Heather Reid Dunn's UVM ePortfolio€¦ · Web view(4) What can we learn from other countries and how they organize curriculum, specifically when it comes to math instruction? International

Heather Reid

EDFS 206 Spring 2012

David Shiman

How Can the United States Improve Math Scores on International Standardized Tests?

“Now, I know longer school days and school years are not wildly popular ideas, not with

Malia and Sasha, not in my family, and probably not in yours. But the challenges of a new

century demand more time in the classroom.” –President Obama (Washington Times, 2009).

Many educators, parents and government officials feel that students in the United States need to

spend more time in school both during the school day and school year to remain globally

competitive in the future. It is perhaps a logical argument that increased time on task in a

particular subject results in improved test scores on standardized tests, but studies show that

extended time in the classroom is not necessarily linked to a rise in test scores. Looking at how

other countries and cultures structure their time could lead to a refreshing new outlook on the

extended time debate in American education. Although direct comparisons should be made with

caution (as cultural differences can be too great to dismiss), this research paper will address the

following questions in comparative education: (1) Are students in the U.S. really falling behind

their international peers on standardized tests? (2) How do other high achieving countries

structure their school day and school year? (3) Do students in other countries actually spend

more time in direct instruction? (4) What can we learn from other countries and how they

organize curriculum, specifically when it comes to math instruction?

International Comparisons on Standardized Tests

“Student performance on international assessments is considered especially relevant as

today's high school graduates enter a global job market, where highly skilled workers are in

increasing demand” (Armario 2010). When looking at how the U.S. stacks up in international

standardized tests, many Americans seem to have a similar opinion; Students in the United States

perform poorly, and there is a national crisis at hand. But are our students really doing “poorly”?

According to a recent study by Peterson, et al, 2011 of Harvard’s Program on Education Policy

and Governance, students from the United States ranked 32 in math proficiency and 17 in

reading proficiency in PISA (Programme for International Student Assessment) standardized

tests given to 15 year-old students in 2011. In math, the nations ranked 23st to 31st did not have a

significant difference in scores in comparison to the United States, however 22 nations scored

significantly better in math. In terms of reading, only 10 countries had statistically significant

higher scores than the United States.

Other studies also show math scores on international assessments in the below average

range. In a study by Boe and Shin in 2005, the authors claim that across six surveys in grades 4,

8, 9, and 10, students in the U.S. were outperformed by 44% of the nations, and only 26% of

U.S. students performed in the proficient range or above. The authors also noted, however, that

U.S. students performed well in civics, reading and science, and claim that this shows that U.S.

students are perhaps more well-rounded than their international peers. The Alliance for Excellent

Education Fact Sheet from March 2008 showed that students in math were ranked 25th out of 30

OECD (Organization for Economic Co-operation and Development) countries in math literacy in

2007 and that scores had not changed since 2003 when the ranking was 24th out of 29.

These studies show that although the students of the United States are outcompeted by

many other nations on standardized tests, maybe the judgment of them performing poorly is too

harsh. There is, however, evidence that math is an area of particular weakness for American

students. Why do students perform so much lower in this subject than others such as reading or

civics?

There are many theories about why there is a math proficiency gap between other

countries and the United States. One theory looks at the data coming in from American minority

populations. Some educators claim that there is a large gap been the high achievers in the U.S.

and the lower achievers, and minority groups tend to fall in the lower achievement category. Is

this true for math scores? In order to address this issue, the researchers at Harvard (Peterson, et

al, 2011) decided to only compare white American students’ scores to other nations. They found

that white American students score 42% proficient in math, but where still outscored by 16 other

countries. This clearly shows that the math proficiency issue is an issue across all students in our

nation regardless of racial profile.

