MEMORANDUM - Houston Independent School District · examines the use of Reasoning Mind as a supplemental, fourth-grade computer-based approach to instruction toward improving mathematics

MEMORANDUM September 26, 2011 TO: Board Members FROM: Terry B. Grier, Ed.D. Superintendent of Schools SUBJECT: REASONING MIND PROGRAM EVALUATION, 2010–2011 CONTACT: Carla Stevens, (713) 556-6700 Reasoning Mind (RM) is a technology-based program, designed to teach mathematics and develop logical reasoning skills. RM engages students with interactive content, animations, and games, while exposing students to challenging, individualized assignments at their own pace. The program diagnoses weaknesses in students’ knowledge and provides instructional solutions. This study examines the use of Reasoning Mind as a supplemental, fourth-grade computer-based approach to instruction toward improving mathematics achievement in a sample of fourth-grade students. The study also explores students’ perceptions of the program, students’ attitudes and interests regarding mathematics, and the extent that teachers’ instructional practices were impacted by RM. There was an increase in the proportion of RM students who met TAKS passing standards and who tested commended from 2010 to 2011. The increases were significantly higher for RM students compared to control-group students on the test. Improvements were also noted on the Stanford 10 mathematics tests for RM and control-group students. The gap between African American and Hispanic students relative to the percent of students who met TAKS passing standards was reduced. At the same time, the gap between the proportion of African American and White students who tested commended on the TAKS mathematics test was reduced. Students were, generally, positive about the RM program regarding its ability to help them learn mathematics and increase their interests in mathematics. Teachers indicated benefits of RM training and the positive impact of the program toward improving mathematics achievement.

Should you have any questions or require any further information, please contact me or Carla Stevens in the Department of Research and Accountability, at 713-556-6700.

__TBG

TBG/CS:vh cc: Superintendent’s Direct Reports

Chief School Officers School Improvement Officers Nancy Gregory Rachele Vincent

Lance Menster

Department of Research and Accountability Houston Independent School District

RESEARCH

Reasoning Mind Program Evaluation

2010–2011

E d u c a t i o n a l P r o g r a m R e p o r t

2011 Board of Education

Paula M. Harris PRESIDENT Manuel Rodríguez Jr FIRST VICE PRESIDENT Anne Eastman SECOND VICE PRESIDENT Carol Mims Galloway SECRETARY Michael L. Lunceford ASSISTANT SECRETARY Lawrence Marshall Greg Meyers Harvin C. Moore Juliet K. Stipeche Terry B. Grier, Ed.D. SUPERINTENDENT OF SCHOOLS Carla Stevens ASSISTANT SUPERINTENDENT DEPARTMENT OF RESEARCH AND ACCOUNTABILITY Renmin Ye, Ed.D. INTERMEDIATE APPLICATIONS DEVELOPER Venita R. Holmes, Dr.P.H. RESEARCH MANAGER

Houston Independent School District Hattie Mae White Educational Support Center 4400 West 18th Street Houston, Texas 77092-8501 Website: www.houstonisd.org It is the policy of the Houston Independent School District not to discriminate on the basis of age, color, handicap or disability, ancestry, national origin, marital status, race, religion, sex, veteran status, or political affiliation in its educational or employment programs and activities.

REASONING MIND 2010–2011

1

EXECUTIVE SUMMARY

REASONING MIND

A COMPARATIVE STUDY OF MATHEMATICS ACHIEVEMENT

2010–2011

Program Description

In December 2008, ExxonMobil announced that 21 Houston-area schools, serving more than 1,400

students, will gain access to an innovative, technology-based mathematics curriculum called Reasoning

Mind, as a result of a $1.2 million contribution to the Houston A+ Challenge. This effort was prompted

by ―the decline of student interest in math in the U.S. as a long-term, serious threat to the nation‘s

economy‖ (HISD Archives, ―ExxonMobil Gives,‖ 2008, para. 4). Supporters of the project maintained

that ―poor standardized test results in higher grades can be improved by focusing student efforts on

mastering math fundamentals in the early grades, through use of a comprehensive, coherent curriculum‖

(HISD Archives, ―ExxonMobil Gives,‖ 2008, para. 4).

Reasoning Mind (RM) is a technology-based program, designed to teach mathematics and develop

logical reasoning skills. RM content is based on research of an international curriculum. RM uses an

online community that develops students‘ mathematics knowledge and thinking skills. Students, teachers,

and parents are engaged in the learning process (The Academy of Medicine, Engineering and Science,

2006). RM aims to continuously engage students with interactive content, animations, and games.

