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Assessing to Learn and Learning to Assess

chat archive

Moderator
Good afternoon and welcome to today’s online chat on NCTM’s Focus of the Year on Assessment: “Assessing to Learn and Learning to Assess” with President Cathy Seeley.

Our first question is from
Marshfield, Wisconsin

I have used paired seating with peer coaching—embedding these strategies in daily lessons which have addressed so many common issues that traditional math teachers tend to face. I RARELY ever feel as though my students are not with me. I model a problem and pose the pairs with a similar problem to solve together. Students are engaged in academic discourse and reach HIGH levels of metacognition because of their thoughtful conversations. They are accountable to each other throughout the lesson. My students truly enjoy being consistently engaged in daily lessons. So my question is: Why are there so many teachers (both new and veteran) still forcing students to sit in daily isolation? Why is there not more of an attempt to change the classroom atmosphere—at least to try it? Is this just too big a paradigm shift for teachers who are more “concrete-sequential” thinkers?

Cathy Seeley:
This sounds like a successful approach for you and your students. I suspect that some folks might ask when students are expected to be accountable for their own learning, but you and I might agree that there are many opportunities for this kind of expectation outside of the day-to-day learning environment. Accountability tests and any individual classroom tests call for students to show what they have learned. I agree with you that student interaction and active engagement in their learning is key to acquiring knowledge, and the day-to-day learning situation is a great place for this to happen. Thanks for sharing this approach.

Question from
Mesa, Arizona

Cathy, you mentioned one important aspect of assessment as a tool for helping us discover potential misunderstandings that a student might have. Has anyone found it useful to regularly include on assessments a problem with a student solution that involves common misunderstandings/mistakes and ask students to analyze the solution? If so, what have you found in doing this?

Cathy Seeley:
This seems like a good approach to assessing. It is something being increasingly done in teacher professional development. I suspect students would have to think a lot about the operation and the procedure involved in order to respond well.

We’ll leave it open for others to respond if they are online with us.

Question from
Wooster, Ohio

I was very disappointed with the last two issues of the Mathematics and Arithmetic Teacher. It appears that we now have a political agenda that is showing up in our magazines. I am referring to the article on teaching cultural diversity and the article on the Islamic/Muslim art... I am not against cultural diversity or Muslims... I just think that the journals should be about teaching math.... and I also question the timing of the Islamic art article with our present state of affairs. I am strongly considering not renewing my membership. Thanks for listening.

Cathy Seeley:
I’m sorry that you did not like the articles involving cultural contexts in recent issues of The Mathematics Teacher and Teaching Children Mathematics. The journal panels make every attempt to focus on teaching mathematics so that all students can learn. They also listen to numerous advisory panels of readers like you.

In glancing at the September and August issues of these two journals, the article to which I think you refer was on teaching geometric transformations using Islamic art as a context. Art comes from many different cultures and eras and has always provided an important context for the teaching of geometry. Islamic art in particular has been used as an example in geometry for many years. The journals do not support any particular political agenda, but neither do they exclude applications by specific peoples.

You might choose to write a letter to the editor about some of your concerns. I sincerely hope you continue to be a reader of these journals if they meet your needs.

Question from
Scottsdale, Arizona

Re: “In our own classrooms, we can refine our skills so that we design assessment measures that clearly show what students know…”

As an undergraduate math education major, I’m concerned with the phrase above that includes “we design.” My understanding was that a lot of schools require the teachers to use certain assessment standards, and teachers are not allowed to deviate from the school’s policy. How will I be able to design my own assessments if I am required to adhere to the school or school district’s policy?

Cathy Seeley:
Even in an era of accountability and system-wide assessments, teachers in almost every school I know still play an important role in assessing students’ learning on a day-to-day basis. This statement was intended to reflect the importance of teachers continuing to learn how to best do this. Whether it is a daily quiz, a unit test or a project interview, teachers need expertise in assessing student learning. A subtle use of one word rather than another, an attempt to focus on common errors, or even the choice of what type of assessment to use for a particular purpose, are all examples of teacher expertise called for in the classroom.

