The post Protecting Students from Learning appeared first on Education News.

]]>**by Barry Garelick**

I attended Mumford High School in Detroit, from the fall of 1964 through June of 1967, the end of a period known to some as the golden age of education, and to others as an utter failure. For the record I am in the former camp, a product of an era which in my opinion well-prepared me to major in mathematics. I am soon retiring from a career in environmental protection and will be entering the teaching profession where I will teach math in a manner that has served many others well over many years and which I hope will be tolerated by the people who hire me.

I was in 10th grade, taking Algebra 2. In the study hall period that followed my algebra class I worked the 20 or so homework problems at a double desk which I shared with Raymond, a black student. He would watch me do the day’s homework problems which I worked with the ease and alacrity of an expert pinball player.

While I worked, he would ask questions about what I was doing, and I would explain as best I could, after which he would always say “Pretty good, pretty good”—which served both as an expression of appreciation and a signal that he didn’t really know much about algebra but wanted to find out more. He said he had taken a class in it. In one assignment the page of my book was open to a diagram entitled “Four ways to express a function”. The first was a box with a statement: “To find average blood pressure, add 10 to your age and divide by 2.” The second was an equation P = (A+10)/2. The third was a table of values, and the last was a graph. Raymond asked me why you needed different ways to say what was in the box. I wasn’t entirely sure myself, but explained that the different ways enabled you to see the how things like blood pressure changed with respect to age. Sometimes a graph was better than a table to see this; sometimes it wasn’t. Not a very good explanation, I realized, and over the years I would come back to that question—and Raymond’s curiosity about it—as I would analyze equations, graphs, and tables of values.

The study hall was presided over by a high school counselor whose office was in the corner of the great room. The day came when we were to sign up for next semester’s courses, and she called out the names of the students in her custody. Raymond went in for his appointment. There was some discussion going on inside and suddenly the counselor, not given to sensitivity nor controlling the volume of her speech, blared out in unrelenting anger for all the study hall to hear: “You want to take algebra 2? You didn’t finish Algebra 1, and you got a “D” in the part you did finish! You will take ‘General Arithmetic’, young man!”

Raymond walked back and took his seat next to me. I said I was sorry about what happened, but he didn’t look in my direction. I was 15 and didn’t quite know what to do, so I didn’t do or say anything else to him. He didn’t speak to me for the remainder of the semester, and when I worked my algebra problems he found something else to do.

I never saw him again after that semester though I do know he graduated when I did. I suspect that he didn’t take any more math classes, arithmetic or otherwise. I don’t know whether his interest in math was based on my making it look easy, or whether he would have made a serious effort to get up to speed. I also don’t know whether his poor performance in the algebra course he took was because of poor teaching, lack of ability, or because he was a victim of neglect who had been passed on and promoted to the next grade as many students had been. I doubt his counselor knew either. Whether his counselor would have reacted differently had Raymond been white is also something I don’t know. What I do know is that his interest was strong enough to want to enroll in an algebra course, and the question “Why do you need to learn that stuff?” did not seem to be on his mind.

**The Exchange of One Inequity for Another**

I have written previously and extensively about math as it was “traditionally taught” because I feel strongly about it and it is what I know best. Two of the main criticisms about traditional math – which have also been levied against education in general for the era — are that 1) it relied on memorization and rote problem solving, and 2) it failed thousands of students.

This last criticism refers to the low numbers of students taking algebra and other math classes in the 50’s and 60’s and is taken as evidence that the techniques of traditional math—drills, memorization and word problems that were not necessarily related to the “real world”—worked only for bright students who learned math no matter how it was taught. Another side to this argument, however, is that the low numbers of students who took algebra and other math classes during this period was because of the tracking practices that were in force at the time.

The history of tracking students in public education goes back to the early part of the 1900′s. By the 20′s and 30′s, curricula in high schools had evolved into four different types: college-preparatory, vocational (e.g., plumbing, metal work, electrical, auto), trade-oriented (e.g., accounting, secretarial), and general. Students were tracked into the various curricula based on IQ and other standardized test scores as well as other criteria. By the mid-60’s, Mirel (1993) documents that most of the predominantly black high schools in Detroit had become “general track” institutions that consisted of watered down curricula and “needs based” courses that catered to student interests and life relevance. Social promotion had become the norm within the general track, in which the philosophy was to demand as little as possible of the students. The educational system in the U.S. pitted many groups against each other— skin color was not the only determinant. Children from farms rather than from cities, and children of immigrants, for example, were often assumed to be inferior in cognitive ability and treated accordingly.

During the 60’s and 70’s, radical critics of schools such as Jonathan Kozol, brought accusations of sadistic and racist teachers, said to be hostile to children and who lacked innovation in pedagogy. “Traditional” schooling was seen as an instrument of oppression and schools were recast in a new, “hipper” interpretation of what progressivism was supposed to be about. In moving away from the way things were, the education establishment’s goal was to restore equity to students rather than maintaining the tracking that created dividing lines between social class and race. The end product however was a merging of general track with college prep with the result that college prep was becoming student-centered and needs-based with lower standards, and less homework assigned. Classes such as Film Making and Cooking for Singles were offered, and requirements for English and History courses were reduced if not dropped. Social class and race was no longer a barrier for such classes as evidenced by the increasing numbers of white students began taking them.

By the early 80’s, the “Back to Basics” movement formed to turn back the educational fads and extremes of the late 60’s and the 70’s and reinstitute traditional subjects and curricula. The underlying ideas of the progressives did not go away, however, and the watchword has continued to be equal education for all. While such a goal is laudable, the attempt to bring equity to education by eliminating tracking had the unintended consequence of replacing it with another form of inequity: the elimination of grouping of students according to ability. Thus, students who were poor at reading were placed in classes with students who were advanced readers; students who were not proficient in basic arithmetic were placed in algebra classes. Ability grouping was viewed as a vestige of tracking and many in the education establishment consider the two concepts to be synonymous.

The elimination of ability grouping occurs mostly in the lower grades but also extends to early courses in high school. The practice of such full inclusion is now so commonplace that theories have emerged to justify its practice and to address the problems it brings. “Learning styles” and “multiple intelligences” are now commonplace terms that are taught in schools of education, along with the technique known as “differentiated instruction” to address how to teach students with diverse backgrounds and ability in the subject matter. Teachers are expected to “differentiate instruction” to each student, and to keep whole-group instruction to a minimum. To do this, the teacher gives a “mini-lesson” that lasts 10 to 15 minutes; then students work in small groups and told to work together. The prevailing belief is that by forcing students to solve problems in groups, to rely on each other rather than the teacher, the techniques and concepts needed to solve the problem will emerge through discovery, and students will be forced to learn what is needed in a “just in time” basis This amounts to giving students easy problems, but with hard and sometimes impossible approaches since they have been given little to no effective instruction to the mathematics that results in effective mathematics problem solvers.

