The post UK, China Increasing International Education Cooperation appeared first on Education News.

]]>The UK and China, which already have tight educational connections, are planning on expanding their partnership with programs designed to increase exchange between the nations.

Many Chinese students who want to study abroad go to the UK. China’s Minister of Education Yuan Guiren says that both countries have initiated programs to enhance their higher education collaboration.

In each of the past few years, China has increased the number of full scholarships. In 2014, 64,000 Chinese students studied in the UK.

According to Richard Macauley of Quartz, even young children are going to the UK from China for schooling and make up 14% of the country’s total population of international students.

Programs will be encouraging students to travel from the UK to China, too. The government invited 200 British students to study in China at no cost. The British government will be sending 80,000 students to study in China in the coming years, according to CCTV.com.

Statistics show that Chinese universities are growing in quality, meaning that British students who want to study there will not be missing out on opportunity. Four of the nation’s universities were included in the Times Higher Education top 100 rankings, writes Alice Gast.

Earlier this year, the government tried teaching math in English schools with traditional Chinese teaching methods. According to Schools Minister Nick Gibb, this was extremely successful, with students who historically scored poorly in math doing particularly well. Now, groups of school teachers have traveled to Shanghai to study Chinese teaching techniques, and 30 Chinese teachers were transported to the UK to work with students and educators. Gibbs said:

When that’s brought to England and the approach has been tried in English schools, it’s been hugely successful. Teachers have been pleasantly surprised by how much some of the less-able children are achieving in maths as a consequence of this approach.

Gibbs described one Chinese teacher in a Harris academy, who spent an entire lesson describing how to multiply two double-digit figures ending in zero. He said:

I walked around the classroom and all the children were understanding what was happening and could perform the calculation.

The program’s focus on math was inspired by China’s notoriously successful math achievement. They consistently score the highest in the PISA exam, the Programme for International Student Assessment test administered by OECD. In 2012, Shanghai ranked first in math, reading, and science, ahead of both Singapore and Hong Kong, according to Xie Qiao of CRIEnglish.

However, not everyone’s assessment of the program is as optimistic as Gibb’s. The three-part documentary Are Our Kids Tough Enough? showed that Chinese teachers struggled to discipline and control Western students, and the UK teachers disagreed with their methods. Over the course of four weeks, five Chinese teachers took charge of 50 students at a comprehensive school in Hampshire. The experience was very different from what the students were used to: the teenagers wore uniforms, attended from 7am to 7pm, had two meal breaks, and had the responsibility of cleaning their own classrooms. Lessons involved repetition, note-taking, and some group exercises. After the month was over, the students scored 10% higher in math and science than their peers.

Research so far has shown that Chinese teaching methods bring about a small improvement in performance, but experts say that there isn’t enough data and the methods need to be tested with a larger base.

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]]>The post Bedtime Math Stories Can Increase Kids’ Math Skills, Study Says appeared first on Education News.

]]>Children who read bedtime stories with math questions boosted their math learning skills, a new study out of the University of Chicago says.

Apart from boosting student achievement, the math stories also helped math-anxious parents become more comfortable discussing math problems at home, which in turn can further boost student progress at school.

“Structured, positive interactions around math at home can cut the link between parents’ uneasiness about math and children’s low math achievement,” the researchers conclude in their study published in the Science journal.

The researchers say that math-anxious parents are less likely to talk about math at home and might be reluctant to help their children do their math homework — something that can affect their children’s math competency. The researchers discovered that:

”Bedtime Math encourages a dialogue between parents and kids about math, and offers a way to engage in high-quality math interactions in a low-effort, high-impact way.”

Some 587 first-grade student families across the city of Chicago were given iPads with either the Bedtime Math or a reading app installed for the study’s purposes. Through the Bedtime Math app, parents and their children read stories and answered math-related questions together. The control group that received the reading comprehension app engaged with similar stories but without any math content.

The study showed that the more parents and children engaged with the app, the better the students’ academic achievement was.

For students who engaged with the app multiple times per week, the results were substantial, as they managed to outperform their peers by almost three months, the University of Chicago announced.

Even less-frequent use of the Bedtime Math app showed significant benefits. The use of the app as little as once a week resulted in math achievement gains for students as the end-of-year assessments, the researchers revealed.

But the app was particularly helpful for children with math-anxious parents or parents who were uncomfortable with math content, the Daily Mail reported.

“For many families, reading stories is a regular part of a child’s home routine. But when it comes to math, parents widely believe that it is the responsibility of schools, and they pay less attention to their child’s math learning at home,” said Susan Levine study author. “We found brief, high-quality parent-child interactions around math using Bedtime Math increased children’s math learning during first grade.”

In an interview with NPR and Eric Westervelt, the study authors highlighted the importance of integrating counting and other simple math activities in the daily routines of children because it can be beneficial for students’ math progress.

“[W]e know that parents who talk more with their kids about math — whether you’re counting out the number of cookies or counting the minutes to bedtime — those kids tend to achieve at higher rates in math.”

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]]>The post UK Facing Math Teaching Shortage, Looking Overseas appeared first on Education News.