Through individualized instruction, students are exposed to more challenging assignments at their own

pace. The program diagnoses weaknesses in students‘ knowledge and provides instructional solutions.

In standard implementation, RM is used in conjunction with in-class instruction. Students access the

program by individually logging in online using a computer, where they are guided through grade-

appropriate lessons and corresponding problems. Mathematics problems are ranked according to

difficulty based on students‘ correct answers on past problems. Students can request ―hints‖ to help solve

problems. A ―Genie Solution‖ provides the most effective method for calculating a solution.

Teachers monitor students‘ progress using their own computers. Teachers and students have

immediate feedback on how students are performing on each topic. Students experiencing difficulty on

lessons should be pulled by their teacher for one-to-one ―interventions‖ or small-group tutorials. At the

end of the class, each student receives an individualized program-generated homework assignment based

on their classroom assignment for the day (Fleming, 2011). Individual support is provided to teachers by

RM program coordinators.

Much focus in education has been on improving the mathematics performance of students through

evidence-based best practices. However, Tieso (2002) argued that little systematic research has examined

the effects of curricular enhancements and technology on student achievement. Few studies have

explored the use of technology to raise mathematics achievement of elementary-school students. This

study examines the use of Reasoning Mind as a supplemental, fourth-grade computer-based approach to

instruction toward improving mathematics achievement in a sample of fourth-grade students. The study

also explores students‘ perceptions of the program, students‘ attitudes and interests regarding

mathematics, and the extent that teachers‘ instructional practices were impacted by RM.

HISD RESEARCH AND ACCOUNTABILITY

2

Key Findings

1. How did Reasoning Mind fourth-grade students perform on state-mandated and norm-referenced

mathematics tests compared to control-group students?

The percent of students who met passing standards was comparable for RM and control-group

students in 2010 on the TAKS mathematics test. However, RM students achieved an increase in the

proportion of students who met standard and who tested commended in 2011 by 1.2 and 8.2

percentage points, respectively. The differences were statistically significant (p<.05). Comparatively,

the control group showed a substantial decrease in their met standard rates, but a moderate increase in

their commended rates (-10.9 and 4.9 percentage points, respectively).

Paired samples results on the Stanford 10 test revealed that RM students had a slightly higher mean

NCE than the control group on the 2010 pretest; however, the performance of control-group students

exceeded the performance of RM students on the posttest in 2011. RM students gained only 4.0

points, while the control group gained 5.0 points. The differences in performance for both groups was

statistically significant (p<.01).

TAKS vertical scale scores for a paired-sample of RM and control-group students revealed gains over

the two-year study period for both groups. However, gains were higher for RM students (84.69)

compared to control-group students (79.84). Results were statistically significant for both groups

(p<.01).

2. How did RM students in historically underachieving groups perform on mathematics tests?

RM non-economically-disadvantaged students outperformed economically-disadvantaged students

in 2010 relative to meeting TAKS mathematics passing standards (91.5 vs. 86.6); however, an

increase in the percentage of economically-disadvantaged students passing the test resulted in a

reduction in the gap between the groups in 2011. The gap between the groups was 4.9 percentage

points in 2010, but was reduced to 1.4 percentage points in 2011. The percent of non-economically-

disadvantaged students attaining commended status increased, but decreased for the economically-

disadvantaged students, resulting in an increase in the gap between the groups.

LEP students outperformed non-LEP students in the percent of students who met TAKS

mathematics passing standards in 2010 and in 2011. In addition, the percent of LEP students who

met passing standards increased over the two-year period. The gaps between the groups was 4.6

percentage points in 2010 and decreased to 2.7 percentage points in 2011.

Lower percentages of African Americans than Hispanic and White students met TAKS mathematics

passing and commended standards in 2010 and 2011. The gap between African Americans and their

ethnic comparison groups was at least 6.7 percent points in 2010. However, the gap between

African American and Hispanic students was reduced by 1.6 percentage points, but increased

slightly with White students by .2 percentage points. The gap between Hispanic and White students

also increased from 1.0 to 4.4 percentage points.

The commended rates for all groups increased over the study period, with Hispanic students

experiencing the highest increase of 10 percentage points and African American students achieving

an 8.8 percentage-point increase. There was a substantial reduction in the gap between African


3

American and White sudents relative to commended status by nearly nine percentage points. The

proportion of Hispanic students that attained commended status was slightly above White students in

2010, but overwhelmingly exceeded their rates in 2011 by 10.5 percentage points.

