Why Don't They Get It?

Copyright 2000 by Jean Hoover
Included here with permission of the author

At a staff meeting last spring, teachers from each grade level shared their concerns and frustrations with students' understandings of math concepts. They identified the particular confusions with which students arrived at their grade level each year and described the impact on teaching their assigned curriculum. For example, fifth graders could not do long division if they were unable to regroup in subtraction; fourth graders found it difficult to understand the two-digit by two-digit multiplication procedure if they did not understand place value. Neither could they compare fractions symbolically if they did not understand the concept of numerator and denominator. As each grade level team shared with the whole staff, each assured the other that they had taught those concepts. So the question for everyone became, "So why don't they get it?"

As a math resource teacher in this school, I had worked with teachers at all the grade levels over the past two years. The district's grade level objectives, and the state's standards of learning guided math instruction. Teachers followed the district's chart that correlated the objectives with the math text and outlined the pacing of instruction for each quarter. If we were teaching the objectives through the approved math text, and meeting the time lines, then why did teachers have to re-teach concepts from previous grades?

Background

Our school is a culturally diverse elementary school, grades K to 5, in the Northern Virginia area. The population of more than 700 students has about 24 different primary languages represented. Within the district, our school is eleventh highest in poverty and mobility. Most of the 33 classroom teachers are European American. There are also six English As Second Language teachers and four Learning Disabilities teachers.

The school did not meet the state requirements for passing the Standards of Learning (SOL) tests in the spring of 1999 and was accredited with provision. District programs to support the Standards of Learning tests have been quickly designed and implemented before clear expectations or school plans were in place. This has resulted in confusion, a sense of crisis management, and more staff meetings. Considerable time has been given to review student scores on a variety of tests, to identify at-risk students, to monitor student progress, and to develop plans for additional support.

There have been changes in programs and in grade level assignments in an effort to improve student achievement. Although renovations to add nine additional classrooms were completed last year, trailers have been brought in this year to handle the increase in enrollment since September.

The administrator is a high-energy leader who is closely involved with what goes on in the classrooms. She sets high expectations for quality instruction and holds teachers accountable for students' performance. She believes a sense of "dis-equilibrium" promotes reflection on one's practice and professional growth. She continually reflects on "what else the school can do" to make a difference in student scores and is willing to try new approaches that are research-based. She encourages the staff to participate in county staff development workshops and programs.

About 73% of the teachers have taught six years or less. They are eager to learn and open to new ideas. Overall, the staff demonstrates strong work ethics and a commitment to make a difference.

Starting Point

So "Why don't they get it?" What was going on? Was there a mismatch between the way students experienced math at school and the way they experienced math at home (CIP question 3.3)? Did they see connections between math and their everyday experiences? Did our classroom tasks isolate them from authentic practice? Might the school culture be contributing to the problem (CIP question 3.2)?

A recent study (Ensign, 1997) about using personal experiences in math lessons found that teachers rarely connect school math with students' experiences out of school, despite the encouragement of the National Council of Teachers of Mathematics. The most meaningful connections should be to students' personal experiences, not to situations contrived by others. Ensign (1997) viewed the hypothetical problems in texts as less meaningful than those that emerge from the students themselves.

D'Agostino's (1996) study of academic achievement and authentic instruction also reported the lack of opportunity for students to engage in meaningful tasks related to their lives outside of school. Most importantly, the study noted that connections to out-of-school experiences and higher order learning were the two most important principles for disadvantaged school experiences but were rarely emphasized.

I looked for ways to connect school math and the students' "real worlds" (CIP question 3.3). With so many different cultures at our school, I decided to identify common experiences that families might have in any culture. I also included a question that asked parents to describe how they used math at home. At Back-to-School Night, I gave out about 120 parent surveys to English and non-English speaking families. The 39 surveys that came back described such activities as helping in the kitchen or with meals; watching TV or movies; eating out; and cleaning the house. Parents identified "math" as measuring, telling time, counting money, and the math homework assignments.

Initial Interventions

Starting with the concept of measurement in third grade, I introduced and taught several lessons on liquid capacity in two classes. Since many students had experiences helping in the kitchen or with meals, we began with a discussion of "leftovers." How many had watched their mothers select just the right size container in which to put the leftovers- not too big, not too small? Everyone wanted to talk! Hands went up! They wanted to share their kitchen experiences, even if their English was not perfect. We talked about measuring tools for food and liquids. I showed them mine. Some students described their measuring tools at home. I encouraged them to play a game with their mothers, trying to see if they could select the right size container for the leftovers. During the next few days, small groups used measuring cups to actually measure liquids and played measurement games. Overall, they seemed to be more involved and motivated. The other third grade classes followed the measuring activities in the text. But a week later, the results of the grade level module tests indicated no difference between the two classes with which I had worked and the other classes on the measurement test questions.

