, 400, 370, etc. She had been with our GED program for almost three years.

What finally helped her were 1) the instructor creating lots of additional problems for her to practice beyond what was in the book 2) Skills Tutor software which she did additional study on at home and through the entire summer and 3) one of her classmates started peer tutoring with her after passing the GED exam. For some reason students sometimes can explain concepts better to another student than we can. Students sometimes have the same challenges with learning the concepts, and having this additional support really helped my student reach the 410 mark. I hope this helps.

I know how it feels to wonder if a student will ever pass the GED test. :) I believe that no matter how fancy we get with learning tools, there is no substitute for practice, practice, practice, good old fashioned determination, and a lot of support and confidence from someone who believes in them.

Tina

Tina Luffman

Coordinator, Developmental Education

Verde Valley Campus

Jackie said:

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?

Tina responded:

I know how it feels to wonder if a student will ever pass the GED test. :) I believe that no matter how fancy we get with learning tools, there is no substitute for practice, practice, practice, good old fashioned determination, and a lot of support and confidence from someone who believes in them.

I will add that, in my experience, math anxiety varies with each person who suffers it and teachers need many different interventions to try in order to conquer it. Certainly math-anxious students need work to reverse their negative perception of their math abilities. Many can do it by opening up about their feelings and their understanding of math with a supportive and knowledgeable person.

However, we need to recognize that those feelings most often have a basis in their experiences with math. They may be the victims of teachers who thought that there was only one way to find an answer or to solve a problem. Often students memorize procedures without understanding what each step does and why it works that way. It's no wonder that they panic at the thought of having to remember the procedure when they are under the pressure of taking a test!

I'd like to start a list of interventions or techniques that you all can add to during the week.

- For computation problems, (including all operations with whole numbers, fractions and percents) work on estimating an answer. Use different approaches to estimating so that students recognize that there is not just one 'rule' to follow.

- Insist that your student talks about his/her reasoning while solving a simple problem that you know she/he can do. (It may be easier to begin by sharing with another student.) You want students to know that their reasoning is as important as getting the right answers.

- Judith Diamond mentioned practicing computation with real-life familiar situations that can help them to understand what they are doing as well as providing a reference when trying to remember how they did it.

It's your turn - what can you add?

Myrna

One strategy I have used for bringing issues of fear, anxiety, and negative self-image regarding math to the fore for open discussion is creating a "math history graph." Each person creates his/her own graph, with school grade levels (K-12) and then adult years across the horizontal axis and 1-10 on the vertical axis. They then draw a line graph charting how they felt about math ("On a scale of 1 to 10, how did you feel about math at each grade?"). All my learners have at least one deep dip and maybe some shallow ones. We all (me included -- I sometimes go first) explain our graphs and tell the stories that go with the dips. My own negative stories are pretty minor, but I think everyone's feelings are validated when we all participate. Often there are opportunities for most to see that feelings were caused by events and the situations don't have to be repeated. Often the stories are, "I didn't understand and the teacher wouldn't explain it again" or "I didn't want to ask again..." or "I couldn't pass the time test..."

Lynda Ginsburg

Senior Research Associate, MetroMath

Rutgers University

Just a brief comment about Math and LD. If skills are taught through connections both with each other and daily life (one we all use, money and percentages ) and students need to practice activities that integrate those skills (such as making a budget, creating graphs and charts for that budget -- including percentages, fractions, percents and addition, mult., div., sub.), then using one skill will generate memory of others.

Judith Diamond

Hi Judy,

Yes, I do agree with you about using the practical aspects of daily life to help math connect with students. It is a rule of mnemonics to link what is known to what is not known to help students remember.

I also like to have the students work together in groups after giving the lesson to hear how they perceive the material and to locate error in understanding. When students work together, they have to restate what the teacher teaches and then explain it to someone else. That helps with memory retention.