3. What were the best predictors of mathematics performance of fourth-grade RM students?

Multiple regression analysis found that ethnicity made the strongest contribution toward explaining

2011 TAKS mathematics performance of African American vs. Hispanic/White students. In the

model comparing Hispanic vs. African American/White students, economic status made the

strongest contribution to the model.

The one-way between-groups analysis of covariance (ANCOVA) was conducted to determine

whether there was a significant difference in the 2011 TAKS mathematics performance of the RM-

student group and the control group, while controlling for 2010 TAKS mathematics performance.

After adjusting for pre-intervention scores, there was no significant difference between the two

groups on the posttest.

A one-way multivariate analysis of variance was performed to investigate group differences in

mathematics performance based on both 2011 TAKS mathematics vertical scales and Stanford 10

mathematics NCEs. When considering performance on both tests at the same time, the RM students

had higher scores than control students on both the TAKS and the Stanford 10 tests.

4. What were students’ perceptions of RM and how were their attitudes and interests in mathematics

influenced by participating in the program?

An overwhelming majority of students indicated that they enjoyed the RM class (88.9 percent) and

expressed that RM helped them understand math better (87.2 percent).

Notably, there was a high degree of uncertainty on items that measured students‘ ability to perform

math. Specifically, 16.8 percent of students indicated that math was harder for them than for many of

their classmates. In addition, about 40.0 percent of respondents expressed ‗yes‘ or ‗maybe‘ on just

not being good at math (20.0 and 20.3 percent, respectively). The majority of students revealed that

they would like to do more math in their life (62.3 percent); however, 33.6 percent replied ‗maybe‘ on

this item.

Between 55.7 and 65.5 percent of students expressed that their grades are better, math is easier, and

they need less help completing their math homework this year (2010–2011) than last year (2009–

2010). However, there was a high level of uncertainty in their mathematics abilities as indicated by

the large proportion of students who replied ‗maybe‘ to these items. Most notably, nearly 30.0 percent

of surveyed students expressed ‗maybe‘ that their grades are better this year in math than last year.

5. To what extent did teachers’ RM training, skills, and instructional delivery practices contribute

toward students’ mathematics achievement?

RM teachers were asked how prepared they were after attending the RM introductory training session


4

in 2010–2011 to use the program. Among the 24 teacher respondents, 70.8 percent indicated that they

were very well prepared to teach students to use the RM ‗student‘ interface and manage the computer

lab classroom environment. In addition, 65.2 percent of the respondents replied that they were very

well prepared to use the RM ‗teacher‘ interface. The highest proportion of teachers indicated that they

were very well prepared in classroom management (75.0 percent).

General comments expressed by RM teachers reflected themes relative to the program improving

math skills of their students. However, there were several concerns about the alignment of RM with

HISD curriculum and students missing other instruction while participating in RM.

Recommendations

1. Gains in the mathematics performance, particularly among historically underperforming student

groups in mathematics provide evidence of the benefits of the program. Continued support for these

students in mathematics might continue to contribute toward closing the achievement gaps.

2. Students and teachers were overwhelmingly positive concerning the benefits of RM toward

improving mathematics achievement. Thus, an extension of the program might enhance benefits

beyond fourth grade and to students at other schools.

3. HISD administrators should continue to work with RM administrators to ensure that scheduling of

students for mathematics instruction includes both core and supplemental instruction.

4. RM administrators should continue to ensure that mathematics concepts delivered through the

program meet state standards and are aligned with Student Expectations (SE) in the Texas Essential

Knowledge and Skills (TEKS).


5

REASONING MIND

A COMPARATIVE STUDY OF MATHEMATICS ACHIEVEMENT

2010–2011

Program Description

Reasoning Mind (RM) is a technology-based program, designed to teach mathematics and develop

logical reasoning skills. RM content is based on research of an international curriculum. RM uses an

online community that develops students‘ mathematics knowledge and thinking skills. Students, teachers,

and parents are engaged in the learning process (Reasoning Mind website, 2011). RM aims to

continuously engage students with interactive content, animations, and games. Through individualized

instruction, students are exposed to more challenging assignments at their own pace. The program

diagnoses weaknesses in students‘ knowledge and provides instructional solutions.

In standard implementation, RM is used in conjunction with in-class instruction. Students access the

program by individually logging in online using a computer, where they are guided through grade-

appropriate lessons and corresponding problems. Mathematics problems are ranked according to

difficulty based on students‘ correct answers on past problems. Students can request ―hints‖ to help solve

problems. A ―Genie Solution‖ provides the most effective method for calculating a solution.

