A 3-year-old sat on the lap of his mother, who was visiting Richard Murphy Elementary School in Boston. Principal Mary Russo couldn't help watching the child, fascinated with how the boy kept peering to the ceiling.
"We have block ceilings, and his eyes were shifting up and down and from right to left," Russo says with a laugh. "I bet that child was counting [the blocks]. I'm not sure, of course. But he was seeing a pattern. It was really quite amazing. And as a teacher, it's your job to find out what children know and what they need to learn to be proficient."
The idea that children come to school with mathematical thinking already ingrained is nurtured through a new math program at Murphy as well as other Boston public schools. This program encourages students to continue to think on their own. And while all Boston schools are using the new program and are enjoying rising math scores on the Massachusetts Comprehensive Assessment System exam, Murphy is the most successful. These results are noteworthy because the public school has two bilingual populations and has 85 percent of its students in free or reduced lunch programs.
In 1998, 46 percent of students at the school passed math on the MCAS test. In 2002, 84 percent passed. The percentage of students working at proficient and advanced levels on standards-based assessments has risen. In 1998, 12 percent of students were proficient compared to 27 percent in 2002. In 1998, 8 percent were advanced compared to 15 percent in 2002, Russo says.
With the U.S. is struggling to maintain homeland security and boost its economy, the nation's schools are struggling to juggle budget cuts with improving academics. Disheartening news is that the nation's eighth-graders lie near the middle in math achievement, according to the 1999 Trends in International Mathematics and Science Study, formerly the Third International Mathematics and Science Study. Out of 38 countries, U.S. eighth-graders in 1999 were 19th with a 502 average score as opposed to Singapore's 604.
Mathematics learning and achievement may be in crisis in some areas of the nation, says Johnny Lott, president of the National Council of Teachers of Mathematics. "Crisis situations occur in schools in exactly the same ways that they occur between countries-when there is a lack of communication and trust," Lott says. "In such school situations, there is an obligation for both parties [schools and families] to make the effort and learn and understand why the situation exists, and what can be done to improve it."
TERC's Investigations in Number, Data and Space is a math curriculum program based on national standards and developed with classroom teachers. As an activity-based program, it encourages students to think creatively, develop their own problem-solving strategies and work cooperatively. It also empowers students in that they use their own thinking to solve a problem. Teachers later ask them how they devised their solution instead of simply giving them a formula to follow and memorize.
Many attribute Murphy's success to strong leadership and dedication from Russo to give teachers support and the freedom to leave the classroom to attend professional development.
"Mary is exceptionally committed and exceptionally devoted," says Sid Smith, director of curriculum and instruction in the Boston district.
After visiting Murphy School, Lott says, "It's a pretty impressive place." The outside of the building looks "beaten and banged," he adds, but "when you walk inside it's a very different feeling. It's refreshing. ...The teachers were supported. The kids appeared to be learning. I just liked the way Mary Russo has used aides and groups of people to help those kids."
Murphy is one of six Learning Site Schools in the district, meaning other district teachers and administrators visit to learn how to implement a successful program.
"I think there's a sense of teamwork and collaboration in the school," Russo adds. "We're all working together. ... We do it as a team."
Need for Change
In 1998, low MCAS math scores across the district were proof enough that change was necessary. "We knew we needed to change our [instructional] materials to get them better in line with state standards," Smith says. "We went through a rather lengthy process looking for materials."
Russo says when she saw the failure rate at her own school, she knew change was a must. "We asked ourselves some questions. 'What is this telling us about the math program here? What should students know and we're not teaching? And what are the implications for teaching math at my grade level?' "
Boston administrators chose TERC's Investigations mainly because it was based in Cambridge and the physical closeness was important for professional development purposes; it was standards-based and supported children's conceptual understanding of math; and research results were favorable, Smith says.
The district has spent about $15 million in city, Title I funds and a grant from the National Science Foundation over the past three years for K-12 math programs.
When the program was first implemented, many parents feared it would not help their children, and that it was "fuzzy math," Russo says. "Now, kids have mathematical thinking skills. They are thinkers. They love math. Even the struggling learners can express how to solve problems."
What it's all about
The TERC program involves a host of professional development, including five-day seminars to develop math ideas, Saturday and summer sessions as well as supplemental after-school programs using Great Source's math programs. Teachers also watch math coaches teach in front of students.
The program changes the old way of doing math. That way involved teachers writing problems on the blackboard and then explaining the lesson for 10 minutes. Children, sitting at desks in rows, would complete problems in workbooks, some of which would be reviewed by the teacher if there was enough time, and have more workbook problems for homework.