]]>British schools are facing a shortage of math teachers, and the situation is so dire in some schools that physical education teachers and teacher assistants are filling in. Education Secretary Nicky Morgan admitted the math teacher shortage comes at a time when the UK wants more students to study math and embark on a teaching career path.

Morgan said that math is one of the most popular A-level exams and could eventually lead to more math graduates choosing career in education:

“One of the messages we have to get out is that we need great people to be teachers and we need to make it easier for people to get into teaching and to do the training.”

Morgan mentioned several government initiatives aimed at solving the shortage crisis:

“We do need more [teachers]. That’s why the prime minister announced a program in March of attracting more generous bursaries, attracting more maths graduates, but also helping those already working in schools teaching maths to increase their skills and confidence in doing so.”

This year, the UK government failed to meets its recruitment target for trainee teachers. At the same time, two London schools hired 66 teachers from Jamaica to address their shortages.

According to the UK’s Express., the Department of Education will launch and advertise a program to invite foreign teachers from Europe, Singapore and China to address the staff shortage. An email leaked to the Times Educational Supplement states:

“The department has recently embarked on an exploratory STEM international recruitment program. The aim of the STEM international recruitment project is to boost direct recruitment of high-quality mathematics and physics teachers coming from overseas.”

The email by the Department of Education official also states that the United Kingdom is seeking to build relationships with other countries.

Teachers unions greeted the gesture by emphasizing that the move doesn’t actually solve the problem. Mary Bousted, Association of Teachers and Lecturers (ATL) union leader, said:

“This is overdue recognition and acceptance by the Government that we have a teacher shortage. Until the Government recognizes that teachers’ pay is too low and the impact of constant Government-induced policy changes, and does something to improve working conditions, teachers will continue to hemorrhage from our schools.”

Morgan admitted that the problem is complex:

“I would not disagree, there are challenges in teacher recruitment,” pointing out the recovering economy as a major factor.

According to the Guardian, schools are doubling up classes and using non-math teachers to offer math lessons because of the staff shortage.

Labour party committee member Ian Mearns says the math teacher shortage is estimated at 5,000 staff with the crisis being particularly evident in Further Education colleges that offers GCSE math exam re-takes.

Schools are turning to PE and geography teachers, as well as teacher assistants, to lead math classes.

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]]>The post Israel Debuts Plan to Encourage 5-year Math Sequence appeared first on Education News.

]]>Israel’s Education Minister Naftali Bennett and former President Shimon Peres have created a campaign to improve the nation’s math education, with three YouTube videos have been released so far promoting the program.

The goal is to enable every student to take five units of mathematics at their school, which constitutes a full load of math courses, with the slogan “Give to yourself, give to the country — Give Five!”

The number of Israeli students taking five units of math has been dropping. In 2006, 12,900 students took the full sequence; in 2013, just 9,100 did. This adds up to about 9.1% of Israel’s students, writes Sharon Udasin of the Jerusalem Post.

Bennett said that focusing on math education is a matter of national security for a nation perpetually on the defensive:

The threat to mathematical studies is a strategic threat, and for a strategic threat a national program is necessary.

I know that there are many who disagree with me regarding the need to massively strengthen mathematics, but the role of a leader is to determine national objectives and pursue them with all our might– and we’ll double the number of students within four years. Gone are the days that a child wanted to take a five-unit matriculation exam, but could not do so because of his place of residence. In the national mathematics program, the child will strengthen his own future and will also help the future of the State of Israel.

According to Yarden Skop of Haaretz, they aim to double the number enrolled in five math unit to 18,000 within four years, double the number of teachers providing five-unit courses from 1,000 to 2,000, and add 15,000 hours to math instruction. Math education will also focus more on small group learning and the individual monitoring of progress.

According to Dabid Shamah with the Times of Israel, NIS 75 million, which is about $20 million USD, will be allocated to the program.

To strengthen the program, the ministry plans on adding incentives for both students and teachers. Every student who takes the five-unit matriculation exam will get at least 30 bonus points on their application when applying to university.

A National Public Forum for the Study of Mathematics will be created that will bring together educators, high-tech professionals, the IDF, and other organizations. 500 high-tech professionals will also be tasked with assisting teachers by holding school meetings and arranging field trips. Companies already involved include Intel, SanDisk, Microsoft, and Marvell Israel. “Five Club” learning communities will be created to foster professional development for math teachers.

In one video, reports Arutz Shiva, Peres plays an unruly student who submits the correct answer to a trigonometry question via paper airplane. Peres said:

Israel has been blessed with talents capable of reaching unforeseen heights, but they must be cultivated. We cannot accept a situation in which in the State of Israel children who are capable of studying five units at school cannot do so due to lack of means. A financial deficit is possible to repair later– an educational deficit is not possible to repair.

In order to stand up to global competition in the international market, the state must invest the maximum, to make first-class science possible for students. Science and technology professionals rely on mathematics, and therefore, the advancement of studies and vigorous striving for scientific excellence are an existential necessity and a primary interest for the future of Israel.

This year, 100 new five-unit tracks will be opening, and five-unit math courses will be allowed to continue with just 6 students instead of the previous minimum of 15.

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]]>The post Access Denied: Algebra in Eighth Grade and Egalitarianism appeared first on Education News.