Teachers monitor students‘ progress using their own computers. Teachers and students have

immediate feedback on how students are performing on each topic. Students experiencing difficulty on

lessons should be pulled by their teacher for one-to-one ―interventions‖ or small-group tutorials. At the

end of the class, each student receives an individualized program-generated homework assignment based

on their classroom assignment for the day (Fleming, 2011). Individual support is provided to teachers by

RM program coordinators.

Much focus in education has been on improving the mathematics performance of students through

evidence-based best practices. However, Tieso (2002) argued that little systematic research has examined

the effects of curricular enhancements and technology on student achievement. Few studies have

explored the use of technology to raise mathematics achievement of elementary-school students. This

study examines the use of Reasoning Mind as a supplemental, fourth-grade computer-based approach to

instruction toward improving mathematics achievement in a sample of fourth-grade students. The study

also explores students‘ perceptions of the program, students‘ attitudes and interests regarding

mathematics, and the extent that teachers‘ instructional practices were impacted by RM.

Purpose of the Evaluation Report

1. How did Reasoning Mind fourth-grade students perform on state-mandated and norm-referenced


2. How did RM students in historically underachieving groups perform in mathematics?

3. What were the best predictors of mathematics performance of fourth-grade RM students?

4. What were students‘ perceptions of RM and how were their attitudes and interests in mathematics


5. To what extent did teachers‘ RM training, skills, and instructional delivery practices contribute

toward students‘ mathematics achievement?


6

Review of Literature

The No Child Left Behind Act, 2001 requires that schools demonstrate ‗adequate yearly progress‘ in

students‘ math performance, which must meet or exceed state standard by 2014. Nationwide, many U.S.

students show mastery of only basic mathematics, and only a small proportion of students achieve at high

levels (Agodini, Deke, Atkins-Burnett, Harris, & Murphy, 2008). On the National Assessment of

Educational Progress, only 39 percent of fourth-graders performed at or above Proficient in 2009, which

was unchanged from 2007 (National Center for Education Statistics (NCES), 2009). In Texas, only 26

percent of fourth-grade students scored at or above Proficient on the test. Differences in math

performance continued to exist between fourth graders from different ethnic and socioeconomic

backgrounds, with math achievement of minority students and those from poor backgrounds consistently

lagging behind achievement of students from more affluent backgrounds. Specifically, there was a 26-

point gap in mathematics scores between White and Black students on NAEP 2009, and a 21-point score

gap between White and Hispanic students. The gaps were not significantly different from the gaps in

2007 (NCES, 2009). In Texas, the gaps were even higher between White and Black students by 38 points

and between White and Hispanic students by 35 points. Fourth-grade students who were not eligible for

free lunch continued to have higher scores on average than those eligible for reduced-price lunch, who in

turn scored higher than those eligible for free lunch in the nation and in Texas.

Adodini, et. al. maintains that ―what is taught to students and how it is taught (that is, curriculum and

its pedagogical approach) may be important factors in a school‘s ability to improve student math

achievement‖ (p.2). Different approaches are employed to teach math. Traditional approaches are based

on the perspective that children will develop a strong understanding of mathematical principles by first

being taught facts and procedures, and then applying those skills to solve real-life problems. Reform

approaches are based on the belief that mathematical principles are better learned in the context of solving

real-life problems through student-directed activities. Many researchers are challenging educators to

employ more innovative approaches to mathematics education. This is partly due to cognitive research

highlighting the multifaceted process required to learn mathematics (National Research Council, 2005,

2007, 2009). Mundie (2011) maintains that ―Technology has the potential to help reinvent the education

process, and excite and inspire young learners to embrace science, math and technology‖ (p.1).

Education reform that supports the use of technology has been documented at the national level based

on state results. A study conducted by the U.S. Department of Education (2005) found that, in Texas, the

majority of fourth-grade students do not use computers weekly to practice or review mathematics topics,

to extend mathematics learning with enrichment activities, or to research mathematics topics. Fourth-

grade teachers were equally as unlikely to use computers weekly to develop mathematics curricula or

assignments, to look up mathematics information, or to present mathematics concepts to students.

Nevertheless, the use of technology with elementary school students has promise to promote research-

based practices in mathematics instruction, prepare students for more rigorous math courses, and diagnose

and remedy the deficiencies of students who lack mathematics proficiency (National Education

Technology Trends, 2007).

