#
The State of Math Standards

July 25, 2007

## The State of Math Standards

**Guests: Francis M. “Skip” Fennell**, the president of the National Council of Teachers of Mathematics;

**Tom Loveless**, a senior scholar at the Brookings Institution; and

**Sean Cavanagh**, a staff writer for

*Education Week*.

**Sean Cavanagh (Moderator):**

Let’s get started with today’s online chat, which focuses on the state of math standards around the country. With all of the talk about the need to boost students’ skills in math and science, many state and local officials are grappling with the question of how high a bar they should set in math. Tom and Skip will provide some of their thoughts on this topic.

Question from **Ryan Grant, 1st Grade Teacher, Medical Lake School District**:

My concern with strengthening math standards is that we risk leaving many behind in the rush to get ahead. Is there a way to balance our societal need for more thorough math instruction with the reality that many kids struggle with mathematics?

**Tom Loveless:**

I understand the concern. It does take some kids a longer time to learn math than others. We would truly be leaving these children behind, however, if we didn’t make sure that they learn the mathematics that they need to know.

Question from **Darnel Grandell, Math Specialist, NCCVo-Tech School District**:

We are a high school district and have been teaching an integrated curriculum for 8 years. We are always struggling to keep teachers and parents and colleges convinced that this curriculum is as good or better than any traditional algebra sequence. When the committee writes focal points for high school, I truly hope it won’t go to all algebra standards for 9th grade, geometry standards for 10th grade, algebra 2 for 11th grade. Some of us have worked too hard to keep the flavor of the National Standards to take steps backwards if this happens. What are your comments?

**Francis M. “Skip” Fennell:**

NCTM’s High School Curriculum Project is just beginning. Our writing group meets in a few weeks. Our approach will not be to exclusively endorse or support a single subject (algebra, geometry, etc.) or integrated approach to high school mathematics. We will examine major issues which include important mathematics for the high school years, etc. and then move toward additional publications which may, then, get at specifics (algebra, integrated, etc.). I don’t sense, in any way, that the publication(s) would be a step backward.

Question from **Leslie Skantz-Hodgson, Director of Curriculum and Media Instruction, Smith Vocational and Agricultural High School**:

Just what exactly are other countries doing, that we are not, to get high performance in math?

**Tom Loveless:**

No one knows for sure, but I’ll give you my best guess. High achieving nations value mathematics, stress its importance starting even before a child enters school, have high expectations for mathematical learning in the elementary grades, and put most students through a rigorous set of high school math courses. Elementary and middle school teachers have taken mathematics courses offered by college math departments. In addition, the curriculum is focused on only essential topics; textbooks are lean and concentrate on a few key ideas.

Question from **Jeanne Cerniglia, mathematics teacher, JRL Middle School, Southeast Local District, Wayne County, Ohio**:

There seems to be a move to go “back to the basics” (skills). While skill mastery may be lagging, my concern is in the area of critical applications - especially in the area of data analysis as it applies to functioning as a responsible citizen nationally and globally. Where can I find research that explores how to connect mathematics and general critical thinking strategies?

**Francis M. “Skip” Fennell:**

I feel that there are critical foundations that are building blocks to learning mathematics. I don’t sense that experienced teachers who know mathematics and student learning have ever left or placed less emphasis on these foundations. Context or as you note, critical applications are helpful and important in showing how foundational topics are used. Such contexts are readily available, particularly at the middle school levels, where you teach. You might look for research from the Jasper Woodbury project as a start re: the importance of context in learning mathematics.

Question from **Neal Capone, K-12 Math Trainer, Regional School Support Center**:

With increased accountability it seems many school leaders are focusing on what they know, getting down to “basics” and returning to “traditional” mastering of procedural based math absent of deep conceptual understanding. In the wake, districts are leaving behind NSF funded progams (whose name is being smeared) and the essential elements of math instruction; Representation, contextualizing math, Problem Solving, Communication, and Reasoning. What can be done to maintain accountability but not allow it to cause administrators to overlook years of what research tells us about learning in an attempt to get a quick math score fix?

**Francis M. “Skip” Fennell:**

Great question! Of course there are foundational topics which we want all students to know and know well. Work with whole numbers, fractions, and geometry are essentials for later mathematics learning. BUT this would not be the entire curriculum. Additionally, the curriculum is more than just topic exposure and getting correct answers on tests. We want students to be able to talk about the mathematics they are learning. We want students to use mathematics. Finally, mathematics is learned with ongoing opportunities for all students to solve problems - every day. Mathematics learning is much more than the quick math score fix you have noted above. Our challenge is to make sure we do it all - make sure students, all students, are proficient with important mathematics in settings which regularly cause them solve problems, make connections, and reason.