]]>By Barry Garelick

The San Francisco Unified School District made the news recently when they decided to eliminate first-year algebra for eighth graders entirely. Algebra will now be offered only as a high school course in that school district.

The decision is not without controversy and many parents have been protesting, saying that it limits the choices qualified students may have. The other side of the argument is that too many students who were unprepared to take algebra in eighth grade were pushed to take it, resulting in many students failing the course.

Of course it is a mistake to allow students to take algebra if they are not mathematically prepared. Students need to have mastery of fractions, percentages, decimals, ratios, and negative numbers and to be able to solve a variety of word problems. But if a student is qualified to take algebra in eighth grade and would do well in it, why not give the student that choice?

But a growing trend among school districts these days is to limit (or as in SFUSD, eliminate entirely) those choices under the guise that Common Core doesn’t encourage acceleration. Districts prefer and think it better that students take algebra starting in high school. Common Core, however, defines four pathways that may be taken, one of which allows for taking algebra earlier than ninth grade:

A “compacted” version of the Traditional pathway where no content is omitted, in which students would complete the content of 7th grade, 8th grade, and the High School Algebra I course in grades 7 (Compacted 7th Grade) and 8 (8th Grade Algebra I), which will enable them to reach Calculus or other college level courses by their senior year. While the K-7 CCSS effectively prepare students for algebra in 8th grade, some standards from 8th grade have been placed in the Accelerated 7th Grade course to make the 8th Grade Algebra I course more manageable. (http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf )

Many schools and districts had such a pathway in place prior to Common Core. Despite this, schools and districts are making it more difficult for students to qualify for the “compacted” version. I witnessed this first hand last year when I was teaching pre-algebra and algebra at a middle school in the San Luis Coastal Unified School District in California during a time when school districts were making the transition to Common Core.

I recall a person from the school district office, who I will call Sally, talking to a group of us math teachers in advance of a “math night” to be held for parents to explain the District’s policy on “compacted” math pathways. Sally described how the District was phasing out the “accelerated math” in which qualified students in eighth grade — and even some in seventh grade — were allowed to take Algebra 1.

She did say they were working on pathways for those students who may be “really, truly” gifted and for whom algebra in seventh or eighth grade may be appropriate. This was likely not going to sit well with some parents, she said.

“There’s been a lot of parent pushback,” she sighed. “I imagine we’ll have the usual Debbie Downers and Negative Nancies in the audience on ‘math night’. But I want to make two things clear: that there’s no shame in taking Grade 8 math; under Common Core it’s equivalent to the traditional Algebra 1.” (This is debatable based on what I’ve observed in Grade 8 math classes) “And secondly, placement in eighth grade Algebra 1 will be more difficult. Fewer students will qualify – Common Core is very challenging.”

This all sounds plausible if you believe that Common Core gets into “deeper learning”. But what it really means is that students will now get a smattering of algebra in eighth grade, and the rest of it in ninth, thus taking two years to do what used to be done in one – and leaving some topics left out. Also, it raises the question that if Common Core algebra is so much deeper than a traditional algebra course, why is the traditional algebra course reserved for an elite corps of eighth grade students?

Sally went on. “Procedures don’t stick with kids; they forget them. They need to learn critical thinking and problem solving.” This brought her discussion to a new test the District would be administering to sixth and seventh graders for algebra placement purposes: the SVMI (Silicon Valley Math Initiative) assessments. These were a new series of tests to be given in addition to placement tests that had been given for years — the Mathematics Diagnostic Testing Project (MDTP). The MDTP was developed by California State University and University of California. It is a straightforward multiple choice exam which has had a good track record for accurately placing students in Algebra 1 for eighth grade. (Districts use them on a voluntary basis; they are not required to use them.)

The new test, which had never been given in the district previously, –was written by a group called the Silicon Valley Mathematics Initiative (SVMI). And while the title of the group conjures images of people of high calling in math, science and engineering who reside in Silicon Valley, it is actually a group of math reform types funded through the reform-minded Noyce Foundation, and who believe in 1) authentic assessments, and 2) themselves – and not necessarily in that order.

“For this new assessment, students will be required to use their prior knowledge to solve new types of problems – types they’ve never seen before,” Sally explained. I spoke up at this point and asked, “If it’s never been given in the District before, how is it going to be considered in making the decision for placement?

“That’s something the District is going to have to determine once we see the results.” The only guidance I was given eventually was that because it’s a new test, it won’t be counted as heavily. Though sounding like it answered my question, it didn’t.

Discussion continued about pathways to calculus by twelfth grade. Students who take Algebra 1 in ninth grade and who wanted to take AP Calculus in twelfth grade could double up their math courses during tenth grade. There! Every question that a Debby Downer or Nervous Nancy could ask was covered!

The explanation that the SVMI test would not be counted as heavily as the MDTP meant nothing to my students, which was no surprise since it didn’t mean all that much to me either. My pre-algebra seventh graders knew it was not good news. And when it came time to administer the test, they were horrified. It contained problems that were tedious as well as some that were poorly posed. If the tests had been used as “formative” assessments to guide classroom instruction and learning, I would have less objection. Specifically, if there were no names attached and they were scored by people not associated with the classroom to be returned to the teacher as discussion items, that would be useful. As actual assessment down to the individual student level — to be used as a filter disguised as placement – it is shameful.

