There is a durable myth that math ability, or interest, for children is only seen under rare circumstances, and, even then, only by those of rare intellect, or genius; but last week Linda Gojak, President of the National Council of Teachers of Mathematics held the rapt, and decidedly eager, attention of Catherine Ditto’s 6th grade class at the Burley Elementary School on Chicago’s Northside.
Using a game called ‘Remove One” where children remove chips from a numbered chart, Gojak then asked the children, after a roll of the dice, to remove one chip, and then created a corresponding chart, with chips of her own, and then asked the students targeted questions that explored both the frequency, and appearance of certain numbers, and any perceived patterns.
The classroom of 23 students, soon erupted, into cheers, and exuberant responses of “Yeah!” or “I got it” as their little hands stretched towards her to answer questions, displaying not only their eagerness, but also their grasp of the subject; whether it was decimal conversion, or number placement, giving testament not only to the skill of their regular teacher, Ditto, but also, their grasp of the subject. Indeed, in a question and answer session, one little girl piped up, eyes shining, “Oh, we could use this to predict probability!”
It was equally impressive to see their careful concentration, the ability to both postulate, and express numbers, and even identify arithmetic formulas, that many adults have long forgotten; along with opportunities for analytical reasoning, group work, and report writing.
Gojak was in Chicago for the Regional Conference and Exposition of the group, who with more than 80,000 members and 230 affiliates, is the “world’s largest organization dedicated to improving mathematics and education in prekindergarten through grade12.”
She told me, after the teach-in, that “We are moving away from traditional methods to help kids deeply understand and identify why these things [methods] work; a lot of kids don’t get math, and also for them to explain the reasoning, and not just [give] the right answer.”
Test Scores in Illinois
Math education has been on the forefront of the goals for Chicago, by many including Mayor Rahm Emanuel, and in September, the U. S. Department of Education noted that 80 percent of Chicago Public School 8th graders “are not grade-level proficient in math” as reported by cnsnews.com.
And, in 2011, the National Assessment of Educational Process tests administered by the Dept. of Education noted, also reported, that, “in the 8th grade math test, Chicago public school 8th graders scored an average of 270 out of 500, compared to an average of 274 for 8th graders in “large city” public schools, and 283 for 8th graders nationally as well as statewide in Illinois.”
With only 17 percent of CPS 8th graders rated as proficient in math, the end result is that, “80 percent of Chicago public school 8th graders were not grade-level proficient in math. According to the U.S. Department of Education, this included 40 percent who rated “basic” in math and 40 percent who rated “below basic.”
Most educators, particularly those in math education, identify the ability to do, and understand math, “as fundamental as reading” in grades K-12; an aspect that Emanuel has sought to achieve through increases on standardized scores, and also through cash incentives, plus teacher stipends
Of course, with the recent teacher’s strike, the issue of test scores became politicized, as he touted the importance of a longer school day – which added to much of the rancor between the Chicago Teachers Union Karen Lewis, and the mayor’s office – before, during, and after the recent teacher strike.
The August reports showed, as in previous decades, that the differences between “meeting” and “exceeding” test scores is indeed a wide one.
But, the fact that the scores were up 1 percentage point show little progress in this vital area, and as reported by the Chicago Tribune, DePaul University’s Center for Urban Education Barbara Radner commented that the CPS figures were “distorted . . . inaccurate, misleading and dangerous” to use as justification for a longer school day as having any real affect. In fact, the question posed by Radner is “what is the best way to teach kids?”
New ways to teach math
Gojak notes that it is important “that kids [should be] doing math in a context”, not in simple isolation, and that “we are trying to lay the foundation to math in the elementary grades, [especially] K through 6.”
She is particularly adamant that “this is preparation to show [later on] what they can or can’t do as adults, and if we don’t teach a bag of rules, then we have a bag of tricks,” meaning that mere tips, don’t convey knowledge in context, but Gojak also emphasizes roles for both parents and teachers, and Ditto added, that “parents have to support us by not saying, ‘Math is hard’, and “that teachers have to take on the role of the learner.”
Throughout the three-day conference, hundreds of teachers, and math educators poured into the downtown Hyatt Regency, where they participated in a wide variety of workshops presented by other educators, vendors, and academics.