Question from **Jane Duffey, Academic Dean, Norfolk Christian Schools:**

In my 20+ years in education, many of which were in math education, I have seen that students do well when the teacher KNOWS math. It’s not about the textbook, the number of manipulatives, NCTM Standards, high stakes tests. It’s about teachers who understand math concepts. It seems, especially at the elementary level, that the focus is on reading. Although important, few teachers really “get it” in math. When that foundation is weak, it sets the stage for the rest of the student’s math life. What is the answer in teacher education?

**Tom Loveless:**

I agree completely. We need to make sure that all teachers who are going to be teaching mathematics know te subject, including elementary school teachers. As a former 6th grade teacher myself, I know this has not always been the case.

Question from **Carole, Policy Analyst**:

Should there be more focus on the skills and abilities students need going into each math courses to better ensure success?

**Tom Loveless:**

Yes. We need to be much clearer about the skills and knowledge needed to suceed at each grade level in math. The problem has always been that we havn’t defined the curriculum specifically enough to accomplish that task. That situation is improving, however.

Question from **Jon Joseph Madison WI School System**:

The most important mathematics I teach high school learners is the math of daily living - doing taxes, computing percents, understanding a mortgage. One of the reasons that parents can’t help the students with the type of math we currently teach is because they have never used it since they graduated from high school. Granted, some students need algebra, geometry and calculus but for the vast majority is this really required?

**Tom Loveless:**

Students must have a thorough grounding in arithmetic, that’s for sure. But an awful lot of jobs in the new economy require knowledge of algebra and geometry as well, and there is no reason why the vast majority of students can’t master those topics. Other nations do it, and so can we. By the way, Teaching the New Basic Skills by Richard Murnane and Frank Levy is a great book to read on this question.

Question from **Mary Sowder, doctoral student, University of Nevada, Las Vegas**:

What have been the effects of NCLB on NCTM Standards? Has NCTM allowed its vision for reform to be compromised by reactionary politics?

**Francis M. “Skip” Fennell:**

The Principles and Standards for School Mathematics (PSSM) were published in 2000, prior to the authorization of No Child Left Behind. The Curriculum Focal Points (2006) did take into account that teachers in this country must assess students every year in grades 3-8, hence our Focal Points are by grade, rather than grade band. However, this decision was to assist teachers at their level of influence - by grade.

Question from **Jon Joseph Madison WI School System**:

The countries that are generally “high performing” do not cope with the type of diversity that we cope with here in the U.S. In addition, those countries do not require all students to reach the same high standards. Some tracking is allowed. Should, and if so why, should this country require the same high math standards for all students?

**Tom Loveless:**

Some countries track more than the United States, others less. But even in a country like Germany, which begins tracking at age 11 or so, students in the vocational tracks receive a curriculum that includes solid mathematics. In Japan, a nation that scores much higher than the US on international math tests, tracking does not begin until high school. The expectations for what all 8th graders will learn in math are much higher than the US. As for diversity in American schools, that makes it, in my view, even more imperative that we have a high--but attainable--standard for all students to meet.

Question from **Bruce Middleton, Math Science Coordinator, Orange County Schools (NC)**:

The current math standards focus on building math understanding at all grade levels while the public calls for a return to factual recall as an indicator of success. Will the National Math Advisory Panel continue to champion teaching for math understanding?

**Francis M. “Skip” Fennell:**

The National Math Panel has five task groups working toward the completion of a final report (go to the National Math Panel website to see the reports provided at the Miami, FL meeting). These include task groups in Conceptual Knowledge and Understanding (note the word understanding), Learning, Instructional Strategies, Teachers/Teaching, and Assessment. My opinion is that “math understanding” as noted above is important to the Panel - across most, if not all, of the task groups.

Question from **Anane Olatunji, Senior Research Scientist, George Washington U.**:

Why have we not made the same strides in mathematics instruction as in reading? What’s different about learning mathematics compared to other subjects?