As far as my eighth grade algebra classes were concerned, they had been “grandfathered” in, and had been placed in the algebra class solely on the basis of the MDTP results. (Students had to score higher than 80% on that test in order to place into algebra the next year). I know there may have been a few parents who pushed to get their children into the algebra class. But from what I could see in my algebra classes, with the exception of about 3 or 4 students out of 60, they were doing well, with most getting A’s and B’s. From my perspective, the MDTP was an effective placement tool. But the allure of Algebra 1 in eighth grade did have the potential of creating a student elite, now made even more so by the additional hurdle of the ill-conceived SVMI exam.

I recall in one of my pre-algebra classes a very bright girl named Gail who said she hoped she placed into Algebra 1. (She in fact scored higher than 80 percent on the MDTP, and did well on the SVMI test.) “I don’t want to be with the stupid people,” she said to the girl who sat behind her. That kind of attitude is probably a dominant factor in causing some school districts to react by opening up algebra in eighth grade for all students no matter how weak their preparation. We’ve seen that such a policy is a mistake. The opposite reaction is San Francisco Unified’s “nobody gets to take algebra until high school” policy.

Other school districts such as mine restricted entry as much as possible through their exclusionary tactics (which also kept down the number of students taking geometry in eighth and ninth grades. At this writing, there are other districts, including the William S. Hart Union High School District that serves the City of Santa Clarita in Los Angeles County, which is using a test written by a math teacher to decide who gets to take algebra in eighth grade. The term “truly gifted” and “the elite” have been used by various teachers to describe the students who qualify.) The eighth grade traditional Algebra 1 class has become an endangered species open only to a newly formed and very small elite.

During my assignment at the middle school (the 2013-14 school year) about 300 students were enrolled in Algebra 1 in the entire District. During the 2014-15 school year, the number dropped substantially to 46. Many of the rest would have otherwise qualified, but for the hurdle imposed by SVMI. By telling my students the explanation I was offered — that the SVMI test would not be counted as heavily as the MDTP — I had unwittingly lied to them. They were now part of the larger and growing class of Gail’s “stupid people.”

Ironically, the policies of San Francisco’s and San Luis Coastal’s school districts will have exactly the opposite effect than what was intended. Bright, well-prepared students whose parents have the information and the means will find other options for their children. Other students, especially lower-socioeconomic children from low-education communities, will be boxed out of advancing themselves through public education. For this group, algebra will be a watered down Common Core version in ninth grade – all in the name of egalitarianism and the greater common good.

—————

**Barry Garelick** has written extensively about math education in various publications including The Atlantic, Education Next, Educational Leadership, and Education News. He recently retired from the U.S. EPA and is teaching middle and high school math in California. He has written a book about his experiences as a long- term substitute in a high school and middle school in California: “Teaching Math in the 21st Century”.

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]]>The post Stanford Study: Brain Scans May Predict Students’ Math Capabilities appeared first on Education News.

]]>Researchers at the Stanford School of Medicine have reported that brain scans may predict which students are likely to improve their math skills in school and which ones won’t, with scans predicting more precisely than IQ or math tests.

NBC News’ Maggie Fox writes that the scientists worked with a group of students who began getting brain scans at the age of 8, and who followed up with scans into their mid-teens.

Even researchers were surprised when they found that certain patterns of brain activity when kids were not doing anything at all could predict how much they would improve in math skills. The accuracy of these predictions was higher than results from IQ tests, reading tests, or math tests, according to the report published in the Journal of Neuroscience.

The researchers were not suggesting that all children should have brain scans, but the information could result in new ways to identify the children who need intensive math coaching, said the authors.

“I can’t take one child, put the child in a brain scanner and say with certainty this is how the child is going to end up,” said Tanya Evans, a psychiatric researcher who worked on the study.

But the study does show which regions of the brain seem most important in developing math skills. Evans adds that the work is similar to studies done on dyslexic children. Dyslexia affects the ability to read printed words.

“A long-term goal of this research is to identify children who might benefit most from targeted math intervention at an early age,” said Vinod Menon, a professor of psychiatry and behavioral sciences who led the research.

The study included 43 students with normal intelligence who were asked to take tests and to sit still for functional magnetic resonance imaging scans and ordinary MRI scans. MRIs map the physical structure of the brain while fMRIs show the function of the brain. Researchers were able to see the parts of the brain that were more active in the children who improved their math skills over the next few years.

“Some of the kids started out really bad and ended up really good,” Evans said. “Some stayed average. Some started out good and got worse.”

This does not necessarily mean that math skills are hard-wired into the brain, says Evans. The idea is to work on ways to improve math skills to see if the brain structures also change.

“Practice makes perfect in everything,” she said. “We are looking at what types of math interventions are most effective.”

The children were studied for six years. The research showed that brain characteristics indicated which kids would be the best in math over the course of the research.

The findings will move scientists closer to their goal of assisting students who struggle with their math skills, writes Stanford University in the publication Bioscience Technology. Vinod Menon, who led the research team, says the work identifies a network of brain areas that provides a scaffold for long-term math skill development in children.

He reports that the next step is to investigate how brain connections change over time in kids who show large versus small improvements in math skills and then to design new interventions to help students improve their short-term learning and long-term skill development. Evans suggests that parents and teachers encourage children to exercise their mental math muscles.