There is some debate about whether or not achievement testing is even a good measure of

how well our schools and students are doing in the world. Although this research paper is basing

success of a nation on international test scores, it should be noted that there are many educators

who disagree with testing as a comparison tool. One example of why this is the case comes from

a study done by Boe and Shin in 2005. According to Boe and Shin (2005), the US performs on

par with fellow western G7 nations. These nations are good nations to compare the United States

to, because they are likely to be economic competitors in the future. Nations like Finland who

perform at a high levels on achievement tests are unlikely to compete economically, and

therefore maybe should not be looked at with much concern. “Not only does the U.S. have the

largest gross domestic product among the G7 nations but it also has by far the largest and most

racially and ethnically diverse population and the largest number of partially autonomous states”

(Boe and Shin 2005). The argument against using international tests as an indicator of “success”

is clear when comparing the United States to very small, homogeneous nations.

Finally, another issue with standardized tests might come in sampling bias with the tests.

There is some suggestion that comparing large nations such as Canada, the United States, and

Mexico with small countries such as Finland or city states such as Shanghai may have

fundamental issues with sampling. When sampling from such a small population, the number of

samples and where the samples are taken from will have a large influence on the results. Bates

(2010) suggests that the scores in Shanghai are too “perfect” and that sample size may have

something to do with this discrepancy. Although there are many potential issues when using

international standardized tests to make comparisons, they provide useful data that can be used to

help nations improve their programs of education and learn from others.

School Year Length Comparison, Time Spent on Teaching and Math

In 2009, Shanghai shocked the world by outscoring all other countries in reading, math

and science (Dillon 2010). Stewart (2009) gives many reasons for the outperformance of Chinese

schools in math and science including, national standards and core curriculum, teachers

specialized for subject matter starting in elementary school, examination driven students, and

finally, time on task. According to Stewart (2009), the Chinese school year is a full month

longer than in the US, and “overall, Chinese students spend twice as many hours studying as

their U.S. peers” (Stewart 2009).

How can we improve our own educational system to improve test scores? Over and over

again, the one argument many Americans keep coming back to is time on task. American

students must not be spending enough time in the classroom. This is why they are outcompeted

on standardized tests at the international level. The school year is too short and the school day

should also be lengthened. The table in Appendix A lists the schools who ranked above the U.S.

in 2011 PISA math scores and the number of days students attend school per year in each of

those countries. As shown by this table, students in countries that outcompete the U.S. on math

standardized tests tend to go to school for more days per year. Some students go to school for as

many as 240 days, and only one country, Iceland, has a shorter school year than the U.S. It

appears to be a clear indicator that lengthening the school year would result in more time on task

and in turn increased test scores. However, upon further investigation this is not necessarily true.

Although students in other countries go to school for more days out of the day, do these

students actually spend more time in math classes? In order to look at how much time students

spend in school and how much of that time is spent on math, five countries with high PISA math

scores in 2011 were examined to look at how much time in the school day is spent on math. The

five countries of examination are Singapore, Korea, Japan, Finland and Canada. First a

comparison was made between how many days these students spend in school during a typical

school year, as see in Figure 1. In Canada, school year is dictated by the local provincial

governments, and so there is a range of 180-200 days per year, but all of the other countries of

comparison go to school for more days than the typical American student.

Figure 1: Number of Days Spent in School per Calendar Year

COUNTRY Days Spent in School per Calendar Year

PISA Math Ranking in 2011

SINGAPORE 200 2

KOREA 220 4

FINLAND 190 5

JAPAN 240 9

CANADA 180-200 10

UNITED STATES 180 32

Next, number of total yearly teaching hours was looked at in figure 2. This data comes

from OECD data from 2009. Of the countries to be investigated, only the United States, Korea,

Finland and Japan are represented in this graph. According to the figure, American educators

spend much more time on classroom instruction than teachers in many other countries. American

teachers spend on average about 1100 hours per year on classroom instruction, while Korean

teachers spend only 550. But does this mean that students in the United States are receiving

double the instruction time? Or are there just more teachers in other countries and instruction

time is actually equivalent? Classroom achievement could be influenced by the amount of time

teachers spend teaching in the classroom, but is perhaps more likely to be effected by how much

instruction or seat time students have over the course of the year. This question needed to be

further investigated. How much time do students spend in class with actual instruction taking

place?