**Tom Loveless:**

Actually, the NAEP data show the opposite. Math scores for 4th graders are up approximately two grade levels since 1990, but reading scores have barely budged. The two subjects differ in several respects. Most importantly, math learning appears less dependent on the experiences and knowledge that children bring from home. The mathematics that children learn is primarily what they are taught in school, whereas many children come to school already reading fluently.

Question from **Joan Rooney Vice President for Provider Management, Tutor.com**:

We are an online, immediate access tutoring service offering help in all math subjects including algebra 1 and 2, geometry, trig and calculus. Students frequently have high level questions on probability. Some curricula seem to include that topic in Algebra 2 but not all. Is there a standard on what grade level or what high school subject should cover probability?

**Francis M. “Skip” Fennell:**

Interesting question. I think probability is a great, great context as students are becoming proficient with fractions (middle grades). Similarly, probability within algebra courses makes a lot of sense to me - again as applications of the algebra being learned. As you may know, many high schools offer an Advanced Placement Statistics course which includes probability. Hope this helps.

Question from **Lindsey Brown, 5th Grade Teacher (Ca)**:

After reading Liping Ma’s book, which highlights the difference between teaching math in China and the U.S., shouldn’t the emphasis be on teaching conceptual and applied math, rather than continuing to increase the number of standards taught (which essentially creates a system where most teachers focus only on the procedures)?

**Tom Loveless:**

The teachers in Ma’s book also had a thorough grasp of procedures. I agree with you that there is no need to increase the number of standards. What we need are fewer standards that focus on essential mathematical knowledge--which includes, I believe, procedural competence, conceptual understanding, and the ability to solve problems. The NCTM Focal Points are a step in the right direction in illustarting what these should look like.

Question from **Robert - Consultant/Author**:

Why do you think rigor is so important when students are bored, can not relate what they learn to their lives, feel unchallenged, and so many disadvantaged students dropping out of HS? Does (Math Rigor = Life Achievement)?

**Tom Loveless:**

Children liked to be challenged. I think we create a lot more boredom because of low expectations than from the curriculum lacking relevance.

Question from **Cindy Couture, Litchfield, NH school board member**:

Seven years ago we opened our first high school aimed at offering the most up-to-date educational opportunities. The only math program offered initially was an integrated math program taken over three years based on recommendations of the NCTM. After the first year, a few vocal parents demanded math the way they rememberd it; Algebra 1, Geometry, Algebra 2. The board was forced to offer two tracks of math - traditional alegbra/geometry and integrated and write in the course of studies that both tracks lead equally to pre-calculus and AP calculus. However, our data has shown that the students who take the integrated track score significantly higher on our state tests, on the math portion of the SAT’s and receive higher AP calculus test scores (for those who go onto Calculus). Yet the traditional track remains the most popular track with parents (where rumors persist that colleges won’t accept integrated math classes) and even middle school teachers who must make math recommendations that divide the students up equally between both tracks to make the classes as even in numbers as possible. When looking at math standards, how can we get the parents and community members on board with changes that will increase student acheivement, when a majority of people seem to want to do things the way it was done when they were in school 20 or 30 years ago?

**Francis M. “Skip” Fennell:**

Your challenge is one that is faced by many. Some districts show an achievement profile similar to yours (integrated math students performing at a higher level - achievement wise) and others show single subject (algebra I, geometry, etc.) students performing at a higher achievement level. As you may know Canada’s approach, like much of the rest of the world, is integrated. What to do? Our high school curriculum project (just beginning) will look at what’s important mathematically at the high school level. Future publications may then examine single subject and integrated approaches. That said, it really does come down to teachers, teacher background, and what seems to work best and “fit” the local needs of a community. Relative to college’s accepting programs - I think colleges want students who know mathematics and, frankly, are interested in studying more of it. I don’t hear much about concerns re: single subject vs integrated approaches leading up to such opportunities.

Question from **Jeanne Cerniglia, mathematics teacher, JRL Middle School, Southeast Local District, Wayne County, Ohio**:

How best can technology impact mathematics understanding and application? Has there been criteria established to evaluate or create new technological applications? Is there a place to go to preview mathematics technology?

**Tom Loveless:**

I don’t think we know the impact yet, especially of some of the newer technologies. The Institute for Education Sciences (IES) has funded some studies of technology, and I would follow the What Works Clearinghouse to see when new evaluations are completed.

