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For young English-language learners, language skills can be a barrier not just to reading but math as well. Educators and researchers working in two school districts here hope that helping students 鈥渢alk through鈥� number problems will assist them in meeting the state鈥檚 new math standards.

It鈥檚 part of Teaching English-Learners Early Mathematics, or TEEM, a pilot partnership between researchers at California State University, San Bernardino, and the Nuview Union and Romoland school districts, in California鈥檚 Inland Empire region. In 2014, the project won a development grant from the federal Investing in Innovation program to use a combination of Japanese 鈥渓esson study鈥� cycles and detailed student math notebooks to help teachers and students write and reflect on their math learning.

鈥淔or so many years, math was about getting the right answer, and if you got the answer, that was it. Now, it鈥檚 about justifying your thinking, and it鈥檚 amazing the number of times kids will get the correct answer, but really don鈥檛 know what they are thinking,鈥� said Shirley Roath, an education administrator and former middle school math teacher for Riverside County, which includes the two districts and is partnering in the TEEM pilot. The 鈥渘umber talk鈥� discussions, she said, instead focus on 鈥渓ooking at the kids and their thinking, not the teacher and her teaching.鈥�

TEEM focuses on early grades, from preschool through 5th grade, and targets high-poverty and English-learner populations; Boulder Ridge Elementary, for example,has 75 percent low-income and 18 percent English-learner students. The project is still collecting baseline data and has not yet evaluated its impact, but Madeline Jetter, the lead researcher for the project at CSUSB, noted that after the first year, teachers鈥� instructional styles are changing; classes are having more complex discussions of underlying math concepts, and teachers are asking students to come up with more diverse ways to solve problems. That, in turn, may help students be better prepared to tackle complex word problems and prealgebra later on.

Lessons Up Close

During one lesson last month, Deana Whyde鈥檚 1st grade class at Boulder Ridge Elementary here crowded on the carpet around a whiteboard marked with two groups of black dots. 鈥淲e鈥檙e going to really test our math brains today,鈥� Whyde said. 鈥淲ho can tell me if these two groups have the same value?鈥�

She led the class through the dots, which were aligned differently in each group, to decide that the groups were equal, then talked about the use of the equal sign to show the same value. Within a few minutes, the students鈥攎ore than a third of whom are English-learners鈥攈ad moved from grouping dots to pondering the 鈥渘umber sentence鈥� 6+5=10+_.

One by one, students talked through what the sentence was trying to say鈥攚hich numbers should be counted in a group, which groups should be compared with each other鈥攁nd then talked each other through the steps to find the answer. After going through two problems together, the children paired off with sets of tokens and counting frames to work through a series of equations together.

Afterwards, Whyde sat down with a handful of other 1st grade teachers and math instructional aides from her own and others鈥� schools, who had watched her with the class, to talk through what happened.

Vicky Kukuruda, a co-director of the TEEM project for the Riverside County office of education, saw that one student consistently added the larger of two numbers to the smaller one rather than the reverse; for example, for 3+7, he marked three tokens and then counted up, getting the correct answer of 10 but taking about twice as long as his peers. Whyde planned to contrast the two methods of counting during the next class to help the boy understand how to speed up.

Cycles of Teaching

The activity was the culmination of one round of TEEM鈥檚 lesson study鈥攁 Japanese model of teacher professional development involving cycles of lesson planning and teaching.

Jetter assigned 69 general and special education teachers, instructional coaches, and aides into small teams by grade level. Each group first discussed research around a particular topic in the state鈥檚 new math standards, such as understanding the equal sign or base-10 counting, and planned a lesson on it.

鈥淭eachers need to set the goals together,鈥� Jetter said. 鈥淭hey look at the standards they know are challenging to teach or challenging for their particular students to learn.鈥�

Later, one group member teaches the lesson to a class while the rest observe, and the group later discusses what worked and didn鈥檛. In the final part, another participant teaches the revised lesson for a different class in the same grade. Afterward, the whole group again discusses differences between the classes in what worked.

The cycles of lesson planning give teachers the opportunity to compare different approaches for different types of students.

鈥淲e don鈥檛 often get to stop in this profession and talk about instruction,鈥� Kukuruda said. 鈥淭eachers don鈥檛 go in at break and say, 鈥楬elp me figure out what went wrong in this lesson.鈥� 鈥�

Yet Whyde also noted that the discussions often reveal differences in how students have been taught to approach math by parents or schools in other countries. (Most of the school鈥檚 English-learners come from Mexican immigrant families.)

鈥淚t鈥檚 a valid way, so you honor the way,鈥� Whyde said.

Watching different classes respond to the same lesson also shows teachers how common ELL instructional approaches can backfire in math. 鈥淗ow many pencils altogether? Some teachers will say whenever you see 鈥榓ll together鈥� it means add up all the numbers,鈥� Jetter said. 鈥淏ut there are many examples where it may not be that鈥� which could confuse English-learners. 鈥淲e want students to really understand the problem.鈥�

Math Journals

TEEM also adapts science-lab-style journals to give students more practice writing about and reflecting on their math learning.

鈥淲hen principals walk through the classrooms and want to know what the class is doing, the quickest way to do that is to ask a child to see his notebook,鈥� Kukuruda said, 鈥渂ecause that should have a record of the teacher鈥檚 teaching and the student鈥檚 learning.鈥�

The notebooks also help teachers provide additional support for young children and those with limited English skills. One kindergarten teacher takes photos of her pupils鈥� work with blocks or other manipulatives to paste into their notebooks to help them remember what they can鈥檛 yet write down. As students progress from grade to grade, they practice writing down and 鈥渟howing their work鈥� for word problems and writing their reflections on what they learn, what confused them, and what questions they have each day.

鈥淭eaching students how to journal, so that all their thoughts are in one place, makes it easier as the year goes on,鈥� said Debbie Baadilla, a 1st grade teacher at neighboring Harvest Valley Elementary and a member of Whyde鈥檚 TEEM group. She has found students often go back through their notebooks to remind themselves of how to solve particular problems. 鈥淚t鈥檚 their time management, their document management. It鈥檚 not just about math; it鈥檚 about putting everything together.鈥