The new way of teaching math involves desks arranged in groups and students solving problems with their team members. Children solve problems in their own way and explain their thinking to the classroom. "Every kid's thinking is valued," Russo says. And problems could be posed to children by having them line up in class according to height and then asking them to figure out the class' median height.
Student math work is also plastered on walls throughout the building, from kindergartners' pictures on graphs to fifth graders' geometry and algebra concepts.
Professional development is key
"The whole pedagogy is questioning strategies," says Russo. "You have to listen to a child's thinking and you have to ask the questions to elicit thinking."
Teachers are given planning lessons and model lessons to actually learn how to conduct specific lessons. The school's math specialist, Jack Flynn, teams with Valerie Daniel, a district math coach who is there once a week, to demonstrate lessons in front of a classroom while a team of teachers looks on. Substitute teachers cover for teachers during this training.
They usually meet 40 minutes before a class lesson, discuss what the students learned up until that point, what is involved in the new lesson and what the expectations are of children. Then Daniel or the math specialist gives the lesson to students, while teachers listen to student responses during the class lesson.
Daniel, a former secondary school math teacher, also works one-on-one with teachers. She meets with teachers before lessons and discusses what children are expected to do.
Lenses on Learning at the Educational Development Center in Newton is a training program for principals to help deepen the understanding of math instruction based on investigative approaches, what a class should look like, and what kind of conversations and dialogue should take place among students and teachers. Russo has already taken part in the supervision of the program.
Computer teachers are also trained in the software so when fifth graders are in technology class, for example, they can create polygons on a computer screen.
Russo led her school to success in part with determination and by using MCAS assessment data and her own mid-year and end-of-year assessments associated with the curriculum, says Linda Ruiz Davenport, senior program director of elementary mathematics for Boston's 87 elementary schools. Teachers review assessment results for each child with Russo and Flynn. When they see areas where students need more support or students who are struggling with certain concepts, they look at where those areas are addressed in the curriculum and then focus on those areas so students can improve. The school also closely follows a pacing chart, which shows what unit teachers must be teaching during which weeks during the year.
"They're vigilant about gathering information on strengths and weaknesses and attacking them," Smith says. "They are exceptionally systematic in making sure it works."
Math Leadership Teams are also created in schools to develop leadership. Russo initially recruited 12 teachers to get involved in the program, having them attend the seminars and work with the Investigations' curriculum and elementary math coach. The second year of the math plan brought on 12 additional teachers at Murphy.
The teachers also attend the Curriculum Institute, which is an in-house, one-week program offered during the summer or early fall. The seminar explores how children learn about math and how children think about math.
Getting Parents to Buy In
Today's math in the Investigations curriculum is unlike anything parents learned in their day, which included rote memorization of multiplication tables. The math program encourages parental involvement beyond ensuring children are simply just doing their homework. So teachers and administrators are challenged to figure out how to engage parents as partners to improve mathematics teaching.
Now, many Murphy parents are supportive and are a critical part of the process. Almost 90 percent of parents showed up for a recent school/parent child report card conference, where parents received their child's report card and met with the teacher for a half-hour session. Parents see photographs of their child engaged in math activities and view student work created in the computer lab. Parents also take part in Math Night, where parents and children are invited to school. And they meet with Daniel, the math coach at Murphy, to talk about the type of math the students are learning.
Davenport says future plans include involving more parents and at a more intense level. The district plans to offer parent workshops so parents can learn how to talk to their children about math problems, how to ask the right questions of children, and how to show their children that they could solve problems in several ways. Davenport adds that while students are taught to explain their thinking on a particular problem, "parents don't know what that will look like." So parents have to learn the process so they can encourage their children to think in various ways to solve problems, she says.
Success in Student Empowerment
Educators say it's still too early to tell how well the math program works in the Boston district overall, though test scores are showing slight increases. Hopes are high.
"We have a long way to go," Smith says. He adds that the elementary program should prepare children for algebra-the "biggest challenge kids face when they hit middle and high school"-because the elementary math program teaches simple algebra and geometric concepts, including graphing with x and y.
"I would say overall the student response is enthusiastic," Davenport says. "I met with two principals on Monday, and they were talking to me about the math work in their schools. Students are now saying math is their favorite subject and asking if they could do more math [in class.] And when principals visit more classrooms, they are impressed with the mathematical thinking they are seeing.
"And students are very interested in examining their own thinking and engaging in classroom dialogue. ... Students find they can do this and they are actually able to make sense of things, talk about their solutions. It is very empowering."
Angela Pascopella, email@example.com, is features editor.