The limitations of differentiated instruction work hand-in-hand with other aspects of the educational beliefs that shun “traditional” modes of instruction. (Beals (2009) describes the current trends in very accurate detail.) It is not unusual to hear parents concerned over art-based projects in English classes that call for students writing book reports in the form of a book jacket or poster—in which the artistic merits of the poster or book jacket may count as much as the actual composition. Exercises in grammar have declined to the point that they are almost extinct. Essays now are “student-centered” which is to say that students write about how they feel about certain events that occur in a story, relating it to themselves—this extends to history classes as well. They may be asked how Hester Prynne would write a profile about herself on Facebook, or George Washington on the eve of battle. Objective analysis, along with grammatical drill, sentence and paragraph structure and other tenets of a basic education are considered passé and not in keeping with the current watchword of 21st century education.

Brighter students are seated with students of lower ability in the belief that the brighter students will teach the slower ones what is needed. And frequently this occurs, though the fact that the brighter students are often obtaining their knowledge via parents, tutors or learning centers is an inconvenient truth that is rarely if ever acknowledged. The result is that brighter students are bored, and slower students are either lost, or seek explanations from those students in the know. Another inconvenient truth is that in lower income communities, there are unlikely to be students who have obtained their knowledge through outside sources; they are entirely dependent on their schools.

Students forced to endure this form of education do not progress as rapidly and do not master the essentials necessary to be successful in high school math courses. Even many of the classes for gifted and talented students are conducted in this manner. For example, one gifted class for seventh graders designed a new playground to a budget. The parent who told me this was quite proud to add that the playground was built with minor changes. The project took the bulk of the semester and there wasn’t much else in the way of geometry, proportions, rates, and pre-algebra concepts such as negative numbers, exponents and radicals—unless such concepts were visited on a “just in time” basis as discussed above.

In lower grade math classes, teaching mathematical procedures and algorithms has given way to more pictorial explanations, using alternative methods of adding, subtracting, multiplying and dividing in the name of providing students with “deep understanding”. Process trumps content. The results are that such students are passed on into algebra courses in high school with little to no mastery of the arithmetic procedures that are essential to move on to more abstract versions of the same. As such, they do not qualify for the honors track courses, nor—ultimately—AP calculus.

Many who make it to the honors have received the instruction and knowledge they need through tutoring/learning centers or their parents. In some cases, there are schools whose gifted and talented program consists of a traditional approach for math and other subjects. Thus, students who qualify for such programs are exempted from the one-size-fits-all, student-centered classes. In either case, students entering high school have been unintentionally split into groups of students, some of whom will qualify for honors classes and those who will not. Depending on the high school, the non-honors courses may be watered down versions often by necessity. These students are passed on through the system in some schools; in others they receive failing grades. Students, through circumstances beyond their control, may end up “tracked” in sub-standard courses and will be ill-prepared to take math courses in college, thus shutting out possibilities of a career in the sciences or engineering.

A recent study by William Schmidt of Michigan State University (Schmidt, et al., 2011) also observes the differences in learning opportunities and concludes that the differences are a function of the education system structure. Thus, there are differences in content depending on the area of the school district and that there is a fundamental relationship between content coverage and achievement. Schmidt states that with respect to mathematics, if the districts examined in his study were to hold generally for the U.S. then “any student can be disadvantaged simply due to differences in the rigor of the mathematics taught in the district in which they happen to attend school.” While a variety of factors contribute to the disadvantaging of students as discussed above, eliminating ability grouping is a big one. Through the efforts and philosophies of otherwise well-meaning individuals, full inclusion and equality for all has served as a form of tracking.

**Not Good Enough for Traditional**

Critics of the traditional model of education–particularly math–argue that traditional methods worked only for the gifted kids (for whom it is assumed they will learn what they need to know no matter how it is taught). And the corollary to such thinking is that students not gifted are not good enough for the traditional method. The move to homogenize skill levels in the classrooms has been entrenched now for several decades. It has come to the point now that students who have been forced through circumstances into non-honors tracks, and judged to not be able to handle the “traditional mode” of education and are thus “protected” from it. And in being protected from learning they are therefore not presented with the choice to work hard—and many happily comply in a system that caters to it.

Which raises the question of whether higher expectations and more teacher-centered instruction yield better results. Vern Williams is a middle school math teacher in Virginia, who teaches gifted students and served as a member of the President’s National Math Advisory Panel. He relates a story about how he was recently assigned a tutorial class made up of students who had failed and barely passed Virginia’s sixth grade math exams. When he first started teaching the class they wanted to play games, but Williams challenged them and included material that he was teaching to his seventh grade (gifted) algebra classes. He reports “Many of the students wanted to ditch their regular ‘baby’ classes and just attend mine. They viewed my class as not only interesting but serious.”

But students who have been put on the protection-from-learning track fulfill the low expectations that have been conferred upon them. The education establishment’s view of this situation is a shrug, and—despite their justifications for the inquiry-based and student-centered approach that brings out all children’s’ “innate” knowledge of math—respond with “Maybe your child just isn’t good in math”. The admonition carries to subjects beyond math and is extended to “Maybe your child isn’t college material.” And while it is true that a “college for all” goal is unrealistic, the view that so many students somehow are lacking in cognitive ability raises serious questions. Simply put, you no longer have to be a minority to be told you may not have cognitive ability. As Schmidt (2011) states in his paper: “To attribute achievement differences solely to differences in student efforts and abilities is grossly unfair and simpleminded and ignores the fundamental relationship between content coverage and achievement.”

There is now an in-bred resistance against ability grouping using explicit instruction. That such approaches may result in higher achievement, with more students qualifying for gifted and honors programs, is something that the education establishment has come to deny by default. What they have chosen instead is an inherent and insidious tracking system that leaves many students behind. They have eliminated the achievement gap by eliminating achievement. And many of those left behind disdain and despise education and the people who managed to achieve what they could not—just as I imagine Raymond must have many years ago.

—————

References

Beals, Katharine. 2009. “Raising a Left-Brain Child in a Right-Brain World”. Trumpeter. (Chapter 3).