Another great tool with math is the manipulatives. We have various colored disks that represent fractions. One disk is whole which equals 1 or 1/1. The next is broken in half, and another into thirds and so on. When students lay three 1/4 disks on top of a 1/2 and a 1/4 disk, they can see in a tangible manner how 1/2 + 1/4 really does = 3/4.

I also tell students to draw the word problems to figure out how to solve the math problems. Some students really work well with drawing the five piles of ten logs to know that they need to multiply to see how many logs they have.

Tina

Tina Luffman

Coordinator, Developmental Education

Verde Valley Campus

I’ve added Lynda’s graph idea and Tina’s suggestions below to the list of ideas. Great additions!

Tina mentioned using manipulatives to learn about fractions and that reminded me of the website from NCTM that I found: http://www.nctm.org/news/assessment/2005_12nb.htm Will This Be on the Test?

Check it out and see what you think about the test item involving fractions. Too tricky or really clever?

Myrna

Myrna,

In your book The Problem Solver you tackle algebraic concepts in the very beginning of the book. This is in contrast to many books on the market. I use this technique as well. My students are caught by the fact that algebra (a scary term for some) is so simple and can be used for many reasons. However, some people are skeptical that this will result in better scores or better understanding.

Can you discuss the contrasts of learning math beginning with whole numbers and working up to algrebra versus using algebra as a problem solving method with all number systems throughout the math learning process. Are the results better scores sooner?

Thanks,

Lisa Mullins

Hawkins County Adult Ed

Rogersville, Tennessee

Hi Lisa,

I'm happy to hear that you and your students are enjoying the book. Introducing algebraic thinking early in student's math study has now become widespread in the reform math efforts in K-12. (It is also a hallmark of the new EMPower series for adults.) In 1992, when I wrote the first edition of the book, I based my early-algebra-integration decision on my own experience as one who had taught algebra to students at many levels and as an 'insider' with respect to the GED Math test. (I had just left my job at GEDTS.)

The overarching principle when formulating items for the GED math test is to assess the "major and lasting outcomes and skills of a high school education." For the most part, this means that the skills and concepts that are tested are ones that have some practical value. With respect to algebra, I felt that using the concept of a variable, solving simple equations, and graphing linear functions were the most obvious topics to be represented.

As an algebra teacher, I had seen the difficulty that students had in making the transition to using variables and had added extra lessons to the textbooks that reviewed arithmetic principles by using variables in place of specific numbers - that is, I used algebra to generalize arithmetic. So, it was an easy decision for me to integrate algebra early - both from a mathematics pedagogy standpoint and from an adult student attitude perspective (knowing that many feel insulted by a review of arithmetic even if their entrance scores indicate that need).

As to your question about the results obtained when students are introduced to algebraic ideas early in their mathematics study, I'm afraid that I have no data to substantiate better scores sooner. (That topic may be one that a practitioner would like to investigate as a project for the ANN practitioner research grants.)

Thanks for the question,

Myrna

I would agree with the recent posts about the materials presented in both Myrna's GED Math Problem solver and the new Empower series. Since our topic of discussion is math anxiety and assessment, I would say that this approach to teaching math content conceptually definitely helps to reduce the anxiety students bring to the math classroom. Recently I have been piloting the Empower books on Benchmark Fractions and Split it Up and am amazed by how quickly and confidently my students can see the relationship between decimals, fractions and percents. What is even more amazing is how easily they can solve percent problems, particularly percent problems that require finding the total. All of this is done conceptually thinking about what the part is and building to the total.

Pam Meader

President

Adult Numeracy Network

Hi there. I thought you might be interested in a math resource that was developed by Steve Hinds, a staff developer for adult literacy programs in the City University of New York. Here's a quote from a workshop Steve recently offered at the Literacy Assistance Center in NYC. He says "Adult Literacy programs traditionally limit students in low-level classes to computation practice out of workbooks. Algebra, data and geometry topics are considered too difficult for these students until they have 'mastered the basics.' Steve believes that students can increase their mathematical reasoning, number sense and enjoyment of math through the kinds of exercises he presents on the CUNY web site. Check it out. Go to <www.literacy.cuny.edu>. *(You need a user name and password to enter this site, but you can go to the CUNY web site to inquire further.)*

Mae Dick

Thanks, Mae, for this web site. It is encouraging to see that more people around the country are recommending that all content areas of math be studied in ABE at all levels of student learning. It brings up an interesting question:

"What is influencing so many ABE teachers to focus only on numerical computation procedures at the early levels?"