Headlines & Global News’ Aditi Simiai Tiwari reports that the researchers hope to establish a baseline for understanding development that will, in turn, help experts develop and validate programs for the remediation of children with learning disabilities.

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]]>The post Math-Anxious Parents Affect Their Children’s Math Achievement appeared first on Education News.

]]>Parents who have math anxiety may pass that nervousness on to their children, says a new study published in the journal Psychological Science.

Erin A. Maloney of the University of Chicago led researchers in the analysis of math attitudes and abilities of over 400 first- and second-grade students through the use of information from a larger, unrelated study. Melissa Dahl, writing for New York Magazine, reports that the children were tested two times on their math skills, first at the beginning of the school year and again at the end of the year.

They were also asked on the test how nervous math, and everything to do with math, made them feel. Parents took surveys to measure their math anxiety and how much they assisted their children with their math homework throughout the school year. The results were that kids with parents who were anxious about math learned less math during the year, and they were more likely to become anxious about mathematics.

The catch is that the kids became anxious only if their parents helped them with their math homework.

“Notably, when parents reported helping with math homework less often, children’s math achievement and attitudes were not related to parents’ math anxiety,” Maloney and her co-authors write in their paper.

The takeaway is that if parents are nervous about math to the extent that their kids pick up on their anxiety, it is probably a good idea for those parents to step away from the math homework table and find a tutor who loves math to help their children.

Psychologists Sian Beilock and Susan Levine, who were part of the team that developed the paper “Inter-generational Effects of Parents’ Math Anxiety on Children’s Math Achievement and Anxiety,” explained that previous research had found that teachers who were anxious about math had students who learned less math during the school year, writes Susie Allen of UChicagoNews.

“We often don’t think about how important parents’ own attitudes are in determining their children’s academic achievement. But our work suggests that if a parent is walking around saying ‘Oh, I don’t like math’ or ‘This stuff makes me nervous,’ kids pick up on this messaging and it affects their success,” explained Beilock, professor in psychology.

As a control measure, the researchers also analyzed reading performance, but found that it was not related to parents’ math anxiety. The relationship between parents’ math anxiety and children’s math achievement, the research suggests, stems more from math attitudes than from genetics. One solution may be developing tools to teach parents how to help their children with math in the most effective way. This could include traditional board games, math books, computer games, or internet apps.

The Telegraph’s Javier Espinoza writes that math-anxious parents “are breeding a generation of innumerate children.” Levine put it this way:

“Math-anxious parents may be less effective in explaining math concepts to children and may not respond well when children make a mistake or solve a problem in a novel way.”

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]]>The post The Never-Ending Story: Procedures vs. Understanding in Math appeared first on Education News.

]]>**Finding the Balance between Procedural Fluency and Conceptual Understanding in Teaching Early Grade Mathematics to Students with Learning Disabilities**

By Barry Garelick

I went to school in the 50’s and 60’s when students first learned how to add and subtract in second grade. After spending some time memorizing the basic addition and subtraction facts and learning how to add and subtract single digit numbers, I was excited to hear my teacher announce one day that we would now learn how to solve problems like 43 + 52 and 95 – 64. In teaching the method, the teacher explained how the procedure relied on place value – what the ones place and tens place meant. I became bored with the explanation, began to daydream and missed the description of the procedure. The teacher then announced that we would now take a test on what we had just learned.

Faced with having to solve ten two-digit addition problems, I fell quickly behind the rest of the class. The teacher announced that she would not go on until everyone turned in their test. Students now put pressure on me as I desperately drew sticks on the side of my paper to “count up” to the answers. Finally, a girl across from me whispered “Add the ones column first and then the tens.” This advice made perfect sense to me and I finished the problems quickly. Although I had missed the explanation of why the ones and tens columns were added separately, it wasn’t long until I understood why after hearing the explanation again when the time came for learning how to “carry”. I was now receptive to what was going on with the procedure.

**Procedures as “Magic Corridors” to Understanding**

The issue of balance between procedural fluency and conceptual understanding continues to dominate discussions within the education community. The vignette above illustrates how procedural fluency may lead to understanding. This is true for all students, but is particularly relevant for students who may have learning disabilities.

Such students may find contextual explanations burdensome and hard to follow, resulting in feelings of frustration and inadequacy. It is not unusual in the lower grades for LD students – as well as non-LD students – to become impatient and wish that teachers would “just tell me how to do it.”

For many students, the “why” of the procedure is easier to navigate once fluency is developed for the particular procedure. The reason for this is given in large part through Cognitive Load Theory (Sweller, et al, 1994), which states that working memory gets overloaded quickly when trying to juggle many things at once before achieving automaticity of certain procedures.

An example of this is the plight of a visitor to a new city trying to find his way around. In getting from Point A to Point B, the visitor may be given instruction that consists of taking main roads; the route is simple enough so that he is not overburdened by complex instructions. In fact, well-meaning advice on shortcuts and alternative back roads may cause confusion and is often resisted by the visitor, who when unsure of himself insists on the “tried and true” method.