Question from **Barbara Osterwisch, Consultant, PLATO Learning, Inc**:

When speaking with district administrators, their concerns about student achievement in math appear to concentrate on upper elementary, middle school, and high school. What are your thoughts on the current state of early elementary math instruction in the majority of classrooms (rote vs. building conceptual understanding) and the role this plays in subsequent math education?

**Tom Loveless:**

I think we have a lot of work to do on improving early elementary math instruction. I do not believe the problem stems from rote learning vs conceptual understanding. Teachers who really know mathematics understand the need for both, how they are integrated in good instruction, and the pitfalls of emphasizing either one at the expense of the other.

Question from **Christine Johnson, Assistant Director, Florida Center for Research in STEM, FSU**:

How are states disseminating information about revised standards and supporting districts in their implementation?

**Francis M. “Skip” Fennell:**

This, of course, varies. Some states are using the web as a portal for curriculum review, related feedback, etc. Some are using state department meetings to convey this information. At least one state I know is using their NCTM affiliate to guide such a review, etc.

Question from **George Viebranz, Executive Director, Ohio Mathematics and Science Coalition**:

For Mr. Loveless: In a 2003 presentation to the U.S. Department of Education you spoke of your concern for students developing better computational skills, as evidenced by NAEP trend data. You cautioned, though, that developing strong comutational skills does not mean that we need a back-to-basics movement in this country. Would you summarize any progress you think the mathematics education community has made over the past 5 years in 1) Strengthening students’ computational skills, and 2) preparing students for the range of mathematics beyond computational skills, and, in particular, the processes of doing mathematics.

**Tom Loveless:**

Thank you for summarizing my remarks so well. I think the NCTM Focal Points are a huge step forward. They set a proper tone for understanding how computational skills are intertwined with--not separate from--other aspects of mathematics. I have been a critic of NCTM in the past so I want to be sure to praise their recent efforts. We still need a serious examination of students’ computation skills, which I believe is one area where American students have made very little progress over the past two decades.

Question from **Christine Johnson, Assistant Director, Florida Center for Research in STEM, FSU**:

How are states measuring the rigor of their standards?

**Francis M. “Skip” Fennell:**

I don’t know that they are - and this is a concern. If a state has 76 or whatever objectives at a given grade level, how important are these objectives? Which objectives are most important? Are these objectives about mathematics or about istruction? I could go on and on here - but won’t!

Question from **Janet Kaltreider, Principal, Palmyra Area Middle School**:

The sub-group that continually presents a challenge to our achievement levels are our special needs students. What can we expect to see in research and development to meet the needs of these students?

**Francis M. “Skip” Fennell:**

Great question again! Special needs students are a challenge to all teachers. My opinion is that none of us have been prepared to deal with such needs. I think we must find ways to more actively collaborate with special education colleagues to help with intervention programs to assist students - all students. Furthermore, I know of secondary programs where a co-teaching model involving mathematics teachers and special education teachers collaborate on planning and teaching. I think research regarding formative assessment (Fuchs, et al) provide valuable guidance related to intervention via formative assessment.

Question from **Sean Cavanagh**:

This is question for both of you. You’re both serving on the National Math Advisory Panel, which is expected to produce a report next year for the White House on effectives strategies for teaching and learning in math, and preparing students for Algebra, specifically. Could you please describe your impressions of the panel’s work -- specifically, what are the greatest challenges the panelists have encountered so far, in your view?

**Tom Loveless:**

The math panel has been a terrific experience for me professionally. Being able to work with so many top notch people from a variety of disciplines and with such different areas of expertise has been great. The greatest challenge for panelists so far, I think, has been simply how to get the math panel’s work completed while not neglecting our other professional commitments.

Question from **A. Gregory, JHS math teacher, NYC**:

It’s clear that in order to better prepare students in math, we will need teachers with a stronger grasp of the subject -- and to this end, schools are seeking out math majors to teach junior high and high school students. Yet I’m not sure that we’re making enough of an effort to give these teachers a sufficient understanding of adolescents and how they learn. We need people who know math AND know kids. How can this be addressed?

**Tom Loveless:**

I agree. As much as I worship at the altar of teachers’ content knowledge..it’s not enough. Pre-service math teachers need courses in developmental pychology. They also need lots of practice teaching with well-structured feedback from mentors and fellow teachers. Math teachers need to know math, but they also need to know how to teach.

Question from **Christine Johnson, Assistant Director, Florida Center for Research in STEM, FSU**:

1. What evidence are states using to demonstrate that their standards are “World-Class” - i.e., on par with those of the top-performing nations?