I worked with a small group of fourth graders for a few days on the concept of area. While classroom instruction had used plastic tiles to measure area on grid paper, our small group made construction paper tools, one ft. by one ft., to measure the area of small rugs, or floor space. The concept of area became more realistic when they measured actual objects at home such as countertops or tablecloths. The students were enthusiastic. Although the teacher liked the idea and felt that it was just what they needed, it required too much time. She needed to move on.

Grade level teams, kindergarten through second grade, met with me weekly to plan and discuss math. These meetings were opportunities to emphasize the connections to home through activities that included concrete materials relevant to our learners, objects from their homes and natural settings. I suggested collecting data about objects, such as doorknobs, light switches, pillows at home. The teachers could use these data to work with mathematical concepts such as, sequencing and comparing numbers, graphing, writing story problems or building numbers with the base ten blocks. I showed an example of a counting slip with a picture of a familiar object at home and a space for the name of the family member that helped them. The form required little teacher preparation, involved the families, and promoted more math conversations at school. One teacher sent home six of these slips at one time. Another teacher sent one slip home, waited two days before the slips all came back, but created a wonderful line plot graph with the class. Another teacher asked for these slips after I explained the value in using data from home.

However, this interest and activity did not continue for long. Snow days and report cards disrupted our weekly meetings. The idea of linking instruction to home experiences seemed to lose momentum as the focus shifted to the teachers' particular concerns.

Frustrations and Other Questions to Consider

In early December, one teacher remarked that in 26 years of teaching she had never seen such a harried staff. They hurried through the halls. Most conversations were short and goal directed. Everyone felt the urgency to raise the students' scores. The political importance and the publicity of the SOL tests heightened the tension. Teachers wrestled with the public notion of the school's "failure."

During the first workshop designed to meet the district's requirement for SOL training, the eight upper grade teachers talked openly. The pressure to raise students' scores on the state Standards of Learning in all four content areas had created much frustration. Schools, in which 70% of the students did not pass these state tests within a given time line, would be "reconstituted," that is the staff would be replaced. "We can't concentrate on everything. It's too much." "We're running from dealing with one thing to another." "SOLs have changed how we do things -tell a body of facts." The teachers' emotions interfered with engaging their attention. Brain research shows that a brain occupied with a perceived threat can not focus on learning. Strong emotions can become counterproductive to school goals if they interfere with making good decisions and implementing sound instructional practice (Jensen, 1998). I was a witness to that!

Best practice in teaching mathematics emphasizes being a facilitator of learning. It includes using manipulatives, a problem-solving approach, cooperative groups, discussions, writing and justification of thinking (Hyde, Daniels, & Zemelman, 1993). Teachers' comments revealed that their sense of responsibility for the vast amount of curriculum tested in every subject was leading them more toward teacher directed instruction. Group discussions and inquiry approach did not seem to fit in the time schedule. One teacher's response to my lessons was, "That was great when you did it, but it takes too much time."

How was this climate of stress contributing to the problem of students' understanding (CIP question 3.2)? The opportunities to make sense of concepts seemed to be vanishing as direct instruction became the practice. There were no interventions that could change SOL requirements. But now there appeared to be a mismatch between the culture that the state mandated tests created in the classroom and the culture that the teachers wanted in their classrooms (a variation on CIP question 3.3).

In talking to many of the teachers individually, their responses indicated their sense of conflict with what they knew to be good instruction: " -can't make connections- have to cover material- if you don't cover, it'll show up on test- more teacher directed- more conscious of moving on- added more (topics)- don't have time to do everything well- less discussion." One teacher's comments were especially revealing: "I wish I had time to think. I wish I had time to think about how to make it meaningful. Given the time for math, what can I do?" Another teacher expressed her sense of helplessness, "If I didn't have to test so much- had time to take notes on what I notice- if the state would let go of the SOLs for one year, we could take copious notes, and then compare and discuss with our colleagues-." A resource teacher's response captured the frustration, "We can't [help them, the classroom teachers]. If we could let go of other things and just focus on one thing." What a powerless feeling!

Even first and second grade teachers expressed their frustration during our weekly meetings. "- [I] never had to document specific objectives on all my plans [before]. Let me work with the kids as kids and build a relationship." "No matter what I do, how long I work, it won't be enough."

Over the weeks, conversations turned to "transfers," "leaving teaching," "too much pressure," and " too much paperwork and not enough teaching kids." These teachers faced a daunting task--deal with the emotional issues of children from refugee camps, interrupted learning of students whose families withdraw them for weeks at a time, cultural/ social adjustments of children from other countries, AND improve academic achievement. Since teachers also questioned the value and developmental appropriateness of some of the objectives in the state standards, teaching that curriculum increased the tension. State testing requirements had created a culture in conflict with the classroom culture in which the teachers believed. We all felt powerless.