Is it the state standard documents, the workbooks, the NRS indicators, the TABE test, or their own experience learning math? What do you see out there?

Myrna

Hello Myrna and all,

I enjoyed the link you gave us yesterday. I am very interested in the open-ended questions section. I think it is a great guide for formulating open-ended math questions.

One challenge I encounter when I provide open-ended questions for my learners is being prepared for the "out of the box" thinking. In other words, when a learner thinks of the problem in a original way and solves it correctly, I am left dumbfounded as to why it worked. What should I do at that point?

Also, the learners often want a fast, set in stone, rule to help them solve a problem. For example, percentages can be calculated using a number of strategies. Some students want one good way to solve percentages and they are confused if I provide alternative methods of solving. I think this contributes to math anxiety. How would you handle this situation? Thanks,

Lisa Mullins

Tennessee

Lisa said:

"Also, the learners often want a fast, set in stone, rule to help them solve a problem. For example, percentages can be calculated using a number of strategies. Some students want one good way to solve percentages and they are confused if I provide alternative methods of solving. I think this contributes to math anxiety."

I encounter this issue a lot when I do workshops with teachers. From previous posts you know that, in my opinion, it induces anxiety when students think that there is only one right way to get an answer to a problem and they need to remember it during the stressful atmosphere of a high stakes test like the GED. A person who can be flexible in solving problems is one who is confident both in testing situations and in meeting the demands of the real world.

I recommended using estimation, not only for its intrinsic value in the real world, but also as a vehicle to convince students that they can think differently and still be correct. (They are more likely to accept that with estimation than with something like computation techniques that were taught in such a didactic manner.) Others have commented that group work is also helpful in that they see others' methods and have the opportunity to discuss them. Being flexible instead of being at the mercy of "the right way" is a goal that teachers need to work on every day with their students. We all know that the key to being flexible is having a deeper conceptual understanding of the subject than merely knowing a procedure.

Sheila Tobias uses the words, "learned helplessness" in describing math anxious people. On a recent Oprah show where Bill Gates was the guest and the topic was the burgeoning HS dropout problem, they used the same phrase to characterize the attitude of the majority of dropouts. They have been encouraged to imitate, not to think for themselves.

Myrna

Myrna, Judy, and others,

I am cross-posting this question to both the Women Literacy and Assessment lists, and hope that anyone who wishes to will join in.

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 an 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 "aquaphobic" 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?

David Rosen

I attended some of San Francisco's best public schools and so I thought I was to blame for my learning anxieties.

I really didn't understand the process and mechanics of writing until I participated in the Bay Area Writer's Process while I was struggling with my Ph.D. dissertation.

Here are some of the things I learned about writing and learning almost anything:

- Writing (learning) is a process

2) Remote writing, mind mapping, experimentation all help one to relax...use colors or crayons to begin if that will relax you... - Writing need not be an isolating and lonely process...writing can be and probably should be shared.
- Finished, published products have been shared with many people before reaching your eyes.
- "Writing Prose" is the book that helped me crack a pretty serious writing anxiety.

Bertie

I’ve found that reading about writing from prolific and successful writers — their struggles, methods, anxiety — has been inspirational.

A recent website I visited is Thomas Sowell’s page on his own experiences as a writer (http://www.tsowell.com/About_Writing.html). I just want to make the disclaimer that if you’re an editor or have editorial aspirations (like me), you will probably want to skip the parts he has to say about working with editors, copywriters, and the rest of the publishing world...While he is humorous(!) and takes a light-hearted approach, it’s hit home a couple of times...