**Francis M. “Skip” Fennell:**

In developing the Curriculum Focal Points, NCTM carefully reviewed international curriculum documents to assist in the decision making related to the mathematics topics and grade levels suggested for the focal points. I also know that several states have, at the least, reviewed international curriculum materials to assist in their curriculum review process.

Question from **Gerry Charlebois, Executive Director of Advanced Academics, CFBISD**

What is your philosophy on serving advanced students in math, especially in the elementary and intermediate grades?

**Tom Loveless:**

I believe in acceleration for mathematically advanced students. Math is one of the most hierarchical subjects taught in school. One of the worst things we can do is teach students material that they already know simply because all of their peers haven’t also mastered it. In the elementary grades, flexible grouping of advanced kids seems to work best. And in middle school, put kids in algebra when they are ready for it, not based on some one-size-fits-all schedule.

Question from **Karl Graf, Math Dept. Chair; San Antonio Academy of Texas**:

We’ve known for years that the U.S. provides a math “education” that is “a mile wide and an inch deep.” What can be done to slow the pace and shorten the list of yearly objectives that are imposed upon us math teachers so that true in-depth exploration of the foundational concepts can be addressed in a way that REAL mathematics education can be achieved?

**Francis M. “Skip” Fennell:**

I am shamelessly promoting the Curriculum Focal Points as at LEAST one way to have the discussion about what is important at particular grade levels. The intent of the Focal Points was to actually get at the core of your question. Far too many teachers at the PreK-8 levels see too many mathematics objectives every year, which leads to the shallow treatment of most of them. Students need to learn and learn well - important mathematics, hence the need for, at least an emphasis on particular topics of emphasis at each level of instruction, PreK-8.

Question from **Dana S. Simmons, Executive Director of Secondary Education, Flint Community Schools**:

Please share your recommendations regarding the developmentally appropriate age for our students to successfully engage in a high school algebra course.

**Tom Loveless:**

I think students should take an algebra course after mastering arithmetic--including operations with whole numbers, fractions, decimals, percents, and integers. By mastery I mean, as I indicated in an earlier answer, procedural competence, conceptual understanding, and proficiency in problem solving. The mastery of arithmetic will be accomplished at different ages by different students. I would focus on what students know, not their age, in deciding whether they are ready for algebra.

Question from **Melissa Walker, Math Department Chair, MLK High School**:

What is a realistic way for teachers to be trained to implement a standards-based curriculum? How do you overcome a serious lack of time with the pressing need for mandatory training (both in content and pedagogy)?

**Tom Loveless:**

As a teacher, I favored summer workshops or math institutes with generous stipends for attendance. Maybe it was just me, but at the end of the day, I was too exhausted to get much out of inservice.

Question from **Joe Zimmerman, Teacher, Gary, Indiana**:

How much testing, outside the regular unit tests, is necessary to determine student progress in math?

**Tom Loveless:**

I personally would like to see good assessment data collected at least twice a year, preferably at the end of the school year (for summative purposes) and at the beginning of the year (for formative purposes). That also allows schools to take into account summer effects. Teachers have to get the data in a timely fashion in the fall, however, if the information is going to inform their instruction.

Question from **Connie Perez Ebrahimi, Managing Director, Huntington Learning Center**:

EdWeek in China: Asian Equation, Published Online: June 5th, 2007. As it relates to your topic and a recent article I read in EdWeek, it appears that the Chinese are looking more towards what we are doing as educators in teaching math! As quoted, “China’s government is seeking to inject more American-style flexibility into its math and science curriculum, by placing less emphasis on exams and more focus on cultivating students’ creative and analytical skills, which school officials believe are lacking.” My question, taking this into account, what is it specifically U.S. school lack in developing a better math student??

**Francis M. “Skip” Fennell:**

I don’t know that it is the school or school system as much as it may be our culture. We would want more students to value mathematics and recognize its importance AND we would want their parents to hold to a similar sentiment relative to the importance of mathematics (every teacher I know has story after story about parents who proudly proclaim “ya know I was never good in math either,” which is NOT the point). Math is important. Knowing math opens doors. Our culture is one of creativity and we have coined the “out of the box” thinking that other cultures (as you note) seek. We need to find ways to address mathematics background along with nurturing a positive disposition toward to this amazingly enabling subject. This is our challenge

Question from **Dr. Mark Rosenbaum, Ed. Consultant**:

Reform math programs based on a constructivist philosophy are being challenged for their lack of direct skill instruction. Why not use a “balanced mathematics” approach, similar to the “balanced literacy” approach now being used in language arts?