Figure 2: Time Teachers Spend on Classroom Instruction Per Year (Rampell 2009)

To find out, Trends in International Mathematics and Science Study (TIMSS) data was

looked at to find out how much actual class time is being used for math instruction. According to

the TIMSS data from 2007, there is some variation, but on average in the fourth grade, schools

across the globe spent 23 hours in instruction per week with 18% of that time (about one-fifth) is

spent on math instruction (Mullis, Martin, and Foy 2008). In the eighth grade, 27 hours were

spent on instructional time with 14% of that time spent on math instruction. Figure 3 breaks this

data up by country to analyze amount of time spent on instructional time and specifically on

math based on TIMSS data from 2007. This figure shows that although the United States is in

school for less calendar days than the five highlighted countries, only the Canadian Province of

Ontario has students spending more time studying math in the school day. The TIMSS study also

had data on total yearly hours spent on math. The students in the United States spent more time

studying math than students in Singapore, Japan, and Korea. Again, only students in the

Canadian Province of Ontario spent more time in math instruction than students in the U.S.

Although American students go to school for a shorter school year, they spend more time in the

classroom receiving math instruction during the year. The time on task for American students in

actually longer! This indicates that a longer school year and day may not necessarily be the

solution for American schools to compete mathematically with higher achieving countries.

Figure 3: Data from Eighth Graders in TIMSS 2007(Mullis, Martin, and Foy 2008)

COUNTRY Time Spent on Instruction (in hours per week)

Time Spent on Math Instruction (as a percentage of total instruction)

Time Spent on Math Instruction (in hours per week)

Total Yearly Math Instruction (in hours)

SINGAPORE 29 13 3.77 124

KOREA 29 11 3.19 104

FINLAND Did not participate in

TIMSS

Did not participate in

TIMSS

JAPAN 25 10 2.5 105

CANADA (ONTARIO) 26 16 4.16 159

UNITED STATES 31 13 4.03 148

What Can the United States Learn from Other Countries about Math Education?

Since time on task may not be the solution to improve test scores for American students,

the remainder of this research paper looked at ways the American math curriculum and

methodology of teachers might change. There are obvious cultural differences that lend to high

achievement in some countries over others. In many countries in Asia, the value of education and

high stakes testing in society has different meaning than it does here in the United States. There

are many reasons why other countries outperform the U.S. on international standardized tests,

but we can still learn from others. What can we learn about math education from other countries?

Singapore

Students in Singapore have consistently been achieving at high levels on international

standardized tests in math. In 2011, Singapore ranked number 2 on the PISA math tests. Since

the early 1990s, the country has made some vast improvements in the math curriculum that the

U.S. can learn from (Leinwand and Ginsberg 2007). Leinwand and Ginsberg (2007) claim that

although Singapore is a small country, there are some similarities demographically, and the U.S.

can learn from Singapore math to push curriculum reform in five critical areas.

In Singapore, the math curriculum is developed at the national level starting with the

standards framework. This framework is often referred to as the Singapore model or Singapore

math and has gathered some educational fame across the globe. The Singapore model places

problem solving at the middle of all conceptual and process standards as seen in the figure 4. The

Singapore Standards “present a balanced, integrated vision that connects and describes skills,

concepts, processes, attitudes, and metacognition” (Leinwand and Ginsberg 2007). When the

article by Leinwand and Ginsberg was written in 2007, the U.S. only had a vision for national

math standards set out by the NCTM in 2000. However, this is a direction the United States is

currently moving in with the creation of the Common Core standards.

Figure 4: Singapore’s Mathematics Framework (Leinwand and Ginsberg 2007).