Good luck, and keep writing!

Varshna Narumanchi-Jackson

It is uncanny that David would mention puzzles and swimming as analogies to math anxiety. We just met a few months ago and he doesn't know that, not only am I a devoted puzzle person, but I taught swimming for many years!

I started to write some detailed comparisons between the steps in learning to swim and similar benchmarks when learning to be comfortable with math, but that soon got too complex. However, I can confidently say that in both cases, an anxious person overcomes fear by becoming familiar with how the "medium" works. For example, the learner gains security by knowing how buoyancy is affected by the different positions of your body (you can float and glide on top of the water more effectively when your head is submerged) and how numbers act in consistent ways in various applications (the properties hold whether you are finding an average or a perimeter.

Stimulating questions!

Myrna

Hello Myrna,

Please do write a detailed comparison between learning to swim, doing puzzles, and learning math -- on the ALE Wiki and/or for publication elsewhere. The complexities and details would be fascinating. Many of us could benefit, as teachers and learners, from your experience.

David J. Rosen

One of the greatest joys of being a math teacher is to see students dread and hate of math turn to joy for math. One student that comes to mind just recently graduated from a technical college. She shared with me that it took her 9 years to consider coming back to school and facing math. I was so fortunate to have her for a student and watch her fear of math melt away. One way I address math phobia is through journal writing. Students are required to respond to a math prompt, provide examples, make connections and lastly to reflect on their learning. It is in the reflections that the fear and struggles are revealed. I journal back, giving them encouragement and offering suggestions.

This particular student's journals showed her excitement in finally understanding math and seeing connections. She continues today to send me emails about math websites she has found or successes she has had since being in college. She was so proud to share that she got an A in technical physics and graduated with honors.

I truly believe we must develop a safe environment for math learners, one in which they dare to take risks and not feel stupid in trying and one that offers support in their struggles.

Pam Meader

President, Adult Numeracy Network

Hi Pam,

One of the things that is so enjoyable about an online discussion is that occasionally you read something that changes the way you see things and that you will clip and save and use. Your idea of journals and how you structure them might not resonate with all students…for some writing is just another headache…but I can see it being a really meaningful connection both to math and to their teacher for others. Thanks.

Judith Diamond

Adult Learning Resource Center

Greetings,

Judith has summed up the experience of this week of discussion very well. While every comment may not have been perfectly suited for your particular situation, we did learn from each other. My week as a guest on the list serve is over, but I will continue to be available here as just another member of the assessment discussion list. Thanks to Marie for arranging this opportunity to bring math and numeracy to the forefront and thanks to all of you who participated.

Myrna

Hi everyone,

What a great and rich discussion this is, thank you all for making this so! There has been a wonderful exchange of interventions, techniques, and strategies to draw from in working with students in math. This is the last day with our guest, so I encourage you to ask any final questions or make any comments.

Myrna asked this question in a post or two ago and I also would like to hear from folks on what they think:

"What is influencing so many ABE teachers to focus only on numerical computation procedures at the early levels?"

Is it the state standard documents, the workbooks, the NRS indicators, the TABE test, or their own experience learning math? What do you see out there?

Myrna also mentioned ANN in another post, and I just wanted to make sure folks had the information on this: Adult Numeracy Network http://www.literacynet.org/ann/

Ok! Let’s hear any final thoughts! It’s your last chance!

Marie Cora

Assessment Discussion List Moderator

Myrna and all,

I believe the reason I place many students into numeracy workbooks first is that I want to be sure students can do basic adding, subtracting, multiplying, and dividing so that when they perform the other functions of fractions, decimals, percents, algebra, and geometry, that their incorrect responses are due to not understanding the new level of math rather than just making a calculation error. Of course, even we as instructors still make calculation errors, but I would like to minimize the frustration. I have had numerous students with math anxiety or other math disability get really frustrated with themselves when getting the answer wrong adding fractions, for example, when all they did was make a simple calculation error. Identifying where the error came from is paramount to these students' sense of capability.