Question from
Skippack, Pennsylvania

After raising my daughters, I have decided to teach. I will be student teaching this spring. As a soon-to-be educator, my concern is that assessments often are not specific enough to determine a child’s true capacity for comprehension. It is rare that I see one-on-one teacher assessment with their students. It is prominent, both in the past and present, that the standardized test continues to dominate and rank a child’s abilities with mathematics. Are there specific suggestions that you would share that I should utilize, from the start, when assessing K–5 graders? How can I do a better job?
Thank you.

Cathy Seeley:
I absolutely agree with you that assessment close to the student, rather than large-scale assessment, provides the best measure of student learning on a day-to-day basis. It is this kind of classroom or individual assessment that can best guide student learning. Accountability testing serves an important purpose, but such tests can only point us in the direction of what students know or don’t know for sure. Diagnosing specific strengths and deficiencies is generally something best done by the teacher at the classroom level.

Question from
Wilsonville, Oregon

What role should standardized forms of assessment play in student placement and grade succession? My K-8 private school uses different tests for each of these areas and I am curious about its effective usage.

Cathy Seeley:
Using standardized assessments for either placing students in classrooms or determining promotion have both advantages and disadvantages. Such assessments, if designed well, might serve the purpose of focusing on high standards and expecting all students to learn. On the other hand, sometimes such assessments can provide misleading information. If the assessment only examines end results, or superficial levels of skills, without getting at what a student really understands, or if the assessment provides only limited opportunities for students to demonstrate learning for particular types of problems, we might not know for sure which students are best prepared to go on. Also, many teachers know that not all students show us well what they know on tests, particularly if the testing situation is a high-stress environment, like in a cafeteria with strict time limits. Various NCTM standards and resources over the past 15 years have emphasized the need for more than one measure any time important decisions are being made for students. Other measures closer to the student, especially done by the classroom teacher, can provide valuable insights into what the student really knows.

Question from
Mesa, Arizona

What are your feelings regarding state standardized assessments required for high school graduation?

Cathy Seeley:
Having high standards and expecting all students to learn challenging mathematics are very important and something too many schools in this country did not regularly do during the past several decades. So, as a concept, the use of a graduation test seems reasonable.

There are some related problems to using a single test as the sole criterion for graduation, however. The first problem lies in the quality and depth of the assessment itself. We do not have many examples of assessments that are well respected by both educators and mathematicians in terms of getting at student knowledge of mathematics. Furthermore, standardized assessments that involve contexts not commonly known to students might enter unintended barriers for some students. Most important, the use of such assessments might say more about opportunity to learn, rather than about what students have done. The bottom line is that accountability is good and necessary; the quality of the test is critical; and how we prepare students with real learning can make or break the system.

Question from
Missoula, Montana

What is the real value of a teacher’s chapter or unit test today with all the emphasis on Adequate Yearly Progress? Do these have to or need to correlate with assessments used for AYP?

Cathy Seeley:
The teacher continues to be in the most direct role for determining what a student knows every day. Ideally, the teacher is using appropriate classroom assessments from daily quizzes through chapter/unit tests, intended to measure what students are learning based on the district/state standards/expectations. We would also hope that the accountability assessments used to determine Adequate Yearly Progress would be based on the same standards/expectations. So in a well-aligned system, these classroom assessments and the end-of-year assessments would be very much in sync. Both play an important role for student learning. And, again, no single measure is likely to completely tell us what mathematics a student knows.

Question from
Boston

After assessing a skill you find that one-half of the students missed the concept. Do you provide extension activities for the students who have mastered the concept and reteach the concept to the rest? Or do you use the proficient students to help those who have not done well or do you move on since 50 percent have mastered the concept?

Cathy Seeley:
I wish there was a ‘one-size-fits-all’ response I could offer. Either option might work, depending on the content and how important it was for the mathematics to be studied next. I certainly don’t think able students should be routinely held back in order for others to catch up; this is not helping every student achieve to their fullest. However, if enough students have missed something, it may be worth having the whole class focus on the same content again, perhaps from a different perspective or using a different approach.