Mirel, Jeffrey; David L. Angus. Equality, Curriculum, and the Decline of the Academic Ideal: Detroit, 1930-68; History of Education Quarterly, Vol. 33, No. 2 (Summer, 1993), pp. 177-207

Schmidt, W., et al. 2011. Content Coverage Differences across Districts/States: A Persisting Challenge for U.S. Education Policy, American Journal of Education, Vol. 117, No. 3; University of Chicago Press; (May 2011), p. 422

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]]>The post Survey: UK Parents Struggling to Help with Basic Math Homework appeared first on Education News.

]]>Of 1,000 parents of United Kingdom primary school children surveyed, 46% said that they felt ill-equipped to help their children with their math homework – especially in the long division execution.

Other areas that are proving to be difficult for parents are conversion of decimals, fractions, and percentages. Math was considered the hardest subject to help their children with by 34%, while 8% said that English was the most difficult.

“Often, parents struggle to help with children’s maths homework because the method of teaching – for long division, subtraction etc – has changed. The Maths Factor sets out to specifically help parents, so parents can preview the next lesson for their child. In fact, many parents have found that they have actually got quite good at maths by watching the videos themselves.”

Research published this week, commissioned by Pearson, reveals that half of the parents surveyed are not aware of the changes in the math national curriculum in the UK for primary math, introduced this September, nor are they aware that the curriculum is designed to be more challenging.

Carol Vorderman, a former television game show host, also created The Maths Factor, an online math school for primary-age children. She says that the primary years of math study are crucial to the success of students as they make their way up to the higher levels of math education. Vorderman also says that if students are struggling with math at age 11, they, for the most part, will not pass their GCSE in the subject. She wants to make sure that parents have the support and guidance they need.

The *Press Association* reports that about half of the parents who participated in the survey could not do math problems designed for ten-year-olds. 19% of parents said they did not feel confident about helping their children with long multiplication and 6% said helping with multiplication tables would be difficult. Only 9% said they did not find math useful in their everyday life, and 82% believe that math at the primary school can help children solve more complex problems in later life.

Vorderman agreed with the majority:

Ms Vorderman said: “Maths skills are essential in everyday life and it’s perhaps concerning to see a divide opening up between those who are aware of the new curriculum and those who aren’t, and between those who have the confidence to help their children and those who don’t. As a parent myself, I know how busy life gets, but with a bit of support we can all easily become confident with numbers.”

Despite parents admitting that they did not feel they were up to the task of helping their children with their math homework, 82% of the survey subjects said they find math useful in working life, which was second only to English at 85%, reports Aled Blake, writing for *Wales News*.

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]]>The post LEGO Education’s MoreToMath Brings Bricks to Math Education appeared first on Education News.

]]>LEGOs, the long time favorite building blocks during playtime, are now also the building blocks of elementary mathematical education as LEGO Education announces the presale of their newest program: Lego Education MoreToMath 1-2.

The innovative classroom resource uses LEGO bricks to make abstract math tangible for first and second grade students, according to *Brick by Brick*, LEGO Education’s blog.

The hands-on tools include a LEGO brick set specifically designed for classrooms, training videos for teachers, curriculum, interactive whiteboard software, and worksheets for teachers and students that access the students grasp of the eight practices of mathematical problem solving that the Common Core Math standards have outlined.

Leshia Hoot, LEGO Education’s senior segment manager for preschool and elementary education, explained that educators were voicing their struggles about teaching the new Common Core math practices. MoreToMath is designed to help teach real world problem solving that supports the Common Core expectations, reports *Education World.*

“One of the primary things that we lack in our classrooms is the motivation piece and engagement in mathematics, and a lot of that has to do with reluctance of the teachers to know how to use hands on materials in the classroom. So, this particular product will offer teachers an opportunity to do something that is easily transferable from the textbook knowledge that they need to teach the kids and is easily blended into their daily mathematical teaching,” says Dr. Shirley Disseler, a co-developer of Lego Education MoreToMath 1-2.

Students are expected to learn 5 key learning values, as outlined by LEGO Education on Lego.com. The first is problem solving skills, understanding the basics of mathematical problem solving, comprehending problems, perseverance, modeling, representation, reasoning, and precision. Second, comprehension skills gained from hands on activities that reinforce algebraic thinking, areas of numeracy, operations in base 10, measurement, geometry, data, and spatial awareness. LEGO says that collaboration skills, communication skills, and technology skills are all developed with this product.

Students learn these lessons with LEGO figures Max and Mia and they work in pairs to complete each activity. While children have the actual Logo bricks to work with as they solve problems, they can easily share answers with each other using the smart white board software.

Dr. Disseler adds, “The other thing that is important with this product, that you don’t see in other products, is that it gives the kids visual, tactical and kinesthetic ways to show and do their math. [It] gives them an opportunity to converse about mathematical vocabulary, what their learning, learn to ask question of one another and actually be their own thinkers.”

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]]>The post One Step Ahead of the Everyday Math Train Wreck appeared first on Education News.

]]>**by Barry Garelick**

The first math tutoring session with my daughter and her friend Laura had ended. I sat in the dining room, slumped in my chair. “You look sick,” my wife said.

“I am,” I said.

My daughter—subjected to the vagaries of Everyday Mathematics (1), a math program her school had selected and put in effect when she was in the third grade—was having difficulty with key concepts and computations. She was now in 6^{th} grade, and with fractional division, percentages and decimals on the agenda, I wanted to make sure she mastered these things. So, near the beginning of 6th grade, I decided to start tutoring her using the textbooks used in Singapore’s schools. I was familiar with the books to know they are effective (2). To make the prospect more palatable, I suggested tutoring her friend at the same time, since Laura’s mother had mentioned to me that her daughter was also having problems in math.

I figured I would start with the fourth grade unit on fractions which was all about adding and subtracting fractions, which they had already done, and then move rapidly into fifth grade, and start on the rudiments of multiplication. “This’ll be easy,” I thought. “They’ve had all this before in 4th and 5th grades.”

We only made it into two pages of text in the fourth grade book. I came to find out that despite their being in 6th grade, the concept of equivalent fractions (1/2 = 2/4 = 3/6 and so on) was new to them. This was the beginning of my attempt to teach my daughter what she needed to know about fractions while trying to stay one step ahead of the train wreck of Everyday Math (EM).

**Train Wreck Defined**

To understand why I refer to Everyday Math as a train wreck, I need to provide some context. First of all, some information about me: I majored in mathematics and have been working in the field of environmental protection for 36 years. I not only use mathematics myself, but I work with engineers and scientists which requires a fairly good proficiency in it.