The visitor views these main routes as magic corridors that get him from Point A to B easily. He may have no idea how they connect with other streets, what direction they’re going, or other attributes. With time, after using these magic corridors, the visitor begins see the big picture and notices how various streets intersect with the road he has been taking. He may now even be aware of how the roads curve and change direction, when at first he thought of them as more or less straight. The increased comfort and familiarity the visitor now has brings with it an increased receptivity to learning about – and trying – alternative routes and shortcuts. In some instances he may even have gained enough confidence to discover some paths on his own.

In math, learning a procedure or skill is a combination of big picture understanding and procedural details. Research by Rittle-Johnson et. al., (2001) supports a strong interaction between understanding and procedures and that the push-pull relationship is necessary. Daniel Ansari (2011), a leading scholar of cognitive developmental psychology who studies brain activity during the learning of mathematics, also maintains that neither skill nor understanding should be underemphasized — they provide mutual scaffolding and both are essential.

Sometimes understanding comes before learning the procedure, sometimes afterward. The important point is recognizing when students are going to be receptive to learning the big picture understandings about what is really happening when they perform a procedure or solve a particular type of problem. Like visitors to a strange city, for many students, understanding comes after some degree of mastery of a particular skill or procedure.

For students with learning disabilities, explicit instruction on procedure should take precedence. A recent study (Morgan, et al, 2014) indicates that direct and explicit instruction given to first grade students with learning disabilities in math has positive effects. Conversely, student-centered activities (such as manipulatives, calculators, movement and music) did not result in achievement gains by such students. Of particular significance is that the study also found that direct and explicit instruction benefited those students without learning disabilities in math. To this end, we would add that an undue emphasis on understanding can decrease the amount of needed explicit instruction for students.

For many concepts in elementary math, it is the skill or procedure itself upon which understanding is built. The child develops his or her understanding by repeatedly practicing the pure skill until it is realized conceptually through familiarity and tactile experience that forges pathways and connections in the brain. But in terms of sequential priority, there is no chicken-and-egg problem: more often than not, skill must come first, because it is difficult to develop understanding in a vacuum. Procedural fluency provides the appropriate context within which understanding can be developed. It is important to note, however, that for some children, there may be certain procedures for which understanding remains elusive. It is even more important to note that such situation need not prevent such children from performing procedures and solving problems.

This is not to say that the conceptual underpinning should be omitted when teaching a procedure or skill. But while some explanation of the context is necessary to motivate the procedure, the issue is the degree of emphasis. Students with learning disabilities should be given explanations of how to proceed sooner rather than later. As discussed in more detail in the next section, after the standard procedure(s) are mastered alternative methods designed to provide deeper understanding of the concepts behind the procedure can then be provided when students are more receptive to such alternatives. It is also important to recognize that there will be some students who may not fully comprehend the concepts behind a procedure or problem solving technique at the same pace as other cohorts.

**Worked Examples and Scaffolding**

In teaching procedures for solving both word problems and numeric-only problems, an effective practice is one in which students imitate the techniques illustrated in a worked example. (Sweller, 2006). Subsequent problems given in class or in homework assignments progress to variants of the original problem that require them to stretch beyond the temporary support provided by the initial worked example; i.e., by “scaffolding”. Scaffolding is a process in which students are given problems that become increasingly more challenging, and for which temporary supports are removed. In so doing, students gain proficiency at one level of problem-solving which serves to both build confidence and prepare them for a subsequent leap in difficulty. For example, an initial worked example may be “John has 13 marbles and gives away 8. How many does he have left?” The process is simple subtraction. A variant of the original problem may be: “John has 13 marbles. He lost 3 but a friend gave him 4 new ones. How many marbles does he now have?” Subsequent variants may include problems like “John has 14 marbles and Tom has 5. After John gives 3 of his marbles to Tom, how many do each of them now have?”

Continuing with the example of adding and subtracting, in early grades some students, particularly those with learning disabilities, have difficulty in memorizing the addition and subtraction facts. On top of the memorization difficulties, students then face the additional challenge of applying this knowledge to solving problems. One approach to overcome this difficulty has been used for years in elementary math texts, in which students are provided with a minimum of facts to memorize and then given word problems using only those facts the student has mastered. Such procedure minimizes situations in which working memory encounters interference and becomes overloaded as described in Geary (in press). For example, a student may be tasked with memorizing the fact families for 3 through 5. After initial mastery of these facts, the student is then given word problems that use only those facts. For example, “John has 2 apples and gets 3 more, what is the total?” and “John has some apples and receives 3 more; he now has 5 apples. How many did he have to start with?” Additional fact families can then be added, along with the various types of problems. Applying the new facts (along with the ones mastered previously) then provides a constant reinforcement of memorization of the facts and applications of the problem solving procedures. The word problems themselves should also be scaffolded in increasing difficulty as the student commits more addition and subtraction facts to memory.

Once the foundational skills of addition and subtraction are in place, alternative strategies such as those suggested in Common Core in the earlier grades may now be introduced. One such strategy is known as “making tens” which involves breaking up a sum such as 8 + 6 into smaller sums to “make tens” within it. For example 8 + 6 may be expressed as 8 +2 + 4. To do this, students need to know what numbers may be added to others to make ten. In the above example, they must know that 8 and 2 make ten. The two in this case is obtained by taking (i.e., subtracting) two from the six. Thus 8 + 2 + 4 becomes 10 + 4, creating a short-cut that may be useful to some students. It also reinforces conceptual understandings of how subtraction and addition work .