One of the most packed of the interactive workshops was that of Janet Moore of the National Aeronautics and Space Administration (NASA) who literally had scores of math teachers huddled over their tables like undergraduates cramming for a final exam, as they used classroom math to investigate the mysteries of the supernova. Using ratios, proportions, triangles, conversions, and even rulers, the interest was intense, and Moore told us, afterwards in an email, that, while the initial reaction was panic that:
“At first, many teachers feel uncomfortable with such an open-ended task. They worry that their students won’t be able to figure it out, and they don’t like that there isn’t an answer “in the back of the book,” so to speak. But after working through the activity themselves and getting a chance to imagine what the activity could look like in their classrooms, the teachers get excited. They realize that this kind of activity, with appropriate structure in the classroom, can help develop the problem-solving and critical-thinking skills that we want all of our students to have.”
Critical thinking skills are certainly not a new educational concept, but for mathematics, especially on the K-6 scale, the focus has become essential.
Common Core Standards: Help or Hindrance?
One of the most welcomed, yet controversial issues, in math education are the Common Core State Standards for early childhood settings, where research has shown “that mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become more focused and coherent in offer to improve mathematics achievement in this country.”
As noted on their website, and presented in 2010, “The The Common Core State Standards Initiative is a state-led effort coordinated by the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO). The standards were developed in collaboration with teachers, school administrators, and experts, to provide a clear and consistent framework to prepare our children for college and the workforce.”
As laudable as this effort, is and certainly one that many might welcome, there is also a mixed reaction by some.
Zalman Usiskin, an educator, who is best known as the Director of the University of Chicago School Mathematics Project , held an informative, and fast-paced session, with SRO crowds as he led listeners on a tour of what has, and hasn’t worked in the classroom, even shocking some, when he said that such traditional math problems as the time-honored story problems, that most of us encountered in elementary school, left much to be desired, and in fact, “the problem is with applied mathematics, not with stories” and furthermore that “many traditional word problems are not applications.”
Usiskin also noted in a post-conference email that:
“The Common Core was built on the assumption that mathematics education in our country is worse today than it was 10, 20, or 30 years ago despite massive efforts at improvement. The data do not back that assumption; indeed, they show vast improvement in performance on NAEP by our elementary and middle school students, better performance on ACTs and SATs by high school students, and an extraordinary increase in the number of students scoring high on Advanced Placement calculus tests. Our best curricula are not much different from those of the top-scoring countries in the world because countries have often looked to each other for innovations, but the overall value and respect we give our teachers is far lower. We should be doing everything we can to improve work conditions in our schools and, by doing so, to make teaching a more attractive profession for our best students to enter. The difficulty of improving school conditions is that they are often related to the wealth of the citizens and the community in which the schools are located.”
The latter is especially seen in Chicago, with its tax base meeting educational needs where schools such as Burley (which has a Great Schools rating of 9 out of 10, based on a comparison of test result of all schools in the state) show a marked difference than those in less affluent neighborhoods.
But, at the 2011 NCTM conference, he also noted the weaknesses of the CCSS, when he identified that the number one problem was a “mismatch between standards for mathematical practice and standards for mathematical content,” plus an “overemphasis on paper-and-pencil computation”, which he also noted this year, stating while calculators are often disdained, or even forbidden by some teachers (especially in K-12 education), that they do a better, albeit a more “accurate job.”
He also bemoaned the fact, in 2011, that there was a “lack of consideration of those going directly from high school to the workplace,” with the result that many lacked the necessary quantitative and financial literacy.”
Teachers as Learners
Ditto’s comments on teachers as learners was evident during the conference at the Hyatt on Wacker Drive, as, at times, it resembled a college campus as hundreds of math educators streamed through the halls, backpacks slung over their shoulders, athletic sneakers on their feet, and clutching bottles of water, while looking earnestly at their materials, as they made their way to various workshops, and also vendor booths.
One in particular was “Math-U-See” staffed by father and son duo, Dan and Gary Sinclair, who are the distributors for an intervention for students in Tier 3; those that have not responded to interventions after general math education in Tier 1, and, who under Tier 2, still are struggling.
Using old-school methods for new learning, but built on foundational learning, and developed by Steve Demme, for home-based schooling, Math-U-See helps not only the student, but also, the teacher, by using a visual aid of plastic building blocks.
Dan Sinclair told us in a telephone interview before the conference, that his product “teaches the teacher” as they are able to monitor the progress of each student, and “that the focus should be on the teacher, providing them with the math content knowledge and tools, then teaching the student until the student can teach the teacher. This helps to focus on the Tier 3 discrepancies , and especially those with special education needs.”