The primary reason I begin most students with basic calculation skills is due to our program's methodology. We are instructed as new instructors to give the TABE and then to give a math pretest even if the student is 11th grade + level. (One interesting finding I have is having recent high school students come to me able to do geometry and algebra, but they have forgotten how to divide. I am sure many of you have had similar experiences.) This pretest identifies challenge points in +, -, X, & ./. as well as decimals, fractions, percents, ratio, proportion, and measurement. Then we are instructed to place the students into the lowest level book and work them up to the top level using study guides. We are a highly linearly structured program. The reason for this linear system setup, I believe, is indeed because we often only see students for a month before they disappear, and we need to get an educational gain from these students in about as many weeks to maintain our funding.

However, I do have the entire class do all lessons no matter what their grade level is on their most recent TABE. Even if a student just started coming to class and are at a fourth grade math level, he or she will do the algebra lesson with the rest of us. I am a firm believer that just because a student doesn't know his/her timestables yet, that doesn't mean that same student won't be able to understand that if 10 + a = 12, a = 2. I also believe that when a student sees that he/she can do algebra, it builds self esteem.

I hope this answers you question. I hope to hear other people's ideas as well!

Thanks,

Tina Luffman

Coordinator, Developmental Education

Verde Valley Campus

Tina and all,

Each of your postings brings up so many interesting aspects. For example, in Tina’s message below, I see that the program uses the TABE to diagnose learner weaknesses in computation when they enter the program and then focuses instruction on the computation basics by using workbooks and study guides. It seems as though Tina is agreeing with that policy in that the students show a quick gain in skills and funding is maintained. That is certainly an important aspect – we need to keep the doors open.

She also mentions that she includes all levels of students in an algebra lesson and even the low-level learners gain self esteem (and learn about variables and making generalizations) by succeeding with it. However, it is safe to assume that this learning does not have direct value in helping to raise their scores when they retake the TABE for accountability purposes because the test items at the early levels concern themselves mostly with naked computation (no context). This exposes a huge problem for math assessment, and in turn for math instruction, in ABE. If there is value added to the students’ learning by early algebra exposure, it should be recognized in the accountability measures.

In the meantime, what can a program or its teachers do? You all have made great suggestions: use manipulatives or realia to facilitate deeper understanding of the operations with number, teach computational skills along with conceptual understanding, insist that computations be motivated by a real situation or an application in measurement or data, use benchmarks and estimation as a check for reasonableness. These tactics serve both masters – improving student understanding and attitude and, at the same time, raising test scores. Actually, there may be a third – keeping students in the program longer than a month.

Thanks for sharing this, Tina. I also would like to hear other’s opinions.

Myrna

Tina and all,

Most adult education workbooks still use the scope and sequence that you've referred to below (add, subtract, etc. with whole numbers before moving on to fractions, then decimals, then percents . . . and, if students are fortunate enough to make it through all that, they tackle algebra). However, in K - 12, the curriculum is now typically based on the research on how people learn math. Algebra, data, number sense, and geometry are taught at all levels and are integrated.

It's very rare to find an adult who cannot figure out what half of an amount is. Yet, we don't allow them to work on fractions until they have mastered all their whole number facts. It's actually much easier to figure what 1/2 of 240 is than to multiply 240 x 24 yet that's not the order of skills presented in typical adult ed. math workbooks.

You can show students the application of number sense skills by having them explore geometry concepts such as perimeter and area. Students, when they draw pictures of rectangular shapes can add and group and see how multiplication is repeated addition.

They can explore algebraic reasoning by looking at patterns in their lives: for example, if I make $10 an hour, I can make a simple table to show how much I would make in 2 hours, 5 hours, etc. Again, this gives them an opportunity to practice their basic facts but in the context of algebra. Those simple patterns (such as $$ per hour) lead to general rules, which can then eventually lead to expressions (total pay = $10 x number of hours worked).