The second way we can learn from Singapore math is in alignment. In the U.S. math

teachers are pulled in many directions by the local math curriculum, the textbook, state

standards, and state testing. It is challenging to design a classroom curriculum that meets all of

the needs of the different driving forces. “In Singapore, each element of the system—the

framework, a common set of national standards, texts, tests, and teacher preparation programs—

is carefully aligned to clear and common goals” (Leinwand and Ginsberg 2007).

The third, fourth and fifth areas to look at Singapore math are all related to the national

math textbooks. The third area is focus. According to the Leinwand and Ginsberg (2007), the

textbooks in the Singapore model have fewer pages and fewer lessons per grade level in

comparison to U.S. textbooks. Each grade focuses on fewer concepts, but explores those

concepts in more depth. This way, students don’t spend as much time reviewing and repeating

concepts each year. The fourth area is in textbook integration of concrete, pictorial, and abstract

representations of a math problem. Singapore textbooks provide multiple representations of data

to help students develop understanding. This is linked to studies on how the brain develops

mathematical reasoning (Leinwand and Ginsberg 2007). The fifth area is in the richness of the

math problems. Leinwand and Ginsberg claim that the problems in Singapore math textbooks

tend to be higher order problems that require multiple steps to reach a solution. Many U.S.

textbooks have lower level one-step problems that only require recall to reach a solution.

Korea

Many studies have looked at how textbooks are designed in high achieving countries

such as Korea. According to Son in 2011, Korean schools have a curriculum that is designed by

the Korean Ministry of Education, and there is a national program that all students learn from.

The curriculum is called the 7th Korean Course of Study, because it has been changed seven

times since the country started public education in the 1950s. There is only one math textbook

series used by all students in grades 1-6 that was developed by the Ministry of Education. In his

article, Son touches upon how the Korean mathematical curriculum seems much more advanced

than then U.S. curriculum when compared at each grade level. His article specifically looks at

the introduction of fractions into the math curriculum and how fractions are taught. Most U.S.

and Japanese textbooks introduce fractions for the first time in 4th grade, while the Korean

curriculum introduces fractions in 3rd grade. The article goes on to look at how lessons are

designed within the textbook. Most lessons have four or five activities, and the first activity is

called, “Learn from real life” where the math lesson is immediately connected to some prior

knowledge of the students. The next two activities apply the concept, and the final two activities

are for additional practice. The textbooks also ask questions such as “Why do you think that is

true? Or why do you think that is the case?” (Son 2001). This type of questioning helps students

to share and investigate multiple solutions to problems and stimulate independent thinking.

Japan

As a major economic competitor, Japan is looked at with a watchful eye by educators in

the United States to learn from and compete with. Japanese math instruction has many important

differences that could be looked at when designing American math reform. Similar to Singapore

and Korea, the Japanese Ministry of Education standardizes all math textbooks, and students all

learn the same curriculum regardless of geographical location.

Stigler, Gallimore, and Hiebert (2000) looked at TIMSS videos of teachers in the United

States, Japan and Germany to see what cross-cultural similarities and differences could be found

in math instructional techniques. The researchers found that teachers tend to have very similar

practices within the same culture (despite opinions that teachers’ methodology varies greatly

here in the U.S.) (Stigler et al. 2000). Stigler and his fellow researchers looked at randomly

selected videos from 8th grade math classrooms. In the study, there were 100 videos from

Germany, 50 from Japan, and 81 from the United States. The researchers analyzed the videos

and coded for whether or not a lesson was task controlled or solver controlled. Some lessons

involved a teacher presenting a problem type or giving lecture and asking students to follow the

same procedure to come up with solutions to similar problems. This is an example of task

controlled. Other lessons teachers presented the students with a math problem before teaching

the concept, prompting the students to work together and seek solutions based on prior

knowledge; this is solver controlled. The results of the study showed that 63% of Japanese

lessons were solver controlled, with only 30% of German lessons and 14% of American lessons

being solver controlled. Stigler et al (2000) also looked at what types of tasks the students

attended to during seat work and put these tasks into three categories: practicing routine

procedures, applying procedures in new situations and inventing new procedures. Their data is

seen below in figure 5. This data shows that students in the United States spend more time on

“skill and drill” kind of work, while Japanese students are more involved in creative problem

solving and applying skills to new situations.