Everyday Mathematics was developed at the University of Chicago through a grant from the Education and Human Resources Division of the National Science Foundation in the early 90’s. It has been implemented in many public schools in the U.S. Parents have often protested its adoption and in some cases have prevented it from being used, or succeeded in getting the program halted. For example, after a local parent group put pressure on the Bridgewater-Raritan Schools in New Jersey, a very comprehensive program evaluation was conducted (http://www.brrsd.k12.nj.us/files/filesystem/Math%20Evaluation%20Report.pdf) which resulted in a 9-0 school Board vote to replace Everyday Mathematics with a more balanced and traditional program, HSP Math by Harcourt School Publishers. In other cases (such as in Palo Alto, California most recently), it has been adopted despite protests from parents.

The Singapore math texts are part of the Primary Mathematics curriculum, developed in 1981 by Curriculum Planning & Development Institute of Singapore. Singapore’s math texts have been distributed in the U.S. by a private venture in Oregon, singaporemath.com, formed after the results of the international test TIMSS spurred the curiosity of homeschoolers and prominent mathematicians alike.

As I mentioned, my daughter’s school in Fairfax County, Virginia started using the program when she was in third grade. By fourth grade, I was seeing some of the confusion caused by EM’s alternative algorithms. This aspect of EM has been written about extensively so I won’t dwell on it here [*i, ii, iii*] except to say I wanted to make sure my daughter understood the standard algorithms for two-digit multiplication and for long division. Her teacher insisted they use the alternative algorithms offered by EM; she did not teach the standard algorithm for long division. Some of the teachers at her school offered tutoring services, so we hired one of them to teach her the standard algorithms.

The teacher/tutor did as we instructed and after four sessions, my daughter was excited to show me how she could do long division. She wrote out a long division problem but got stuck along the way when she didn’t know the answer to 28 divided by 7. Long division is predicated on students knowing their multiplication facts. My daughter was not alone in this; many of the students in her class did not know them. Perhaps her tutor had discussed what to do in such instances. It was apparent that whatever she told her was not to brush up on her facts, but rather go back to first principles, since my daughter was now drawing 28 little lines on the sheet of paper and grouping them by 7’s. I decided to inquire.

“WHAT ON EARTH ARE YOU DOING?” I asked. My daughter began to cry.

I felt bad about yelling. Later, my wife, daughter and I sat down and reached an

agreement. It was too expensive to keep on having her tutored– I had spent $200 so far on tutoring and really could not afford any more. We would therefore halt her tutoring and I would take over provided that I would not yell.

I helped her on an ad hoc basis. If she needed help, I would step in. The problem is that when she needed help, it was generally too late, and I would end up having to do damage control. One problem I was having was that EM does not use a textbook. Students do worksheets every day from their “math journal” a paperbound book that they bring home. Without a textbook, however, it is not always apparent what was taught—particularly when the student doesn’t remember. Any explanation that a student has received about how to solve such problems is done in class. The technique is contained in the Teacher’s Manual, but that is something neither students nor parents have. There is a student’s reference manual, a hardbound book containing topics in alphabetical order and which can provide some guidance, but does not necessarily cover what was said in class. Thus, there is no textbook a student (or parent) can refer to go over a worked example of the type of problem being worked. Worse, sometimes problems are given for which students have no prior knowledge or preparation. They appear to be reasonable problems—it is just not evident to the parent who steps in to help the struggling child that they have had little or no preparation for such problems. Then there is the issue of sequencing, or lack thereof—which I will discuss later.

By the time my daughter was in fifth grade, she would get a problem like 8÷0.3. They had not had fractional division, and limited work with decimals—certainly nothing like this problem before. A typical dialogue would then proceed as follows:

Me: What did the teacher say about how to solve this?

Daughter: I don’t know.

Me: Whattya mean you don’t know? You were there weren’t you?

Daughter: I don’t know what he said; he just said do the problems.

Me: Well, how do they expect you to do this? You’ve never had anything like this before. SO OF COURSE THEY GIVE YOU SOMETHING THAT YOU CAN’T DO AND YOU’RE SUPPOSED TO FIGURE IT OUT?

Wife: (offstage) what’s the yelling about?

Daughter: It’s OK, he’s not yelling at me.

Me: I’m not yelling at her.

Wife: (offstage) I heard yelling. Are you getting mad at her?

Daughter: He’s not getting mad at me; he’s mad at the book.

My daughter’s fifth grade teacher shared my disdain for EM and supplemented it heavily with photocopies of pages from an older textbook. I told him once in an email that I was not happy with EM and asked him his opinion. I’ve asked other teachers this question and they usually chose not to answer—perhaps out of fear for their jobs. I was surprised therefore when he responded: “I totally agree with you on everything you said about Everyday Math. It has been very difficult for me to use the book.”

Despite his knowledge and good teaching, there was still lack of a textbook and he was still consigned to the pacing and sequence of EM. I believe these factors contributed to the lack of knowledge about fractions exhibited by my daughter and Laura.

**The Long March to Fractional Division**

Knowing that in 6^{th} grade, they would learn fractional division, as well as decimals and percents, I feared a train wreck if I didn’t get to my daughter first. Given how little they knew about fractions during the first lesson, I felt that my fears were justified.

Fortunately, things progressed nicely with the two girls after that first lesson. But I only had about four weeks before they hit fractional division—not a lot of time. Therefore, I decided to teach each chapter on fraction in the Singapore Math, from 4^{th} grade to 6^{th} grade textbooks in a concentrated burst. Although I really should have started all this back in 4^{th} grade, doing it this way had an unexpected benefit: they saw almost immediately the connections between multiplication and division of fractions. This was no coincidence—the curriculum is very carefully sequenced. And while fractional division isn’t presented formally until the 6^{th} grade, students are working on aspects of fraction division long before they reach the 6^{th} grade. By the time students reach the 6^{th} grade unit on fraction division, they have done hundreds of these problems leading to an understanding of the meaning of and connection between fraction multiplication and division.

The heavy lifting with Singapore worked well; when they got to EM, it was a review. It was almost anticlimactic. It was a one page worksheet asking questions such as “How many ¾ inch segments are there in 3 inches?” After four such questions, the text presented a formula in a box in the middle of the page, titled “Division of Fractions Algorithm”. The algorithm was stated as a/b÷ c/d = a/b * d/c. Unlike in Singapore Math, there was nothing to connect any invert and multiply relationships to previous material. In fact there was nothing that appeared to lead up to this—just a rule to be memorized despite EM’s pledge to teach “deep understanding”. As I and many other parents I’ve spoken with have found, EM lacks the sequencing to pull it off; and that is the crux of the train wrecks that were to come.