Schmoker and Marzano (1999) indicated that "...U.S. schools would benefit from decreasing the amount of content they try to cover. And teacher morale and self-efficacy improve when we confidently lay out a more manageable number of essential topics to be taught and assessed in greater depth (p.3). They note the results of the Third International Math and Science study which states that textbooks in the United States cover significantly more topics than those in other countries. Under these circumstances, teachers are unable to create the depth of understanding necessary for students. Schmoker and Marzano (1994) recommend that districts prioritize standards, but this is not an option for our teachers in this district. They are responsible to teach all the standards. One teacher remarked, "If you don't cover it, it'll show up (on the test)."

Fullan (2000), dean of the Ontario Institute for Studies in Education, describes how "...the external context of the school has changed over the past five years" (p.582). The outside forces of government policies, parents, community, and state requirements for increased performance and teacher accountability have moved inside the walls of the school. This has created a sense of excessive demands, overload, and fragmentation for teachers.

Newmann (1991), a professor at the Wisconsin Center for Educational Research, has written about restructuring education. He highlights the negative effect of schools' emphasis on coverage rather than depth of understanding, in particular on students who are low income or who have different cultural backgrounds. He advocates "substantive discourse", depth of understanding, and the production of knowledge that has value beyond competence in school. It's interesting to note the distinction between "substantive conversation" and typical classroom conversations. The purpose of teacher talk and conversations is to reproduce and transmit that which the teacher deems important. In "substantive conversations", the students have more ownership of their viewpoints, interpretations or solutions.

As I pushed forward in my own "math mission," a teacher shared her frustration with results of a recent module test. "I teach that [graphs and charts] every Monday. I put it up on the board and then on a test they act as if they've never seen it." I asked this teacher to describe how the lesson looked each time she taught it. As I listened, I heard a description of teacher-directed instruction. Had the stress of the state standards moved teachers into "transmitters of curriculum?" What opportunities did the students have for ownership of their learning, to make sense for themselves? Might that be contributing to why "they don't get it"? What would happen if the students were engaged more as a community of learners? What if, instead of seeking an answer, students seek to examine their thinking about the problem? What if teachers encouraged students to share their ideas about what they view as difficult, confusing, a good starting point, and strategies for ways to solve? What if teachers used the content to help them think about how they learn and become involved in the process?

Other Interventions

I talked about using a rubric for writing and solving three-digit story problem. One teacher had the students' help her create the rubric that they would use during the final activities. Afterward, she noted more engagement in the task, many students checking the rubric as they worked, and better quality products in the end. In another class, I asked for feedback on a performance checklist they had used, they suggested some changes to the wording, but voted to use it again. Did it give them a sense of ownership or control over their learning?

I decided to approach the primary teachers with a new program developed by the non-profit Technical Education Research Center (TERC) in 1995. The curriculum was research based, and not designed commercially by a textbook company to teach state standards. It used tasks that made connections to home. This created more authentic practice and reduced the mismatch between school and home cultures (CIP question 3.3). The program also supported many teachers' belief in "best practice" because it approached mathematics as "making sense of concepts." Most teachers were at odds with the "testing" culture that the state standards had generated. After correlating the activities to the Standards of Learning and the Program of Studies objectives for multiplication and division, I shared the unit with the third grade teachers. They implemented the parts they valued, in a way that worked with their own style of teaching. In the weeks that followed, the teachers sought more connection to the symbolic, a uniform assessment tool across the grade level, and a formal test with which to assign grades.

A few weeks later, the module tests indicated significant improvements in class scores. The teachers were pleased with the results. I asked them what they thought made the difference. Their comments were: "more students talked in partnership, more manipulatives, more activities for practice, more games, more fun, a slower pace to build the concept, and the test focused on multiplication rather than a bunch of other topics too." As we moved more into the relationship between multiplication and division, one teacher remarked, "They never would have gotten this last year."

The school's new "all day kindergarten program" offered an opportunity to build mathematical understanding for students. This same research-based program with which I was working in third grade also had units for kindergarten. It provided background knowledge of concept development, engaging activities, and math connections. I shared the ideas and activities with this team at our weekly meetings. It gave them a sense of sound mathematical thinking at this level. The teachers' responses were favorable. They used the activities and reported back on them. A few requested additional units beyond those that were shared at our meetings. Though it is difficult to find evidence of change in students' understanding at this point, the teachers seemed to recognize the mathematical soundness of the program and expressed interest in using the program as a framework next year.