Figure 5: A Comparison of Seatwork in Math Classes by Percentage (Stigler et al 2000)

The researchers also found that classrooms in the U.S. were interrupted by something 30% of the

time, while Japanese lessons were never interrupted in any of the videos.

In a later study of the TIMSS videos (with a larger sample of countries), Stigler and

Hiebert (2004) claim that although Japanese teaching methods were strikingly different in math

than other countries, their way is not the only way to high achievement. Japanese students spent

an average of 15 minutes working on a problem, while students in the other high achieving

countries spent as few as 5 minutes per problem (Stigler and Hiebert 2004). In their concluding

remarks, Stigler and Hiebert suggest that curriculum reform would be more effective if we could

look past textbooks, standards, and recruitment of great teachers. They believe that changing the

cultural aspects of teaching methods (so that all teachers within the same culture don’t teach with

the same methodology) will have larger success in math reform.

Finland and Canada

While research into math practices in Singapore, Korea and Japan look at specific

methodology and concepts, math success in Finland and Canada is generally equated to teacher

training and involvement. In Canada, teachers are trained extensively before starting a career and

ongoing professional development happens throughout the career. Teachers participate in unions,

and the unions act cohesively with the schools, school boards, and the local community to give

the students the best possible education (Herrup 2011). Teachers are able to make their own

decisions in the classroom and are valued for their service. Teachers’ voices are also seen as

valuable to education reform (Herrup 2011). Canada uses teacher evaluations to help a teacher

become better, and pay incentives are not based on teacher performance. Teachers in Canada can

also be fired (fairly easily), however, if they are not performing at an adequate level. In Canadian

provinces, healthcare is number one in spending, but education is second (Herrup 2011).

In Finland, teaching is regarded as a prestigious career. Prospective teachers compete for

highly selective programs in government funded teacher education programs. According to

Sahlberg (2011), 5,000 prospective teachers are selected from 20,000 applicants. These teachers

are then must obtain a master’s degree to teach primary, middle or high school level students,

and this preparation usually takes from five to seven and a half total years (Sahlberg 2011). In

addition to content related instruction, students take part in practical classroom training, and this

training comprises 15% - 25% of their total training. Finland does not have a national

standardized testing program, so teachers are evaluated based on their ability to teach students in

a more holistic context (Sahlberg 2011). Sahlberg (2011) discusses many other reasons why

Finnish teachers are the key to the high achievement of students including that teachers have

time to spend on curriculum planning and grading, because classroom instruction time is much

lower than in other countries (as discussed earlier in this paper).

China

Although China is not included in the five country analysis, China is of particular interest

in the last year, due to top scores in the PISA by Shanghai. In this research, the country of China

was included to look at how students are learning math concepts in different ways. Cai (2001)

found that “Chinese students had significantly higher mean scores than the U.S. students on the

computation tasks, simple problem-solving tasks, and the process-constrained tasks. However,

the U.S. students had a significantly higher mean score on the process-open performance

assessment tasks” (2001). The Chinese students’ higher scores stemmed from use of symbolic

representations to solve problems (both with arithmetic and algebraic reasoning). U.S. students

tended to use more visual representations to solve problems; many times drawing pictures to

solve a problem (perhaps a more creative way to problem solve). U.S. teachers can learn from

Chinese educators in terms of how they teach algebraic concepts along with arithmetic concepts

at a much earlier age than was originally thought possible here in the U.S. Students are capable

of learning basic algebraic concepts starting in fourth and fifth grade (Cai 2001), and U.S.

teachers should look to Chinese education to learn how to teach arithmetic and algebraic

reasoning at the same time. This helps students to understand the similarities and differences

between the two approaches to problem solving.