In efforts to add to the body of knowledge, researchers have discovered that, ―the best educational

activities connect not only to important concepts but also to students‘ interests and passions‖ (Games for

Learning Institute, 2011, p.1). Computer-based instruction and computer games are inherently interactive,

and have increasingly become a new and innovative approach to teaching and learning mathematics as

they capture the attention of youth. In addition, computer games allow students to be transported into

another reality and engage in activities that simulate the real world while exploring natural phenomena

that they cannot directly observe (Games Research, 2011; Mundie, 2011).


7

Efforts to improve the learning abilities of specific children‘s needs, has left many school districts

searching for ways to accommodate different learning styles. ―The Technology Principle,‖ states:

―Mathematics instructional programs should use technology to help all students understand mathematics

and should prepare them to use mathematics in an increasingly technological world‖ (p. 40). The role of

technology can serve as a significant tool in promoting problem solving and reasoning abilities among

students.

Researchers Sutton and Krueger (2002) argued ―Many mathematics students spend much of their time

on basic computational skills rather than engaging in mathematically rich problem-solving experiences‖

(p. 26). Teachers have a significant role to play because teachers‘ efforts to increase students‘ knowledge

of math largely depend on the content and teaching capabilities of teachers. ―The most direct route to

improving mathematics achievement for all students is through better mathematics teaching‖ (p. 26).

Research has suggested that the use of technology in the classroom serves as a tool to increase students‘

motivation and perception levels regarding math (Frye and Dornisch, 2008). While traditional

instructional methods have been successful in the classroom, there remain populations of students who

cannot grasp mathematical concepts without the use of teachers‘ incorporation of other methods within

their teaching ability. In order for a student to be successful in learning mathematics, classroom teachers

should integrate the learning styles of students and different facets of technology within their teaching.

This study may build on the body of evidence relative to the effectiveness of a computer-based

mathematics program toward enhancing student achievement, and students‘ perceptions of mathematics,

while enhancing teachers‘ instructional practices.

Methods

Study Population

The study population consisted of fourth-grade students enrolled at 21 HISD elementary schools

during the 2010–2011 academic year. The 21 schools,

reportedly, self-selected to participate in RM for this

project and were under contract with Reasoning Mind.

The participating elementary schools were Almeda,

Bastian, Bell, Briarmeadow, Cook, Cornelius, Emerson,

Garden Oaks, Lyons, Mitchell, Red, Reynolds, Rhoads,

Scott, Valley West, White, Garden Villas, Montgomery,

R. Martinez, Wainwright, and Whidby. It should be

noted that some schools implemented RM in previous

years.

In order to improve the validity of the study, RM

administrators were asked to provide a list of fourth-

grade students who participated in the program in 2010–

2011. A total of 1,375 students were extracted from the

list and found in the Public Identification Management

System database with accurate identification numbers

(PEIMS, 2010-2011). A control group of fourth-grade

students was established based on comparable 2010

Texas Assessment of Knowledge and Skills (TAKS)

vertical scale scores in mathematics with students at the

same RM schools (Table 1). RM students that were not

successfully matched using these criteria were matched

with students enrolled at schools in the same region,

Table 1: RM and Control Study Samples, 2010 2011

RM *Control

Total

N % N %

1,375 100.0 2,458 100.0

Gender

Male 654 47.8 1134 50.4

Female 715 52.2 1116 49.6

Ethnicity

African Am. 419 30.6 676 30.0

Hispanic 863 63.0 1412 62.8

White

Asian

Other

55

19

13

4.0

1.4

0.9

108

32

22

4.8

1.4

1.0

Special Ed. 53 3.9 57 2.5

LEP 408 29.8 992 44.1

G/T 204 14.9 395 17.6

Bilingual 476 34.8 782 34.8

Title I 1369 100.0 2160 96.0

Eco. Disadv. 1227 89.6 2012 89.4

At Risk 805 58.8 1298 57.7

*Note: The control group was matched with RM

students based on TAKS 2010 vertical scale scores at

the same schools or schools in the same geographical

regions of the district.


8

based on the assumption that students enrolled in similar communities and attending schools in the same

area have similar educational exposure. Refer to Table 1 for the demographic characteristics of RM and

control-group students. The groups are fairly comparable relative to ethnic composition, economic status,

and at-risk status. There were noticeably more females and students participating in special education

programs in the RM group than the control group. Limited English proficient (LEP) students dominated

the control group compared to the RM group.

Data Collection and Analysis

Assessment Instruments

Student performance data were collected using the 2010 and 2011 English and Spanish Texas

Assessment of Knowledge and Skills (TAKS) and the 2010 and 2011 Stanford Achievement Test

(Stanford 10). The Stanford 10 is a norm-referenced measure, while the TAKS is a state-mandated,

criterion-referenced test. The 2010 Stanford 10 and TAKS results were used as baseline data, while the

2011 results were used as a post-RM outcome measure. TAKS and Stanford 10 were disaggregated for

comparative analysis by subgroups (at risk, special education, ethnicity, gender, limited English proficient

(LEP)) based on classifications in the test databases.