**Tom Loveless:**

Unfortunately, the body of scientific literature describing what constitutes an effective “balanced approach” is not as well developed in mathematics as it is in reading.

Question from **Bindu, Assessment Developer, Vega Information Systems**:

Hi I have noticed in the released math test items on the net that most of the items are multiple choice and very few (sometimes none) were open response. To develop math thinking and reasoning skills isnt open response items more suitable than multiple choice items? Multiple choice items, rarely give an insight into how the student is thinking out a math problem. OK, they are easy to score, analyze, etc. Multiple choice makes tests are convenient to the test developers and administrators but are not helpful for students in developing the math skills. It is like saying “It is easy for me to record your response to this type of a question. So this is the best way to ask the question”. In India very few educational systems allow multiple choice items. Teachers take home bundles of answer sheets and personally score them, even writing some suggestions and comments on each answer sheet. That way a teacher knows exactly which student is guessing and which student is getting it right for the right reasons. The obsession with item statistics and test performance statistics keeps diluting the rigors of a test. You are asking your students to reach upto to the standards in other countries, but shouldnt your country’s test administrators and scorers too be challenged to reach upto the test administration standards in other countries?

**Tom Loveless:**

The NAEP test has a mix of multiple choice and constructed response items, as do most states. I agree that multiple choice items alone are insufficient to assess math proficiency.

Question from **Jill, math committee member in MN**:

I am concerned that the premise is that there must be a shift in control of education away from local and state control. Do you believe math standards must be dictated from the Federal government or other federal level?

**Tom Loveless:**

No, I do not think the federal government has any more expertise than states or local districts in writing good standards. The important thing is the standards themselves, not the level of government issuing them.

Question from **David Gabel, Research Assistant, CAL**:

Isn’t it rather meaningless to call countries high performing based on tests which emphasize recall of facts and low level cognitive skills?

**Tom Loveless:**

I would not characterize tests that are given internationally in that way. The TIMSS test in math assesses a wide range of skills and knowledge, including what anyone would consider to be high-level, demanding mathematics.

Question from** Alison Corner, Principal, Pawtucketville Memorial, Lowell MA**:

Their is alot of emphasis in K-4 on teaching math as a problem solving exercise. How would you recommend incorporating teaching computation skills for automaticity?

**Tom Loveless:**

Some lessons have to be devoted to computation alone, including why procedures work. Automaticity involves both accuracy and speed so I would stress both in memorizing basic facts in addition, subtraction, multiplication, and division and in the use of algorithms.

Question from **Barry Golden, Ed. Consultant Wisconsin Dept. of Public Instruction**:

Many states seem to be addressing the challenge of rigor by adding a 4th year of math to their graduation requirements. Is this a sensible approach considering it may increase the drop out rates unless there is also more relevance included in the curricula for the non-4 year college bound students?

**Francis M. “Skip” Fennell:**

I think all students should study mathematics every year they are in school. We certainly do this in other subjects (e.g. English). At this writing most states require 3 years of the subject, with more and more states are moving toward 4 years of mathematics. We need to consider a variety of models for the 9-12 mathematics sequence whether this be single subject or integrated curricular approaches. As one example, I do know that Texas is considering a final year (capstone) course. Their work may be of interest to you.

Question from **Meg Fischer math teacher Somerset County Vo-Tech HS**:

What is the correct use of the calculator - I urge my students to rely on it for accuracy, yet other teachers want them to still depend on pencil & paper (and rote memorization). Should calculators be used always, sometimes, or never?

**Francis M. “Skip” Fennell:**

Calculators have a place in the mathematics classroom. I think calculators are instructional tools. When should they be used? NCTM wrote a position statement a few years back entitled Calculators, Computers, and Common Sense. That title captures how teachers must decide when and how the calculator is used to support their work. With basic multiplication facts? No. As an assist with complex problem solving? Sure. Hope this helps.

Question from **Kathryn Michalowski, Asst Principal, Octorara Area High School**:

Would you consider a list of competencies by course? Ex.: An Algebra I student should be able to... When we discovered that a student who couldn’t do the distributive property had 13 sub-competencies to complete, the checklist became necessary to see what a student could and couldn’t do.

