Math

Want Algebra by 8th? Start With Proficiency in Foundational Skills by 4th

Sara Mead — Mon, 22 Sep 2008 15:26:00 -0400

A new report from the Brown Center on Education Policy at the Brookings Institution finds that 120,00 students nationally are enrolled in algebra as eighth graders even though they have math skills comparable to those of the average second grader. That may not sound like a lot of students, but it's nearly 8 percent of all American eighth graders enrolled in algebra courses, and to the extent that these underprepared students are spread across algebra courses with students who are better prepared, their presence may have a negative impact on the quality of algebra instruction offered to a much larger population of students.

Report author Tom Loveless suggests that this finding calls into question the recent policy push, particularly in some high-poverty urban school districts, to enroll increasing numbers of eighth graders (in some cases, all eighth graders) in algebra. But it also highlights the need to get much more serious about improving the quality of math instruction provided to students in the elementary grades. Students arrive in eighth grade doing math at a second grade level only when their elementary schools have seriously failed in teaching them basic math knowledge and skills.

The National Math Panel recommends that children achieve proficiency in whole number operations (addition, subtraction, multiplication, division) by fourth grade. Mastering these skills by the end of fourth grade is an essential prerequisite for students to be able to understand algebra by eighth grade. The substantial number of ill-prepared students in eighth grade algebra classes is a case study in the need for alignment that ensures the standards, curricula, and teaching strategies (as well as teacher trainign and professional development) we use in the early grades are designed to build seemlessly towards the accomplishment of goals we have for children to master in later years. In other words, if we want kids to master algebra by eighth, we need to focus at least as much energy on getting them proficient in whole number operations by fourth. That's a lot harder than simply mandating algebra for all eighth graders, but in the long term the results will be much better.

Photo by flickr user SoulCookie used under a Creative Commons license.

Building Math Skills in the PK-3 Years: Let's Count the Ways

Sara Mead — Mon, 08 Sep 2008 21:00:00 -0400

Washington Post reporter Michael Alison Chandler takes a look at math instruction in the early years, as part of a longer Post series on key issues in math instruction. When it comes to early education, policymakers and practitioners often tend to focus on language and literacy, since abundant evidence shows that it's very important for children to develop a strong foundation in language and literacy by third grade. But building foundational math skills in the early years is also important, and the too-often-overlooked subject is getting much needed attention now in the wake of a recent National Math Panel report that emphasized PK-3 math instruction. When it comes to improving children's PK-3 math development, policymakers need to think about several issues, including pre-k access, math focus in early education programs, teacher training, curriculum, and aligning math standards, curriculum, and teaching strategies across the PK-3 years.

As Chandler notes, children come to school with huge disparities in their math knowledge and skills, reflecting disparities in children's access to pre-k and other quality early education programs, as well as the support (or lack thereof) for early math learning in their home environments. Children who come from supportive home environments and/or attended quality pre-k often start kindergarten with strong counting skills, know all their shapes, and understand key math concepts such as "bigger than" or "less than." But many other children come to school with very little math background. The National Math Panel recommends that all children enter school with a basic understanding of numbers and counting. Helping make sure all children have opportunities to learn these skills before they begin kindergarten, and equalizing the playing field in terms of early exposure to math ideas and skills, is one important reason to support quality pre-k programs.

But ensuring pre-k access isn't enough. Even otherwise high-quality programs can fall short in building children's early math skills. Three factors are important here. First is focus: the emphasis on building early language and literacy skills that has shaped pre-k programs and policy in recent years is by and large a good thing, but sometimes this emphasis can come at the expense of math instruction. At the same time, preschools that follow a more traditional child-centered model may not devote enough attention to developng children's math skills, either. Good pre-k programs need to support children's developing math skills, as well as their language and literacy and their social and emotional development. Pre-k teachers need to be explicitly aware that fostering children's number, counting, and other math skills is a part of their job.

That leads to the second point: Early education teachers need the skills and knowledge to support their students' math development. Many early educators are themselves uncomfortable with math, and that can lead them to downplay math, or make it difficult for them to build young children's understanding of math concepts and skills. Training programs and professional development for early childhood educators need to include content that builds teachers' math knowledge and skills. Training programs also need to find ways to make early educators who may have had negative math experiences in the past more comfortable with the subject. This is particularly important as states expand early education programs that require early educators to hold a bachelor's degree. For many early childhood educators, meeting the math requirements for a BA can be an obstacle. But those courses include important math content that, if taught properly, will improve early educators' ability to support their students' math development. Institutions that train early educators need to develop new ways of helping mid-career adults master college-level math that make them comfortable with the subject, help them understand why what they're learning is relevant to their students' future math learning, and provide them strategies to use their math knowledge in fun ways in the classroom.

But access and quality teachers are only two-thirds of the picture: To ensure children develop foundational math skills, quality early education programs also need curriculum that ensure children are exposed to important math concepts, and in the correct sequence. What exactly constitutes a good math curriculum has become the focus on heated debate among educators and mathematicians. The National Math Panel took some steps to address this, but it's probably not going to cool down any time soom. What is clear is that a good early education math program needs to balance experiences that make math relevant and teach children to think about mathematical concepts with experiences that support the development of more fundamental skills, such as numbers, shapes, and counting for preschool and kindergarten children, and acquisition of "math facts" in the early elementary grads.