The Stanford 10 results included in this report consist of mean Normal Curve Equivalent (NCE)

scores. The NCE provides an equal-interval scale that allows computations (such as averaging or

subtraction). NCEs are useful when measuring academic progress over time and comparing different

subject areas or student groups.

The spring administration of TAKS included met passing standards, commended, and vertical scales.

The vertical scales were used as criteria for selection of a comparison student group. Specifically, RM

students were individually matched with a fourth-grade student at the same school and with comparable

vertical scale scores on the 2010 TAKS. This student served as a match for Stanford 10 as well. With a

vertical scale, a student‘s scale score in one grade can be compared to the student‘s scale score in another

grade as long as the scores are in the same language and subject (TEA, 2010). An advantage to the

vertical scale is that it enables the progress of students who have different initial proficiency levels to be

compared (TEA, 2010). Vertical scales are aligned with the TEKS curriculum at each grade and are

based on the assumption that a student will have received instruction in the grade-specific curriculum

(Texas Education Agency, 2011). The vertical scale scores needed to meet the passing standard and to

achieve commended performance on TAKS English and Spanish mathematics can be found in Appendix

A. The results from the Spanish and English versions of the test were used only when fourth-grade

students were administered the same version of the test in 2011 that they were administered as a third-

grade student in 2010.

The data obtained from the test results and completed surveys were compiled in Microsoft Excel, and

later analyzed using the Statistical Package for Social Sciences (SPSS). Descriptive statistics (both

frequencies and percentages) were reported. Independent t-tests and paired-samples tests were conducted

using parametric data. The McNemar‘s test and Mann-Whitney were conducted based on nonparametric

data. The Analysis of Covariance (ANCOVA) and multivariate analysis were conducted to measure

differences between RM and comparison-group students, controlling for pretest measures. Multiple

regression analysis was conducted to determine best predictors of 2011 mathematics performance,

controlling for ethnicity, economic status, and LEP status.

Survey Administration

Web-based surveys were administered in March 2011 to RM students and teachers at the 21 targeted

campuses. The student survey assessed their experiences with RM and their attitudes toward mathematics

following RM instruction. The teacher survey measured the extent that professional skills and RM

training contributed to student academic achievement in math. Additional information was captured on

teachers‘ perceptions of instructional delivery of RM in the classroom setting.


9

Results

How did Reasoning Mind fourth-grade students perform on state-mandated and norm-referenced


A comparison study was conducted to

determine the impact of RM on student

achievement using 2010 and 2011TAKS and

Stanford 10 mathematics results. Subjects were not

known to be exposed to RM as third graders. A

matched-paired student sample of fourth graders

with comparable 2010 TAKS vertical scale scores

in either the same school or same region were

identified as the control group. There were 1,345

RM students and 2,202 control-group students

identified for the paired test analysis. The results

are presented in Figures 1 and 2.

The percent passing and commended rates on

the TAKS mathematics test depicted in Figure 1

reveal that the percent of students who met passing

standards was comparable for RM and control-group

students in 2010. However, RM students achieved

an increase in the proportion of students who met

passing and commended standards by 2011 (1.2 and

8.2 percentage points). At the same time, the control

group showed a decrease in their passing rate and an

increase in their commended rate (-10.9 and 4.9

percentage points) over the study period.

A nonparametric McNemar test based on the two

years of data for the 1,345 RM students revealed a

statistically significant increase in the met standard

rates of the RM student group from pretest measure

(2010) to posttest (2011) (z=9.054, p=.003). There

was also a statistically significant increase in the

commended rates of RM students from pretest to

posttest (z=43.3, p<.01). Findings from the two

years of data for the sample of 2,202 control group students revealed that the decrease in the percent of

students that met passing standard was not statistically significant (z=2.89, p=.089). However, the

increase in commended rates for the control group was statistically significant (z=55.35, p<.01). A Mann-

Whitney test compared TAKS mathematics pass/fail and commended outcomes of RM and control-group

students. Although the mean rank was higher for RM students than for students in the control group, there

was no statistically significant difference between the groups (z=1.178, p=.239). In contrast, the mean

rank assessing commended status was higher for control group students than RM students; however, no

statistically significant difference was found between the groups (z=.211, p=.833).