**The Spiraling Train Wreck: Numbers with Points in Them**

Despite the victory with fractional division, the following week’s tutoring session left me slouched in my chair with my hand over my eyes.

“You look sick,” my wife said.

“I am,” I said. “Just when you think everything is going great, it isn’t.”

I had planned to focus on word problems in fractional division to cement in the concept, but apparently the day’s math lesson at school had confused Laura, and before my lesson could begin, she asked me the following question:

“I’m confused about something,” she said. “How do you get from a number on top and number on the bottom of a line into a number that has a point in it?”

I had her repeat the question a few times before I understood she was asking how you convert a fraction to a decimal. Now, Laura was bright and she knew what a numerator and denominator were, and what a fraction was, but apparently the EM lesson they were working on sprung this on them without warning

I wasn’t planning on teaching decimals that day, but seeing that the train wreck of conversion of fraction to decimal was upon us, I took this as a cue. Singapore presents conversions for the first time in the 4^{th} grade text [*iv*] showing 6 dimes divided into 3 groups yielding 2 dimes per group, which is expressed first as 6 “tenths” divided by 3 is 2 “tenths”. They then take it to the next step: 0.6÷3 = 0.2. After a few more similar problems, Singapore then introduces 2÷ 4 and shows a boy thinking “2 is 20 tenths.”

At the end of the unit they are solving problems like 2.4÷ 6, 3 ÷ 5 and 4.2 ÷7 as well as non-terminating decimals such as 7 divided by 3. What is striking about this lesson is that while its focus is decimal division, the lesson implicitly teaches how to convert fractions into decimal form by virtue of students having learned earlier that fractions are the same as division. That is, they have learned earlier that 1÷ 4 is the same as ¼. The lesson on dividing decimals was situated in the context of fractions—and treating fractions (i.e., tenths) as units—a unifying theme that extends throughout the Singapore series.

I’ve thought about why Laura could not understand the lesson at school, to the extent she could no longer recognize what a fraction was. I believe it is because while Singapore situates decimals in the context of fractions, EM situates decimals in the context of the unfamiliar. The EM program is predicated on the theory known as the “spiral approach”:

“The *Everyday Mathematics *curriculum incorporates the belief that people rarely learn new concepts or skills the first time they experience them, but fully understand them only after repeated exposures. Students in the program study important concepts over consecutive years; each grade level builds on and extends conceptual understanding.” [*v*]

This does in fact make sense considering that for most people a particular concept or task starts to make more sense after they have moved on to the next level. But this phenomenon occurs when there is mastery at each previous level. For example, I became fairly good at arithmetic and developed a deeper understanding of it after I took algebra; I fully understood analytic geometry after calculus and so on. Each previous bit of learning seems that much more apparent at the next level of understanding.

In EM, however, students are exposed to topics repeatedly, but mastery does not necessarily occur. Topics jump around from day to day. Singapore Math’s very strong and effective sequencing of topics is missing in Everyday Math. While Singapore develops decimals by building on previous knowledge of fractions, in Everyday Math, students are presented with fractions and decimals at the same time. The topic of conversion of fractions to decimals occurs in the fourth grade in the context of equivalent fractions, and is called “renaming a fraction as a decimal”. The “Student Reference Manual presents fractions that can easily be expressed as an equivalent fraction with a denominator of a power of 10 such as ½, or ¾. For fractions that cannot be directly expressed with power of 10 in the denominator, the Student Reference Manual provides the following instruction: “Another way to rename a fraction as a decimal is to divide the numerator by the denominator. You can use a calculator for this division. … For 5/8 key in: 5 ÷ 8; “enter”; Answer: 0.625.” [*vi*]

It is not surprising then that Laura would fail to see what was going on. Without knowing what the connection was between fractions and decimals, the fraction ceased being a fraction in her mind and was just a number on top and a number on the bottom with a line in between. And somehow that strange looking number got transformed into a number with a point in it.

**What the Casual Observer Doesn’t Know**

A casual glance at Everyday Math’s workbook pages does not reveal that there is anything amiss. The problems seem reasonable, and in some cases they are exactly the same type given in Singapore Math. What the casual observer doesn’t know is what sequencing has preceded that particular lesson, nor how that lesson is conducted in class. What is supposed to happen is that students are given a series of problems to work (in small groups). The Teacher’s Manual advises teachers to monitor students as they work through the worksheet and look to see if students can answer certain key questions. If a student cannot, it is an indication that the student needs more help. This means “reteaching”. Reteaching amounts to having students read about the particular topic of concern in the Student Reference Manual.

If the lack of proper sequencing, lack of direct instruction, lack of textbook and lack of mastery of foundational material prevents a student from making the necessary discoveries, he or she can be “pulled aside” and given material to read. So teachers are left with a three ring circus of kids getting it, kids not getting it, and are expected to “adjust the activity” as needed.

By the time EM gets to 6th grade, the workbooks are loaded with Math Boxes—the term for worksheet review sessions that come in the midst of a particular unit and consist of a mixture of problems from past years in the hope that the kids will finally master the material. Students get ever increasing amounts of Math Boxes. The expectation is that the nth time through the spiral is the charm. With EM, every day is a new train wreck of repeated partial learning.

**Connecting Home with School**

The danger of an “after schooling” program such as I was conducting is a tendency for the students to think of the math learned at home to be different or unconnected with the math learned at school. My goal of staying one step ahead of train wrecks worked to get to the topics first, so that by the time they got to it in school, they had seen it before. This was difficult since I was held hostage to EM’s topsy turvy sequencing and occasionally was forced to tackle things like geometry that came out of nowhere. All in all, the crash course that I cobbled together on fractions provided the proper framework to then work with Singapore Math’s lessons on percents, ratios, proportions and rates. The rest of the semester came without undue problems and both girls got A’s in the class I’m happy to say.

I’ve told this story to many people since it happened—mostly people who have asked me what to do when their school has a problematic math program. My last retelling was to my wife; it’s a recurrent theme in our house. We were reminiscing about when I had our daughter’s toy blackboard set up in the dining room, and I was teaching her and Laura the math they weren’t learning at school.

There was no need for me to finish the conversation, because the conclusion is always the same: Poorly structured math programs are not fair to students, parents or teachers. It is unfair to students because they are essentially attending another class after a fully day in addition to finishing their homework for school. It is unfair to parents who have to either teach their kids or hire tutors—and are held hostage to the school’s math program whether they like it or not. And it is not fair to teachers who are expected to teach students based on an ineffective and ill-structured program. Through no fault of the teachers, math taught via EM is math taught poorly. It is by no means easy to teach math correctly. But it is even harder to undo the damage by math taught poorly.