The recent emphasis on early math instruction should reiterate the importance of alignment in the pre-k and early elementary grades. Math knowledge and skills are highly sequential: Each new math skill, fact, or concept must build on a set of knowledge and skills that children already have. If children have gaps in their math knowledge and skills, it becomes increasingly difficult for them to progress in their math understanding. That's why clearly articulated curriculum and alignment are so important in early grades math instruction.

Similarly, activities to develop children's math skills need to be aligned with strategies to develop children's emerging language and literacy skills. Lots of children's early math learning has to deal with developing the vocabulary--numbers, shapes, "less than," "more than"--to talk about math concepts, and children who have poor verbal skills are at a real disadvantage in acquiring math skills, as many examples in Chandler's article illustrate. Ultimately, math is just another example of how, when we're talking about early childhood, everything is all tied up together, and alignment and language have to be at the center of whatever we're doing.

The National Math Panel has recommended that curriculum in the early years focus on the goal of all children achieving proficiency in whole number operations by 4th grade. That's an essential stepping stone to put children on track for mastering algebra in 8th grade, which is an important predictor for whether or not young people will graduate high school college-ready. In order for children to achieve proficiency in whole number operations by 4th grade, the entirety of PK-4 standards, curriculum, and teaching practice needs to be oriented to this goal, starting with high quality pre-k that helps disadvantaged and at-risk children catch up their deficits in math exposure before they get to kindergarten.

But it doesn't just start in pre-k of course: Parents and childcare workers can play an important role in developing children's math literacy before they even get to preschool or pre-k, by using number words when they talk to children; pointing out shapes and numbers when they come up in daily life; and engaging children in counting as part of daily activities (ie: let's count the steps as we go up: 1, 2, 3...). Chandler's article offers some great examples of other activities familes can engage in.

Let’s Count: Boosting Math in PK-3

Christina Satkowski — Tue, 18 Mar 2008 14:54:00 -0400

The National Mathematics Advisory Panel’s (NMAP) new report on math instruction in America has drawn a lot of press attention. Of the dozens of recommendations outlined in the report one thing is abundantly clear: We need to focus more on building core math skills in the early grades PK-3.

We all know that American high school students are falling behind in math. American 15 year olds rank 25th in math among their peers in the 30 most industrialized nations, according to the Program for International Student Assessment (PISA). But another international study, the Trends in Mathematics and Science Study (TIMSS), finds that the international math gap starts even earlier: Only 7 percent of U.S. fourth graders achieved the “advanced” level on TIMSS, compared to 38 percent in Singapore.

Improving PK-3 math instruction is critical to improving our standing in math. We all know that the early years lay an essential foundation of literacy skills that students must acquire to support later learning. But it’s also true that children need to master foundational math skills in the early grades in order to learn more complex math content—in particular, algebra—in middle and high school. Research shows that children who are exposed to a math-rich environment prior to entering school (both at home and in a pre-k classroom) are less likely to struggle with math in later grades. A 2006 study published in Developmental Psychology found that even trivial math talk to pre-schoolers (“you two go get your coats”, “put away four toys”) can boost a child's math skills.

To that end, the NMAP report makes four recommendations for PK-3 math instruction:

Focus curriculum around the goal of ensuring proficiency in whole number operations (addition, subtraction, multiplication, division) by Grade 4, in order to put students on track to learn algebra by Grade 8.
Ensure that students come to school with a basic understanding of numbers and counting. Familiarity with counting and numbers lays a foundation for children to acquire additional math skills and knowledge. Achieving this requires better pre-school and pre-k math instruction, as well as more research on quality early childhood math instruction.
Equip pre-k and early elementary teachers with the skills and knowledge to to recognize their students’ math capabilities and teach them core concepts and content.
Increase use of “math specialists” at the elementary level who have specialized math teaching knowledge and can focus on coordinating math curricula across grade levels.

The panel’s recommendations affirm and the importance of aligned curriculum in grades PK-3. Providing aligned math curricula and instruction beginning in pre-k and continuing through the early elementary years is the best way to ensure that young students build essential math skills at an even, graduated pace that leads to proficiency in whole number operations by fourth grade. Aligning PK-3 math curricula can also help reduce and weed out repetition from grade to grade, which the report identified as one factor slowing children’s acquisition of math skills.

The panel also highlighted an urgent need to improve the math skills and knowledge of PK-3 teachers. Too many early educators are unaware of young children’s cognitive capacity to understand mathematical concepts, or are themselves uncomfortable with and poorly trained in math. We need more research on both how to better prepare elementary educators in math, as well as the instructional methods that work best for teaching early math.

The NMAP report is the highest-profile recommendation in recent years to cement the link between quality math instruction in the early grades and math literacy in high school and beyond. It reminds us all that when it comes to boosting student success, Early Ed counts.

Photo courtesy of flickr user Inkyhack, used under a Creative Commons License.