Figure 1. TAKS math met passing standard and commended

rates of RM students and control group, 2010 and

2011.

Figure 2. Stanford 10 math NCEs of paired samples of RM

and control students, 2010 and 2011.

87.1 87.1

31.5 31.8

88.3

76.9

39.734.8

0

20

40

60

80

100

RM Control RM Control

2010 2011Met Standard Commended

54.1 53.558.1 58.5

0

20

40

60

80

100

RM Control

2010 2011


10

Stanford 10 data were retrieved on a paired sample of RM and control-group students based on 2010

and 2011 NCEs. The results are presented in Figure 2. It is evident that RM students had a slightly higher

mean NCE than the control group at pretest; however, the performance of control-group students

exceeded the performance of RM students at posttest. RM students gained only 4.0 points, while the

control group gained 5.0 points.

Paired samples t-tests were conducted to evaluate the impact of the RM intervention on student‘s

Stanford scores and TAKS scores compared to control-group performance. The findings are represented

in Tables 2 and 3. Table 2 shows a statistically significant increase in Stanford 10 NCEs for the RM

group from pretest (M=54.15, SD=18.73) to posttest [M=58.10, SD=16.73, t(887)=9.22, p<.01] and a

statistically significant increase in NCEs for the control group from pretest (M=53.47, SD=18.57) to

posttest [M=58.53, SD=18.24, t(1435)=14.93,

p<.01]. Paired samples results based on TAKS

vertical scale scores of both groups depicted in

Table 3 reveal gains over the two-year study

period; however, the increase in vertical scale

scores was higher for RM students (84.69)

compared to control-group students (79.84).

Results were statistically significant for both groups

(p<.01).

How did RM students in historically

underachieving groups perform on

mathematics tests?

TAKS passing and commended rates were

disaggregated by ecomonic status, LEP status, and

ethnicity to determine the impact of the program on

students most at risk of underachieving in

mathematics. Results presented in Figure 3

represent data for 1,227 economically

disadvantaged and 142 non-economically-disadvantaged students. Non-economically-disadvantaged

students outperformed their counterparts in 2010 (91.5 vs. 86.6). Economically-disadvantaged students

increased their passing rate to 90.1 percent in 2011, while the passing rate for non-economically-

disadvanataged students remained unchanged. The gap between the groups was 4.9 percentage points in

2010, but was moderately reduced to 1.4 percentage points in 2011. On the other hand, the commended

rates of economically-disadvantaged students remained lower than their counterparts, and the gap

between the groups substantially increased from two percentage points to 12.1 percentage points over the

study period.

Table 2: Descriptive Statistics and Paired Results on Stanford 10 Mathematics Test, Spring 2010 and 2011

2010 2011 Mean Diff t p 95% C.I.

Mathematics Test Mean Std. Mean Std.

RM Cases (n=887) 54.15 18.73 58.06 18.73 3.91 9.22 .000 (3.08, 4.74)

Control Group(n=1435) 53.47 18.57 58.53 18.24 5.06 14.93 .000 (4.39, 5.71)

Table 3: Descriptive Statistics and Paired Results on TAKS Mathematics Test, Spring 2010 and 2011

2010 2011 Mean Diff t p 95% C.I.

Mathematics Test Mean Std. Mean Std.

RM Cases (n=1435) 591.79 92.58 676.48 171.07 84.69 17.93 .000 (75.44, 93.95)

Control Group (n=2202) 592.90 91.75 672.74 172.52 79.84 21.68 .000 (72.62, 87.07)

Figure 3. TAKS math met passing standards and commended

rates of RM students by economic status, 2010 and

2011.

86.691.5

43 45

90.1 91.5

39.3

51.4

0

20

40

60

80

100

Eco. Disadv. Non-Eco. Disadv.

Eco. Disadv. Non-Eco. Disadv.

2010 2011Met Standard Commended


11

82.3

89.0 9086.5

91.694.4

20.7

35.7 34.529.5

45.7

35.2

0

20

40

60

80

100

Afr. Am. Hispanic White Afr. Am. Hispanic White

Percen

t

Met Standard Commended

Similar analysis conducted for LEP and non-

LEP students resulted in data on 601 LEP and 738

non-LEP students. Figure 4 shows that LEP

students outperformed non-LEP students in the

percent of students who met passing standards in

2010 and in 2011. In addition, the percent of LEP

students who met passing standards increased

over the two-year period. The gaps between the

groups was 4.6 percentage points in 2010 and

decreased to 2.7 percentage points in 2011. Both

LEP and non-LEP students experienced increases

in commended rates on the TAKS math test from

2010 to 2011.