Many teachers do not realize that they have been given an unenviable and impossible task. In fact, I have spoken with new teachers who speak of EM and other poorly conceived programs in glowing terms, speaking of them as leading to “deeper understandings of math.” Some have said “I never understood math until I had this program.” But it is their adult insight and experience that is talking and creating the illusion that the math is deep. Children cannot make the connections the adults are making who already have the experience and knowledge of mathematics.

Through my experience teaching my daughter and her friend, I have come to believe that an essential requirement of textbooks is that they teach the teachers. This may happen to some degree with EM, but based on my experience with the program, not much gets transferred to the students. With Singapore Math or any well structured and authentic mathematics program, both teachers and students greatly benefit.

Shortly after this experience, I began taking evening classes at a local university to obtain certification to teach math after retirement. I have no illusions—I’m told that it isn’t easy. I’m not out to save the world—just to educate one child at a time. That said, I will remain forever grateful to my daughter and Laura for having taught me so much about fractions.

**References:**

[*i*] Braams, B. (2003). The many ways of arithmetic in UCSMP Everyday Mathematics. *NYC HOLD website.* February. http://www.nychold.com/em-arith.html

[*ii*] Braams, B. (2003). Spiraling through UCSMP Everyday Mathematics. *NYC HOLD website*, March. http://www.nychold.com/em-spiral.html

[*iii*] Clavel, M. (2003). How not to teach math. *City Journal,* March 7. http://www.city-journal.org/html/eon_3_7_03mc.html

[*iv*] Singapore Math 4A

[*v*] Everyday math; Education Development Center; Newton MA; 2001. Available at http://www2.edc.org/mcc/PDF/perspeverydaymath.pdf

[*vi*] University of Chicago School Mathematics Project; 2004. *Everyday mathematics. Student reference book. 2002. *SRA/McGraw-Hill; Chicago (p. 59)

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]]>The post Undoing the ‘Rote Understanding’ Approach to Common Core Math Standards appeared first on Education News.

]]>*by Barry Garelick*

A video about how the Common Core is teaching young students how to do addition problems is making the rounds on the internet: http://rare.us/story/watch-common-core-take-56-seconds-to-solve-96/

Much ballyhoo is being made of this. Given the prevailing interpretation of Common Core math standards, the furor is understandable. The purveyors of these standards claim that they neither dictate nor prohibit any pedagogical approach, but the wave of videos and articles sweeping the internet like the one above suggest the opposite may be true: that, in fact, the Common Core math standards *are *dictating how teachers are to teach math.

The method of “making ten” is not unique to Common Core. It is how it is implemented that’s the problem. The method is embedded (and explained by way of example) in **Standard 1.OA.C.6: **

*“**Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as… making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9)….”*

The “making ten” method is included in the math program used in Singapore—a nation whose fourth and eighth graders have consistently obtained the highest scores in international math tests. Specifically, in Singapore’s Primary Math textbook for first grade, the procedure for adding by “making tens” is explained. Of particular importance, however, is that the procedure is not the only one used, nor are first graders forced to use it. This may be because many first graders likely come to learn that 8 + 6 equals 14 through memorization, without having to repeatedly compose and decompose numbers in order to achieve the “deep understanding” of addition and subtraction that standards-writers—and the interpreters of same—feel is necessary for six-year-olds.

“Making tens” is not limited to Singapore’s math textbooks, nor is it by any means a new strategy. It has been used for years, as it was in my third-grade arithmetic textbook, written in 1955 as shown in the figure below:

*(Brownell, et. al., 1955)*

The book did not insist on this method; it was introduced as a possible help. Students were required to use it in one set of exercises in my old textbook. Then it was up to the student whether to use it or not. As such, it served more as a side dish than the main dish it is turning out to be; in some cases, students discovered the method on their own. (I have written about this and other methods in a series on common sense approaches to the Common Core math standards: see here and here.)

What has been used as a help in older textbooks and in Singapore, is turning out to be a hindrance in the U.S. under the current interpretations of Common Core. Insisting on calculations based on the “making tens” and other approaches are in my opinion not likely to prove useful for all first graders. Teachers should be free to differentiate instruction so that those students who are able to use these strategies can achieve those goals. It is unrealistic and potentially destructive to interpret the Common Core math standards as requiring that all first grade students use these strategies in the name of “understanding”. That should be the real objection voiced to demonstrations of this method under Common Core—not the method itself.

The mantras of “students shall understand” and “explain” are what Tom Loveless of the Brookings Institution calls the dog whistles of Common Core that are picked up on and responded to by the math reform movement. In my opinion, while not dictating particular teaching styles, the CC math standards have given the math reform movement that has been raging for slightly more than two decades in the United States a massive dose of steroids. Reform math has manifested itself in classrooms across the United States mostly in lower grades, in the form of “discovery-oriented” and “student-centered” classes, in which the teacher becomes a facilitator or “guide on the side” rather than the “sage on the stage” and students work so-called “real world” or “authentic problems.” It also has taken the form of de-emphasizing practices and drills, requiring oral or written “explanations” of problems so obvious they need none, finding more than one way to do a problem, and using cumbersome strategies for basic arithmetic functions.

The reform math ideology is in fact encouraged in the Common Core math standards in some suble and not-so-subtle ways. In particular, CC’s own documentation of the standards states that understanding is a major shift in how math should be taught:

*“The standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives in order to see math as more than a set of mnemonics or discrete procedures.”*

Such philosophy plays into the math reformers’ unwavering beliefs that requiring students to master practices such as “making tens” will result in students understanding how numbers work—as opposed to just “doing” math. In fact, reformers tend to mischaracterize traditionally taught math as teaching only the “doing” and not the understanding; that it is rote memorization of facts and procedures and that students do not learn how to think or problem solve.

Because CC emphasizes understanding rather than just doing, it has become *the *way to teach math and has become synonymous with Common Core. Schools and administrators may resist an approach that does not require students to master a supplemental approach to help add numbers. This is because standardized tests—the mechanism of accountability for many in education—may require reform math approaches to math problems. The fear is that students will do poorly on such tests because they will not know how to write explanations that demonstrate the so-called understanding. But such thinking confuses cause and effect. Forcing students to think of multiple ways to solve a problem, or using “making tens” as a method to explain why, for example, 9 + 6 equals 15, does not in and of itself demonstrate understanding. Those who believe it does seem to be saying: “If we can just get them to do things that *look* like what we imagine a mathematician does, then they will be real mathematicians.” It is an investment in the wrong thing at the wrong time. The “explanations” most often will have little mathematical value and are on a naïve level since students don’t know the subject matter well enough. The result is at best a demonstration of “rote understanding.”