**Tom Loveless:**

Yes. End-of-course testing by states will eventually force school officials to describe with more specificity what particular math courses do and do not cover.

Question from **angela rohen, supervisor curriculum and instruction Wilson Co Schools, TN**:

what one or two things should math teachers be doing in order to posture themselves to be ready for these upcoming revisions?

**Francis M. “Skip” Fennell:**

Assemble them and ask them the following question: When should students learn (and learn well) at your grade level? Rank them. Then discuss how YOU and your district can make this happen. This is just a start!

Question from **Craig Gaska, Principal, Churchill Elementary School**:

What efforts are being made to include publishers in defining math standards and in proving materials to teach the standards and assess student achievement in order to insure alignment with published programs?

**Francis M. “Skip” Fennell:**

NCTM has involved all of the major publishers in reviewing the Curriculum Focal Points. Publishers are allies in the development and delivery of curriculum materials. We must continue to find ways to work together for ALL students.

Question from **Julie, Math Teacher, Cleveland**:

Many states have raised math standards and yet have implemented state test cutoff scores that indicate a student scoring 40% on the test as proficient (Ohio). Should content be trimmed and test cutoff scores raised? Most European and Asian countries cover less but deeper content. How does the NCTM intend to address this well-documented problem with math content coverage in the US?

**Francis M. “Skip” Fennell:**

NCTM’s recent Curriculum Focal Points is one way to at the very least begin a discussion about what is important at particular grade levels in mathematics. Many states are now using the Focal Points in their curriculum revisions. The issue of state proficiency levels is a related, but different concern.

Question from **Shelley Fritz, District Math Resource Teacher, Hillsborough County Schools, Florida**:

With Florida’s Sunshine State Standards currently being revised and modeled after the Focal Points with less of a spiraling approach, there is wide-spread concern that vital curriculum will be missed by students who either come into the next grade level from another state or from a teacher who has not taught the content thoroughly enough. What recommendations do you have for teachers who receive students who have missed mathematics content and this content will not be formally taught or deepened until several grade levels later?

**Francis M. “Skip” Fennell:**

I would think that the Sunshine State Standards would be considered as a model attempt to provide for the most critical mathematics topics at particular grade levels. Teachers will need assistance in working deeper on the critical topics within your curriculum, but I think that your focus will help you with regard to students moving in to Florida.

Question from **Sean Cavanagh**:

This is question for both of you. You’re both serving on the National Math Advisory Panel, which is expected to produce a report next year for the White House on effectives strategies for teaching and learning in math, and preparing students for Algebra, specifically. Could you please describe your impressions of the panel’s work -- specifically, what are the greatest challenges the panelists have encountered so far, in your view?

**Francis M. “Skip” Fennell:**

Frankly, the greatest challenge may be getting the full report out in time AND having it impact mathematics teaching and learning in this country. I am hoping we meet both of these challenges!

Question from **Dr. Earlene J. Hall, Supervisor of Mathematics Detroit Public Schools**:

What types (models) of professional development are school districts using to prepare teachers to understand and implement the new standards? Are there any any resources that are considered good to use in this training? Does anyone have a model that includes collaboration with universities? Thank you ( Greetings Skip, I had the opportunity of meeting you at NCTM)

**Francis M. “Skip” Fennell:**

NCTM is working on publications relative to “implementation” of the Curriculum Focal Points. There is work to be done here in helping teachers on using the time to “dig deeper” on topics of importance. Some colleges and universities are beginning to use the Focal Points as ways to sharpen the content and pedagogical focus within their methods courses. Greetings to you as well!

Question from **Brad Findell, Mathematics Initiatives Administrator, Ohio Dept. of Education**:

With all the attention to standards in recent years (comparing them, rating them, creating them, and revising them), I worry that some people forget about other facets of the educational system that need considerable attention. Would you please say a few words about the facets that you see as most important and why, as well as how that facet relates to standards?

**Francis M. “Skip” Fennell:**

Sure - a major facet (as you note) that must be addressed globally is assessment. What is the role of assessment - not just the state assessments! How is formative assessment used? How should teachers assess for the purposes of intervention? How can the assessment information gathered - daily and formally be used to inform instruction AND key decisions within a grade, school, school district or state?

**Sean Cavanagh (Moderator):**

That’s all for our discussion today of math standards. Thanks for all of the questions from around the country, and thanks to our guests, Skip Fennell and Tom Loveless, for participating.

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