The strategy itself is not new and has appeared in textbooks for decades. (Figure 1 shows an explanation of this procedure in a third grade arithmetic book by Buswell et. al. (1955).

The difference is that in many schools, Common Core has been interpreted and implemented so that students are being given the strategy prior to learning and mastering the foundational procedures. Insisting on calculations based on the “making tens” and other approaches before mastery of the foundational skills are likely to prove a hindrance, generally for first graders and particularly for students with learning disabilities.

Students who have mastered the basic procedures are now in a better position to try new techniques – and even explore on their own. Teachers should therefore differentiate instruction with care so that those students who are able to use these strategies can do so, but not burden those who have not yet achieved proficiency with the fundamental procedures.** **

**Procedure versus “Rote Understanding”**

It has long been held that for students with learning disabilities, explicit, teacher-directed instruction is the most effective method of teaching. A popular textbook on special education (Rosenberg, et. al, 2008) notes that up to 50% of students with learning disabilities have been shown to overcome their learning difficulties when given explicit instruction. The final report of the President’s National Math Advisory Panel (2008) states: “Explicit instruction with students who have mathematical difficulties has shown consistently positive effects on performance with word problems and computation. Results are consistent for students with learning disabilities, as well as other students who perform in the lowest third of a typical class.” (p. xxiii). These statements have been recently confirmed by Morgan, et. al. (2014) cited earlier. The treatment for low achieving, learning disabled and otherwise struggling students in math thus includes memorization and other explicit instructional methods.

Currently, with the adoption and implementation of the Common Core math standards, there has been increased emphasis and focus on students showing “understanding” of the conceptual underpinnings of algorithms and problem-solving procedures. Instead of adding multi-digit numbers using the standard algorithm and learning alternative strategies after mastery of that algorithm is achieved (as we earlier recommended be done), students must do the opposite. That is, they are required to use inefficient strategies that purport to provide the “deep understanding” when they are finally taught to use the more efficient standard algorithm. The prevailing belief is that to do otherwise is to teach by rote without understanding. Students are also being taught to reproduce explanations that make it appear they possess understanding – and more importantly, to make such demonstrations on the standardized tests that require them to do so.

Such an approach is tantamount to 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.” Forcing students to think of multiple ways to solve a problem, for example, or to write an explanation for how they solved a problem or why something works does not in and of itself cause understanding. It is investment in the wrong thing at the wrong time.

The “explanations” most often will have little mathematical value and are naïve because students don’t know the subject matter well enough. The result is at best a demonstration of “rote understanding” – it is a student engaging in the exercise of guessing (or learning) what the teacher wants to hear and repeating it. At worst, it undermines the procedural fluency that students need.

Understanding, critical thinking, and problem solving come when students can draw on a strong foundation of domain content relevant to the topic being learned. As students (non-LD as well as LD) establish a larger repertoire of mastered knowledge and methods, the more articulate they become in explanations.

While some educators argue that procedures and standard algorithms are “rote”, they fail to see that exercising procedures to solve problems requires reasoning with such procedures – which in itself is a form of understanding. This form of understanding is particularly significant for students with LD, and definitely more useful than requiring explanations that students do not understand for procedures they cannot perform.

Barry Garelickhas written extensively about math education in various publications including The Atlantic, Education Next, Educational Leadership, and Education News. He recently retired from the U.S. EPA and is teaching middle and high school math in California. He has written a book about his experiences as a long term substitute in a high school and middle school in California: “Teaching Math in the 21st Century”.

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**References**

Ansari, D. (2011). Disorders of the mathematical brain : Developmental dyscalculia and mathematics anxiety. Presented at *The Art and Science of Math Education, University of Winnipeg, November 19th 2011. *http://mathstats.uwinnipeg.ca/mathedconference/talks/Daniel-Ansari.pdf

Buswell, G.T., Brownell, W. A., & Sauble, I. (1955). Arithmetic we need; Grade 3. *Ginn and Company. New York. p. 68.*

Geary, D. C., & Menon, V. (in press). Fact retrieval deficits in mathematical learning disability: Potential contributions of prefrontal-hippocampal functional organization. In M. Vasserman, & W. S. MacAllister (Eds.), *The Neuropsychology of Learning Disorders: A Handbook for the Multi-disciplinary Team*, New York: Springer

Morgan, P., Farkas, G., MacZuga, S. (2014). Which instructional practices most help first-grade students with and without mathematics difficulties?*; **Educational Evaluation and Policy Analysis Monthly 201X, Vol. XX, No. X, pp. 1–22*. doi: 10.3102/0162373714536608

National Mathematics Advisory Panel. (2008). Foundations of success: Final report. *U.S. Department of Education.* https://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

Rittle-Johnson, B., Siegler, R.S., Alibali, M.W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. *Journal of Educational Psychology, Vol. 93, No. 2, 346-362*. doi: 10.1037//0022-0063.93.2.346

Rosenberg, M.S., Westling, D.L., & McLeskey, J. (2008). Special education for today’s teachers. *Pearson; Merrill, Prentice-Hall. *Upper Saddle River, NJ.