Interestingly, the nations that teach math in the traditional fashion seem to do quite well on tests like PISA, the international exam that is essentially constructed along reform math principles. Perhaps this is because basic foundational skills enable more thinking than a conglomeration of rote understandings.

**Reference:**

Brownell, W.A., Guy T. Buswell, I. Saubel. *“Arithmetic We Need; Grade 3”*; Ginn and Company. 1955

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]]>The post Texas Education Agency Delays Critical Math Test appeared first on Education News.

]]>The Texas Education Agency (TEA) announced that this year’s fifth and eighth graders will not have to pass a high-stakes math assessment given at the end of the school year.

New curriculum standards for mathematics were initiated in the state in the spring of 2012 as part of the Texas Essential Knowledge and Skills, the statewide curriculum standards, but the system was not without flaws.

“There are substantial challenges associated with implementation of the revised mathematics statewide curriculum standards in the STAAR grades 3–8 assessments,” Education Commissioner Michael Williams wrote. “For the 2014–2015 school year, districts will use other relevant academic information to make promotion or retention decisions for mathematics.”

For only this year, students get a free pass on the state math exam, although they will still be required to pass the reading exam. Due to performance standards for the test not being set until the spring of 2015, the exam will only be offered once this year. The May and June offerings will be suspended.

Although the announcement officially came last week, Williams had previously suggested to districts to use other “relevant academic information to make promotion or retention decisions” in math for this coming year.

Students will still take the math exam this year, but the Student Success Initiative (SSI) will be suspended. In other words, their moving on to the next grade will not be dependent on receiving a passing grade.

Last year’s students collectively did not do well on the exam, with only 40% of eighth graders and 45% of fifth graders passing. According to the promotion law, students have three opportunities to pass the exams before being held back.

This is not the first time students have been allowed to graduate to the next grade without passing the exam. The first time was in 2012 when the new state assessment system was put in place.

Coincidentally, the TEA has also delayed the initiation of higher passing standards for the new state exams, STAAR. According to the TEA, if the standards were in place last year, only 14% of fifth graders and 9% of eighth graders would have passed.

“While I firmly believe that our students are capable of reaching the high expectations reflected in the TEKS and the STAAR performance standards, moving to a three-step phase-in plan gives educators additional time to make the significant adjustments in instruction necessary to raise the level of performance of all Texas students,” Williams said in a statement on Thursday announcing the decision.

Critics of the decision believe that the delays will cause students to perform poorly in their academic work.

“The standard needed to pass these tests is already very low and the commissioner has just lowered that passing standard to zero,” said Bill Hammond, the Texas Association of Business’ chief executive officer. “This is another example of going back on high standards, even if it is just for this school year.”

The new math curriculum will be taught for the first time this year.

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]]>The post Study: Tougher Math, Science Courses May Lead to More Dropouts appeared first on Education News.

]]>A study conducted by researchers at Washington University in St. Louis has found that dropout rates increase with a more rigorous course load. These findings are come as especially bad news since many high schools have ramped up their requirements for math and science, reports Jim Dryden from Washington University in St. Louis*. *

The research team said it was likely that the increase in math and science courses is linked to the increased drop out rates.

“There’s been a movement to make education in the United States compare more favorably to education in the rest of the world, and part of that has involved increasing math and science graduation requirements,” explained first author Andrew D. Plunk, PhD, a postdoctoral research fellow in the Department of Psychiatry at Washington University School of Medicine.

However, many students were not prepared for in increase in math and science courses and felt overwhelmed and underprepared which lead them to drop out.

During the 1980s and 1990, many states required schools to have more stringent graduation requirements. The researchers looked at 44 states during that time and examined factors including sex, race, ethnicity, along with moving patterns together with the more difficult requirements to see how they effected educational success, reports Science 2.0*. *

There was no broad benefit found to raising math and science requirements. John O’Connor for State Impact writes Florida was one state that had increased the math and science requirements, with four math courses and three science courses. However, recently the state has backed away from those requirements, no longer making Algebra 2 a requirement. Students are no longer required to pass their final exams; instead the exams are worth 30% of their grades.

Some researchers believe that other factors beside more difficult learning requirements play a large role in drop out rates. Cognitive scientist Daniel Willingham argues that it’s misleading to blame math for higher drop out rates, reports John Higgins from *The Seattle Times. *

He asserts research shows that motivation, self-control, social culture and the feeling of being connected and engaged at schools can be major factors as well.

The implications of high dropout rates go beyond the actual education. Research shows that a high school education is correlated with health.

“Individuals who drop out of high school report more health problems and lower quality of life. Higher dropout rates also can strain the welfare system, which can affect people’s health.”

Another ramification is the increase in crime that can occur. Areas with higher dropout rates also have higher crime rates. Another study found that if the country’s dropout rate could decrease by 1%3 then there would be 8,000 fewer assaults and 400 fewer murders.

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]]>The post Study: Math Success Aided by Knowing Facts, Freeing Working Memory appeared first on Education News.

]]>Dr. Kathy Mann, working for the National Institutes of Health, has discovered that children’s brains reorganize as they are learning math. That means experience does matter and drilling children at home on simple addition and multiplication really could pay off in the long run, says Lauren Neergaard writing for the *Associated Press.*

Children start making the switch from counting in their heads or using fingers to “fact retrieval” at about 8 0r 9 years-old. How well they make the transition from this to memory-based problem-solving will ultimately predict their math mastery. If a child does not make the transition well, they can have difficulties or a slow pace in their math learning down the line.

The question then becomes, what makes the transition difficult for some children?

That is what Stanford researchers wanted to know, and they began the quest by using a brain-scanning MRI on 28 children while they solved simple addition problems. When the children saw a math calculation such as 6+1=7, they were instructed to push a button to signal whether the answer was correct or incorrect.

What the researchers were looking for was how quickly they responded and which regions of the brain lit up when they responded. The scientists met with the students again and observed the children to see if they moved their lips or counted on their fingers and compared the brain data. The students were tested again about one year later. As the subjects got older, their answers were based more on memory, the answers were faster and more accurate, and the changes showed in the brain.