Given the opportunity to collect simple data (such as those who have children and those who do not), students can then create simple graphs and begin to make verbal comparisons, including fractions and percents (over 50% of the class have children).

This early exposure to algebra, geometry, and data, along with number sense, will ensure that students can apply what they are learning in different situations rather than having to learn isolated skills before they understand how those skills are used in other contexts.

Donna

Donna Curry

Center for Literacy Studies

University of Tennessee, Knoxville

Hello Myrna,

As you know, the National Council of Teachers of Mathematics (NCTM) several years ago established standards for the teaching of mathematics. These were the inspiration and basis for adult mathematics curriculum frameworks standards in my state, and possibly others. I believe these standards are embraced by the Adult Numeracy Network. Curriculum materials (EMPower, for example) have been developed to help teachers who want to teach to these standards.

Do we have any adult math assessments which are congruent with these standards? If so, which ones?

If the most widely used pre-post assessment for measuring adult math level gains (Educational Functional Level in NRS language) is the TABE, and if the TABE is measuring the wrong things, then doesn't that mean that teachers who are effectively teaching math in the right way, and students who are learning to think mathematically, to get the most important mathematics learning, are being punished and penalized?

And, from a national perspective, doesn't that mean that the NRS math level gain data are not valid?

Is it time for a revolution in adult numeracy assessment? Should the federal government be making that investment if the private sector is not interested?

David J. Rosen

Hi David and all.

Your statements in the message below are powerful ones. It is indeed time for a revolution in adult numeracy assessment. And, as in any revolution, we can use help from both the grass roots and the establishment.

Although our present-day politicians seem to believe that they need to overstate their side of an argument in order to get what they really want when a compromise is reached, I think we should be clear from the start as to our position. So I will try to amend your statement a little (and welcome suggestions from others):

"If the most widely used pre-post assessment for measuring adult math level gains (Educational Functional Level in NRS language) is the TABE, and if the TABE is measuring ONLY A NARROW BAND OF MATHEMATICAL SKILLS, then doesn't that mean that teachers who are effectively teaching MATHEMATICS IN A FULLER SENSE, and students who are learning to think mathematically to get the most important mathematics learning, are being punished and penalized?

And, from a national perspective, doesn't that mean that the NRS math level gain data are not valid?"

We are not saying that computation algorithms are the WRONG thing, but that they are not the ONLY thing. In addition, we do not yet have the kind of evidence that is required to say that our (and NCTM's) way of instruction is THE RIGHT way. But we are saying that the most important mathematics for today's requirements is not being assessed so the validity of the assessment is in question (using validity to mean the degree to which an instrument is representative of the domain it is testing.)

I have heard numerous complaints about adult numeracy assessment from all areas of the country. In Massachusetts they funded the development of a new test. What do you know about its composition?

Myrna

Dear Colleagues,

I would like to thank Myrna Manly for being our Guest last week and facilitating a super conversation on math and assessment! Thanks as well to all of you who contributed to the discussion – I’m sure subscribers found the discussion as interesting and as informative as I did.

I will prepare the Math Discussion in user-friendly format, and post it this week at the following locations for your use (I’ll send out an alert when it’s posted):

- The archive on the Discussion Lists Homepage (http://lincs.ed.gov/lincs/discussions/discussions.html): click on the Guest Speaker button in the left toolbar for the archives of Guests on the NIFL Lists.
- The ALE Wiki Assessment Section (http://wiki.literacytent.org/index.php/Assessment_Information): click on Discussions.
- You can read the entire thread now if you go to the Assessment archive at: http://lincs.ed.gov/mailman/listinfo/Assessment: click on Read Current Posted Messages.

Thanks again to Myrna for leading such a wonderful discussion on math and assessment. For anyone who wishes to continue the discussion, I encourage you to do so – there were a number of points and questions raised toward the end of the week that I’ve no doubt folks have opinions about.

Thanks to all again,

Marie Cora

Assessment Discussion List Moderator

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