Sweller, P. (1994) Cognitive load theory, learning difficulty, and instructional design. *Leaming and Instruction, Vol. 4, pp. 293-312*

Sweller, P. (2006). The worked example effect and human cognition.*Learning and Instruction, 16(2) 165–169*

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]]>The post US Wins International Mathematics Olympiad for First Time in 21 Years appeared first on Education News.

]]>For the first time in 21 years, the US has won the International Mathematical Olympiad.

The USA team, led by Professor Po-Shen Loh of Carnegie Mellon University, competed against more than 100 countries in Chiang Mai, Thailand. The USA’s last win came in 1994, notes Dominique Mosbergen of the Huffington Post. Since then, the competition has been dominated by the Chinese, who came in second in this competition. Other recent winners include South Korea, which came in third this year, and Russia.

NPR interviewed Loh, who suggested that the difficulty of the questions indicated how strong the field was:

If you can solve even one question, you’re a bit of a genius.

Students in the final competition solve six problems dealing with algebra, geometry, number theory, and combinatorics, among other topics, in 4.5-hour sessions over the course of two days. Answers are not given in simple numbers, but often demand long explanations. The team’s score is the sum of its member’s scores.

According to Michael E. Miller of the Washington Post, this year’s team had all male members: David Stoner, Ryan Alweiss, Allen Liu, Yang Liu, Shyam Narayanan, and Michael Kural. The fact that historically almost all the competitors are male illustrates the dearth of women who are mathematical high achievers and who go on to create careers in the STEM fields. However, progress is being made — this year, the Ukrainian team had an equal number of boys and girls, writes Natalie Schachar of the LA Times.

Loh said that gender balance is happening, albeit slowly:

That is actually something that one hopes will change. The top 12 people in the country on the United States Math Olympiad happen to have two girls in it. One might say, ‘Only 2 out of 12, that’s terrible.’ But I should say in many years, it was, unfortunately, zero.

Some feel that this victory is evidence that the math education situation in America is less dire than it seems. In 2015, 15-year-olds in the US were rated 35th in math and 27th in science out of 64 countries by the Program for International Student Assessment (PISA) test.

Loh said that their success shows that the United States’ best students are globally competitive:

At least in the case with the Olympiads, we’ve been able to prove that our top Americans are certainly at the level of the top people from the other countries.

Loh, who was himself a contestant in 1999, hopes that math education in America will be reformed to interest more students and involve more creativity. He said that making math more engaging could bring diversity of all sorts to the competition:

Ultimately, I think that as the mathematical culture starts to reach out to more people in the United States, we could quite possibly start to see more diversity. And I think that would be a fantastic outcome.

It could be that maybe the way math is sold, in some sense, is one in which it’s just a bunch of formulas to memorize. I think if we are able to communicate to the greater American public that mathematics is not just about memorizing a bunch of formulas, but in fact is as creative as the humanities and arts, quite possibly you might be able to upend the culture difference.

This year’s Math Olympiad was the 56th international competition.

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]]>The post Girls Perform Better in Math with Female Teachers, Data Shows appeared first on Education News.

]]>Who runs the world? Girls – especially when they are taught by fellow females, according to a study conducted at Texas A&M University.

Previous research has shown that females tend to perform better in the classroom than males. They rank higher across the board; from college graduation rates to test scores, they surpass their male counterparts in nearly every academic facet of education, writes Gabriel Fisher for Quartz.

Most recently, researchers Jonathan Meer and Jaegeum Lim found that there was a significant improvement in girls’ math test scores when a woman teaches the subject — an interesting finding, particularly since math is thought of as a male-dominated field.

Meer and Lim analyzed 14,000 test scores from middle school students in South Korea. They found that when a woman taught students math, girls’ scores were nearly 10% of a standard deviation higher than boys. They also found that when girls switched from a male teacher to a female teacher, their math scores went up by 8.5% of a standard deviation compared to boys’ scores.

“Female students outperform male students by roughly a third of a school year

when taught by female teachers than when taught by male teachers,” Meer explained.more

He feels that the increased performance is due to girls feeling more comfortable in class when taught by a female teacher:

“Female students report feeling that their female teachers are more likely to give students an equal chance to participate,” he writes, adding that “their female teachers are more likely to encourage creative expression.”

The researchers chose to conduct a study in South Korea because students are randomly assigned teachers in the country. In the United States, female math teacher have been known to be assigned weaker students, writes Julie Zeilinger for Mic.

This information may be good news for female students who have been shown to hold themselves back in STEM subjects. For example, female students generally underestimate their abilities and predict they will perform worse on tests, while boys overestimate their performance.

However, boys are being left behind academically, and Meer is, “personally deeply worried about male performance in schools.”

Researchers are divided on the specific reasons why male students are less engaged than female students, which makes it hard to diagnose the issue on a large scale. This is why it is important for parents to understand why their boy isn’t engaged and then to work with teachers to solve the problem, reports Shelby Slade for Deseret News.

“We must work equally hard to encourage boys to consider literature, journalism and communications. Boys are often pushed toward math and science, and receive inadequate social support. We need to recognize boys’ differences, and their social and developmental needs,” says educator Sean Kullman.

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