The part of the brain that relays information when new data come in – short-term working memory – and then sends it to the longer-term memory area where it is stored for retrieval is the hippocampus.

“The stronger the connections, the greater each individual’s ability to retrieve facts from memory,” said Dr. Vinod Menon, a psychiatry professor at Stanford and the study’s senior author.

When Menon put 20 adult and 20 adolescents in the MRI he found that the hippocampus hardly came into play, and answers were practically automatic from long-term storage. The brain becomes much more efficient over time. When your brain can solve simple math quickly and easily, it has more working memory free to process more difficult math.

“The study provides new evidence that this experience with math actually changes the hippocampal patterns, or the connections. They become more stable with skill development,” she said. “So learning your addition and multiplication tables and having them in rote memory helps.”

These findings probably carry over to other subject areas. One example is that children who learn to match the sounds of letters with the letters themselves learn to read more quickly. Researchers hope to be able to study why this system does not work for students with math learning disabilities.

The study, from the Stanford University of Medicine, was published this month online at *Nature and Neuroscience*. Erin Digitale of the medical school’s Office of Communication & Public Affairs said some of the findings were a bit of a surprise to the researches.

“It was surprising to us that the hippocampal and prefrontal contributions to memory-based problem-solving during childhood don’t look anything like what we would have expected for the adult brain,” said postdoctoral scholar Shaozheng Qin, PhD, who is the paper’s lead author.

*ZeeNews* of India quotes Dr. Menon:

“This work provides insight into the dynamic changes that occur over the course of cognitive development in each child,” said Vinod Menon, a professor of psychiatry and behavioural sciences and the senior author of the study.

“The hippocampus provides a scaffold for learning and consolidating facts into long-term memory in children,” Menon added.

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]]>The post Study Shows Link Between Music and Learning Retention appeared first on Education News.

]]>New research from Dr. Nina Kraus at Northwestern University suggests that musical training can improve reading skills in children.

The research, being presented to the American Psychological Association, involved hundreds of children in poor areas of Chicago and Los Angeles, all areas with dropout rates of around 50%. All children in the study had similar reading levels and IQs.

One-half of the children were given music lessons for at least five hours each week. The other half were given no musical training. Those that took part in the lessons held constant in their reading skills, while the same skills of those with no training declined.

A decline in reading skills is typically seen among children in impoverished areas, furthering the educational gap, reports Samantha Abramowitz for PBS.

“While more affluent students do better in school than children from lower income backgrounds, we are finding that musical training can alter the nervous system to create a better learner and help offset this academic gap,” said Dr. Kraus.

A second grouping belonging to the Harmony Project, a group that provides instruments and free music tuition to deprived children in urban settings, participated in band or choir lessons at school each day.

After two years of researchers recording their brainwaves in order to discover how the children responded to speech sounds, Dr. Kraus found that those who participated in the music lessons had faster and more accurate responses when distinguishing between sounds in noisy environments such as a classroom, than did the group who had no such musical training.

“Research has shown that there are differences in the brains of children raised in impoverished environments that affect their ability to learn,” Dr. Kraus said.

According to Dr. Kraus, “Music automatically sharpens the nervous system’s response to sounds.” This “remodel” of the brain allows for a stronger connection between sounds and their meanings.

A separate paper from Rice University’s Shepherd School of Music and the University of Maryland, College Park reports that music aids in the development of language skills.

The paper looked into infants and the way they learn language. Co-author Anthony Brandt said “infants listen first to sounds of language and only later to its meaning.” He refers to those sounds as “the most musical aspects of speech.”

“As adults, people focus primarily on the meaning of speech. But babies begin by hearing language as “an intentional and often repetitive vocal performance,” Brandt said. “They listen to it not only for its emotional content but also for its rhythmic and phonemic patterns and consistencies. The meaning of words comes later.”

The paper was published online in this month’s issue of *Frontiers in Cognitive Auditory Neuroscience*.

“We’re spending millions of dollars on drugs to help kids focus and here we have a non-pharmacologic intervention that thousands of disadvantaged kids devote themselves to in their non-school hours — that works,” Harmony Project founder Margaret Martin said.

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]]>The post Montgomery County, Maryland Students Fail Math Exam in Record Numbers appeared first on Education News.

]]>Over one-half of the students in Montgomery County, Maryland failed their math final this year, leaving school officials baffled.

According to state figures, 61% of high school students failed the algebra exam, and 67% failed the geometry final. The statistics are not much better in the honors level, with about one-third of students failing.

Middle-school students, who have in the past done extremely well on tests, did not fair much better with 23% failing. That percentage is almost double last semester.

Out of 19,000 students, 11,000 in total failed their math exams.

These pass/fail rates are not normally released, but an exception was made after parents began comparing scores, causing the Rockville Parent-Teacher-Student Association to ask school officials to investigate the issue.

Parents are concerned their children are not being taught well enough to pass the exams.

“That’s where these kids are being short-shifted, because if they didn’t learn what they needed to learn, they don’t have a base,” Catalina Schrader, whose daughter took the Algebra 1 exam in June as a middle school student, said.

According to Superintendent Joshua Starr, a group will meet this summer to look into the issue, examining teaching, student support, and how well the exams coordinate with the curriculum.

School officials also offered to add 15 percentage points to scores for the Algebra 1 exam, as well as offering free summer sessions and retesting.

“I don’t know what other choice we had than to curve those grades,” said School Board Vice President Patricia O’Neill. She and others said they did not want Montgomery students penalized for problems not of their making. “We can’t hold children accountable for adult problems.”

One teacher at Silver Spring International Middle School went so far as to post the scores without student names. The highest grade was 65%, with only four students earning a passing grade.

Middle school students must pass the exam, worth 25% of their final grade, in order to gain high school credit for the course. Those extra 15 percentage points meant that 758 students throughout the district were able to earn a passing score on the exam.

However, worries continue that the students did not get the support they needed to succeed in Algebra 2 next year.

“Is the problem that they are not getting the content, or is it that the testing is not aligned with what they learned?” asked Schrader. “By adding 15 points, do you really get to the problems or are you glossing over whatever the problem might be?”

Officials are placing the blame on spending more time in preparing students for the state tests that were necessary for graduation and less time on course content. Schools also closed due to the weather, causing classes to lose even more study time. Between the two issues, classes lost two to three weeks of time.

“We have a new curriculum we’re implementing, and that curriculum is not completely aligned,” Erick Lang, Montgomery’s associate superintendent for curriculum and instructional programs, said.

This year marks the first for the curriculum of the Algebra 1 class to have been based on Common Core standards.

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