Question from
Mesa, Arizona

How do you feel about the assessing of inclusion students and their ability to perform on such math tests? More specifically, with the increasing importance of high-stakes testing how do you think these students will place in the general curriculum?

Cathy Seeley:
This is one of the concerns with large-scale assessments. Depending on a student’s particular disability or limitation, there may be accommodations made for testing, and the student’s Individual Education Plan takes priority.

At the same time, it is interesting to note that some teachers have told me that as they raise their expectations for all students, sometimes their inclusion students shine on individual topics throughout the math curriculum.

On a larger scale, I think we must be very careful not to rely solely on once-a-year (or less frequent), large-group testing as the only indicator of student learning for any student. A single measure simply cannot give teachers all the information they need. Teachers continue to be in the best position to assess learning on a daily basis.

Question from
Tempe, Arizona

The NCTM Assessment Standards state that: “Too often, tests designed for other purposes have been used unintentionally as filters that deny underrepresented groups access to the further study of mathematics.” I believe there is a much larger student base affected by the decisions to employ a high-stakes test as a graduation requirement. It is estimated that “7 percent to 10 percent of high-school seniors nationwide fail” high-stakes examinations (The Gannet News Service, 2004). For some states, students who fail these examinations are placed into academic classes setting them onto a path that will ultimately deny them “access to the further study of mathematics” because the curriculum focus is on testing rather than “fostering growth toward high expectations” (NCTM Assessment Standards). I realize that there are cost factors and efficiency requirements involved with statewide examinations; but I was wondering if you have any suggestions as to how we, as educators, can persuade administrators and others with “power” to work toward the “shift in evaluation” recommended by the Assessment Standards—a shift “toward evidence from several courses judged by teachers and away from a single test judged externally.”

Cathy Seeley:
I couldn’t agree with you more that we must help make a shift in the kinds of assessments we use to make important decisions for students. Having worked at the state level for many years, I know that cost and efficiency of administration and scoring are key factors in developing large-scale tests. I hope that NCTM and the broader profession can offer guidance for future large-scale assessments in order to best assess the learning we think is most important. A few promising examples in this area are out there, including state assessments from Connecticut and Washington state.

Question from
Tempe, Arizona

You state that, “Regardless of the purpose of an assessment, one factor is crucial to all assessments. They must be aligned with the particular mathematics that students are expected to learn. I interpret this to mean that test questions should be limited to only the material that has most recently been taught. What advantages or disadvantages do you see to asking one or two questions related directly to material that the student covered a year or two ago? For example, when testing Algebra 2 students on matrices adding an extra credit question that deals with, specifically, geometry.

Cathy Seeley:
Assessment should certainly not reflect only the most recent learning. On the contrary, students should frequently be expected to demonstrate their cumulative mathematics learning. Depending on the purpose of the assessment, sometimes we want to know how well a student is doing on a very specific skill or idea, and other times we will want to get some indication of how well they are maintaining previously learned knowledge and skills. The challenge comes in not spending so much time on disconnected previous knowledge that we miss the opportunity to adequately assess current learning. Ideally, whenever possible we can embed previously learned material into related new material by looking for problem contexts that relate to topics and content previously learned.

Question from
Newark, Delaware

I’m working on the full-day kindergarten study at the University of Delaware and we are looking for an assessment tool to measure kindergarten student progress in mathematics. Is there such an assessment tool?

Cathy Seeley:
Most early childhood experts prefer to use an individual interview technique for students at this level. Some kind of structured inventory can provide consistency, but unfortunately, there are not a lot of readily available options at this point in time. One current instrument that focuses only on number (which is a key part of mathematics at this level, but omits geometry and measurement) is the TEMA by Ginsburg and Baroody. Another project currently under way in this area is the Building Blocks project at SUNY Buffalo, under the direction of Doug Clements and Julie Sarama.

Moderator
Thank you for your participation in today’s chat. The next chat will be at 4:00 p.m. EDT on Monday, October 24. The topic will be “A Flattening World,” the President’s Message in the October NCTM News Bulletin. I hope you’ll join us then.

Cathy Seeley:
Thanks to all. I’m looking forward to our chat next month.

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