Conclusion

In general, students in other countries go to school for a more days than students in the

United States. According to Patall, Cooper, and Allen (2010), a meta-analysis of research on

lengthening the school day and year showed that extending time in school was an effective way

to improve student learning, but mainly for students at risk of failure and with a careful eye on

how the extra school time was used. Should the United States move to a longer school day or

year to become more globally competitive in international achievement tests? This research

shows that although students in the U.S. do not spend as many days in school, overall they spend

more time in school on instruction than PISA leaders. In math specifically, students are spending

more time yearly than in many other countries. If time on task is not the apparent issue, what

kinds of math reforms can be made in the U.S. to improve student achievement?

(1) National Standards: As shown in Singapore, Korea, and Japan, national standards are a

good place for math reform in the U.S. to start. Although the Common Core is an attempt

at nationalizing the curriculum, it is option for states to decide whether or not to adopt the

Common Core. Currently, it is not nationally mandated and not all states have adopted

them. Until we are united on the national level, expectations that all students in the U.S.

will be learning and performing at the same level are unreasonable.

(2) National Textbooks: Also seen in Singapore, Korea, and Japan, national textbooks further

help to unite and align a common curriculum for all math students. In the current U.S.

system, textbook companies decide what curriculum is highlighted, and although schools

have the option to choose their own textbooks, not all do. Some schools cannot afford

textbooks or do not use them (such as my middle school) and creating a national textbook

would require that all students are provided with a valuable resource throughout their

math education. Alignment of the curriculum through standards and textbooks would

help alleviate American teacher struggles of trying to align the curriculum themselves

(state standards, local curriculum, department needs, state testing and national standards).

(3) Teacher Trust: Finland and Canada both show examples of how regarding the profession

with more value as a nation could improve education. The United States needs to figure

out how to recruit and retain more qualified teachers and also train our teachers more

thoroughly. Should all teachers be required to obtain a master’s degree? This is the case

in many states in the U.S. but not all. If the society starts to value teachers more and trust

their ability to educate the students, we might see improvement in standardized test

scores.

(4) Find Time for Teachers: Teachers in the United States spend much more time in

classroom instruction than in other countries. Schools need to find more time for teachers

to get out of the classroom for planning a better curriculum. One way to do this might be

by getting rid of curriculum development positions. Schools will have more funding to

hire regular classroom teachers and give all classroom teachers more time for planning

and grading.

(5) Stop Interrupting the Classroom Environment: The TIMSS video study showed that

classrooms were consistently interrupted in schools in the United States. Teachers,

students and administrators need to find ways to stop this from happening as often or at

all.

Math scores reflect that students in the U.S. are trailing behind their global counterparts,

and there is a need for change in our American math program. “No country has all of the answers

to educational excellence. The key goal for every country is to be open to effective practices

from other countries while maintaining the strengths of its own” (Stewart 2009). There are many

cultural arguments for why countries like Japan, Korea, Singapore, Finland, and Canada score

higher than the United States on international standardized tests. The United States, however, can

and should look beyond those cultural reasons and look to reform math education based on what

we learn from these high achieving nations.

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Appendix A: Length of School Year In Comparison with PISA Rankings in Math 2011

PISA RANKINGS IN MATH

2011

Country Days in School Per Year

1 Shaghai 200

2 Singapore 200

3 Hong Kong 200

4 Korea 220

5 Finland 190

6 Taiwan 200

7 Liechtenstein

8 Switzerland 190

9 Japan 240

10 Canada 180-200

11 Netherlands 200

12 Macaco

13 Belgium

14 New Zealand 190-197

15 Germany 188-208

16 Australia 200

17 Estonia

18 Iceland 170

19 France 180

20 Slovenia

21 Denmark 200

22 Austria 200

23 Slovakia

24 Norway

25 Sweden 200

26 Luxembourg

27 Poland 180

28 Hungary

29 Czech Republic 185