Sinclair is also quick to support Ditto, when he noted that “we need to teach teachers and also to the parents, but especially to overcome learned helplessness,” a factor that he feels is central to address along with “math anxiety”, to further increase, and sharpen, student math skills.
Charter schools to the rescue?
Emanuel, on the other hands, feels that the best bet for increased scores are with charter schools, which have become a major plank in his education reform; yet reports and the research do not support his assertion, because, as we’ve seen, any appreciable difference between charters and the local neighborhood schools is negligible.
But, as the Tribune pointed out, in September, “Chicago Public Schools expect about 53,000 of the district’s roughly 400,000 students will attend charter schools this year, and the number of charters will increase to more than 100.” And, officials also want to add 60 charter schools in the next five years with help form the Bill and Melinda Gates Foundation, “which is trying to expand charters across the country.”
Emanuel is also aided, in this effort, by the wealthy elite with deep pockets, such as venture capitalist Bruce Rauner.
A downside, to charter schools, is that teacher attrition is higher than those in public schools, with a corresponding lack of regularity for their students; some of whom may not be as committed as those public school teachers that we spoke with, since they often quickly are forced to leave for higher wages.
What the future holds
In June of this year Gov. Pat Quinn, a former math teacher, signed into law four new laws to strengthen math education; an initiative by Lt. Governor Sheila Simon, who has expressed publicly her acute disappointment in Illinois math test scores.
According to the press release, “Senate Bill 3244, sponsored by Sen. Michael Frerichs (D-Champaign) and Rep. Linda Chapa LaVia (D-Aurora), was an initiative of Lieutenant Governor Sheila Simon. While visiting community colleges last fall, Simon learned that only 40 percent of Illinois high school students test ready for college-level math.”
It also noted that “the law requires the Illinois State Board of Education to work with stakeholders and educational organizations to create and coordinate the development of mathematics curriculum models.”
The law takes effect January 1, and in an email response to questions on how SB 3244 can help strengthen the Standards, Annie Thompson, Deputy Chief of Staff, Communications, for the Lt. Gov.’s Springfield Office, replied that: “Illinois adopted the Common Core standards in math and English to ensure that all students graduate from high school with the knowledge and skills they will need in order to succeed in higher education and in the workforce. “
She also notes that, “After spending last year visiting all of the state’s community colleges, and now the state’s universities this year, Lt. Governor Simon is working to strengthen math education. The Lt. Governor is committed to making sure that Illinois students entering college are prepared to tackle college-level math.”
As we have seen, there is a wide variety of recommendations to ensure that students, whether in elementary, or high school, receive specific types of targeted help. Thompson also notes that Simon, feels that among the myriad options the following should be done: “Align training programs and professional development for our teachers to the Common Core standards; help teachers to closely monitor student learning and individualize instruction for each student’s needs; increase the availability of online teaching and learning resources: curriculum outlines, lesson plans, practice problems, projects, and enrichment materials.”
Simon, according to Thompson, recommends that educators should, “Align new assessment systems to the Common Core Standards, and include more than just “fill in the bubble” multiple-choice tests once a year, and increase the availability of dual credit, dual enrollment, and advanced placement credits, so that students can demonstrate college readiness while still in high school.”
While everyone agrees that some type of benchmark should be established to ensure a baseline of acceptable results, standardized test scores have, of themselves become controversial, with some accepting them, without question, and others, claiming that teachers are teaching for the test.
Thompson, however, said that, “Standardized tests can be helpful in using one uniform method to evaluate a student’s progress; however, those tests also show a limited evaluation of a student’s learning,” and furthermore that a new computerized test administered several times a year, can aid in the establishment of these baselines through the Partnership for Assessment of Readiness for College and Careers (PARCC); Illinois is one of 23 participating states.
She also stresses the following: “Because no one test can completely reflect a student’s abilities, we are working with education stakeholders to develop additional tools and methods of evaluation.”
And, finally when it comes to K-12 instruction, Thompson says that, “it is important that students learn, use and retain more math knowledge and skills. SB 3244 will establish guides for math teachers to implement the Common Core standards.”
The final answers for increased test scores, or even standards, are not clear cut, and the stakes are high for the future of our city, and the nation, as many of the youngsters, now in school, are destined to be our future leaders, in a world much changed from what we have now; but certainly where those with math fluency, like the students in Ditto’s classroom, may make major decisions affecting not only policy, but budgetary decisions; and in this new world, they, and others, will need every skill, and every intervention that we can give them.