Findings

The Standards of Learning tests themselves had brought about changes--a focus on instructional practice, promotion of teamwork within a grade level and understanding across the grade levels, and an increase in professional conversations. But the changes occurred as a result of "fix it, for short-term gains," rather than "reflection, for long term results." And the change occurred at a price, the stress and burnout.

I hope that my interventions contributed to other kinds of changes. At the February workshop for SOL math training, I noticed a change. Teams seemed more cohesive and focused. Upper grade teachers shared strategies for working with test question format and language structure, ways to review and practice. Veteran teachers offered suggestions to new teachers and to teachers new to the grade level. Second and third grade teams got involved in the activities and games for number sense and mental math. They took notes, asked questions, and even laughed together.

In a questionnaire, I asked what we could do to improve students' understanding of those concepts that they repeatedly "don't get." What would make a difference? Most second, third and fourth grade teachers listed parent involvement and connections to real life experiences. Some specific responses were: "parental involvement," "connections between home and school, to real life, "daily real life math, " and "parents." Had this awareness developed over the past months or were the teachers just at a different point in the year to recognize the importance of these connections?

Implications

Textbook issues have long existed among the teachers. There has been on-going grumbling about the math texts adopted about four years ago. Our math series included module tests and skill books. It also was a framework for teachers new to a grade, the county, or the profession. Also, the district had developed a correlation chart for the text that matched each county objective with the activities on each page. This correlation chart had an unintended consequence. It helped turn the text into a math "basal" instead of a resource. It was a time-saving device, and time is like gold in the day of an elementary teacher! Another problem encountered with the text was the spiraling curriculum. Allsop and Kyger (1999) note that while this approach is appropriate for average achievers and above, the limited time given to each concept causes problems for at risk learners.

Staff development models need to look different. The "listen and learn" approach is not effective. Change occurs over time, with follow up, feedback, and depends in part on the relationship of trust among the participants. This becomes important in my meetings with grade level teams. While I was excited about something, I didnÃt give the teachers an opportunity to create their own understanding or become personally involved with the learning. In essence, I became the transmitter of information for the teachers, and they, in turn, transmitted it to the students.

Developing math connections to common student experiences required additional planning for the teachers. While my initial interventions seemed to increase student participation and quality of conversation, there was no difference in module test scores. Was the test format a mismatch, based more on procedural knowledge? Would it require more time and work to develop concepts through familiar experiences? Heightening student interest is only one step in learning process. Developing new activities or assessments also requires additional time. But, somewhere along the journey this year, teachers recognized value in their students' responses during these activities. In the final questionnaire, they listed "connections to real life experiences" as an element necessary to increase student understanding!

I was committed to the idea of home connections, but the "valuing" needed to come from the teachers.

The emotional climate of the school can promote greater commitment to a goal or it can disrupt the movement toward it. When politicians, state and district leaders approach teachers to change their instruction because their achievement levels are pathetic, few are receptive. It can be perceived as criticism. For those teachers who have worked hard to make a difference, yet do not see the student scores necessary to pass the Standards of Learning, the threat of "total staff reconstitution" is a stinging statement. It implies "bad teaching." Without acknowledgement or encouragement, people will sustain their efforts for a certain length of time. Eventually, they will disengage from the task or leave. I heard teachers at this point of discouragement. As I think about the state leadership in education, I wonder, "Why don't they get it?"

References

Allsop, D., & Kyger, M. (1999). MathVIDS: Math Video Instructional Development Source--Assisting Teachers to Teach Students Who Have Difficulty in Math. Sponsored by the Virginia Department of Education.

D'Agostino, J.V. (1996). Authentic instruction and academic achievement in compensatory education classrooms. Studies in Educational Evaluation, 22, 139-152.

Ensign, J. (1997, March). Linking life's experiences to classroom math. Paper presentation at the Annual Meeting of the American Educational Research Association, Chicago, IL. (ERIC Document Reproduction Service No. ED 412 093)

Fullan, M. (2000). The three stories of education reform. Phi Delta Kappan, April, 581-584.

Hyde, A., Daniels, H., & Zemelman, S. (1993). Best practice in mathematics. In S. Zemelman (Ed.), Best Practice: New Standards for Teaching and Learning in America's Schools. (pp. 69 -90). Portsmouth, NH: Heinemann.

Jensen, E., (1998). Teaching With the Brain in Mind. Alexandria, VA: Association for Supervision and Curriculum Development.

Marzano, R. J. & Schmoker, M. (1999). Realizing the promise of standards-based education. Educational Leadership, [On-line], 56. Available: http://www.ascd.org

Newmann, F. M. (1991). Linking restructuring to authentic student achievement.Phi Delta Kappan , 72, 458-463.