The met standard and commended rates varied

for numbers of African Americans (419 and 407),

Hispanic (863 and 846), and White students (55 and 54) included in the study. The results can be found in

Figure 5. Lower percentages of African Americans than Hispanic and White students met passing and

commended standards in 2010 and 2011. In fact, the gap between African Americans and their ethnic

comparison groups was at least 6.7 percentage points in 2010. Over the study period, the gap between

African American and Hispanic students was reduced by 1.6 percentage points, but increased slightly

between them and White students by .2 percentage points. The gap between Hispanic and White students

also increased from 1.0 to 4.4 percentage points. The commended rates for all groups increased over the

study period, with Hispanic students experiencing the highest increase of 10 percentage points and

African American students achieving an 8.8

percentage-point increase over time. There was a

substantial reduction in the gap between African

American and White sudents relative to commended

status by nearly nine percentage points. The

proportion of Hispanic students that attained

commended status was slightly above White students

in 2010, but overwhelmingly exceeded them in 2011

by 10.5 percentage points.

What are the best predictors of mathematics

performance of fourth-grade RM students?

Multiple regression analysis was conducted to

explore the best predictors of mathematics

performance of RM and control-group students. The

dependent variable was the 2011 TAKS mathematics

vertical scale scores and the independent variables

were economic status, ethnicity and LEP status.

The findings indicate how well these variables

explain 2011 TAKS performance.


rates of RM students by LEP status, 2010 and 2011.


rates of RM students by ethnicity, 2010 and 2011.

Met Standard

89.785.1

35.928.2

91.7 89.0

45.3

36.8

0

20

40

60

80

100

LEP Non-LEP LEP Non- LEP

2010 2011

Met Standard Commended

2010 2011


12

In order to determine the influence of ethnicity and other demographic factors on students‘ math

performance, several models were developed with these factors in the models. Table 4 presents results

from Model 1 (African American students vs. Hispanic/White students) and Model 2 (Hispanic students

vs. African American/White students). In the model comparing African Americans with the

Hispanic/White student group, ethnicity (-.072) made the strongest contribution toward explaining 2011

TAKS performance, considering all of the other variables in the model. Group assignment made the least

contribution in the model. However, in the model comparing Hispanics with the African American/White

student group, economic status made the strongest contribution to the model (-.062), and group

assignment made the least contribution to the model.

Additional multiple regression analyses were conducted comparing the performance of African

American to White students (Model 3) and Hispanic to White students (Model 4), while controlling for

economic status, LEP status, and group assignment. These results are not depicted in a table; however, the

results are as follows. In Model 3 (African American and White students), economic status made the

strongest contribution to the model (B = -.80, t = -2.425, p=.015). Group assignment and ethnicity made

the same contribution to the model (-.050). In Model 4 (Hispanic and White students), group assignment

(-.038), closely followed by economic status (-.36) made the strongest contributions to the model;

however, the results were not statistically significant (t=-1.836, p=.067). Findings from these analyses

demonstrate that students‘ performance in mathematics was more likely influenced by their ethnicity and

economic status, rather than whether or not the student participated in RM.

The one-way between-groups analysis of covariance (ANCOVA) was conducted to determine

whether there was a significant difference in the 2011 TAKS mathematics performance of the RM-student

group and the control group, while controlling for 2010 TAKS mathematics vertical scale scores on the

test (Table 5). The dependent variable in the model was the 2011 TAKS mathematics vertical scale

scores. Preliminary checks were conducted to ensure that there were no violations of the assumptions of

normality, linearity, homogeneity of regression slopes, and reliable measurement of the covariates. After

adjusting for pre-intervention scores, there was no significant difference between the two groups on the

posttest [F(1, 3537=.55. p=.46, partial eta squared=.000]. Therefore, when considering the performance

of students with both 2010 and 2011 TAKS mathematics scores, RM students did not perform

significantly better than the control students.

Table 4: Multiple Regression Analysis Based on TAKS Math Performance of RM Students, Spring 2011

Model 1

African Am. vs. Hispanic/White

Model 2

Hispanic vs. African American/White

B t p B t p

Constant

Ethnicity -.072 -3.353 .001** .056 2.526 .012*

Eco. Disadv. -.049 -2.788 .005** -.062 -3.519 .000**

LEP -.025 -1.128 .259 -.016 -.706 .480

Group Assignment -.010 -.600 .548 -.009 -.553 .580

Table 5. Analysis of Covariance of 2011 Mathematics Performance of RM and Control-group Students

Source df F p Partial Eta Square

2010 TAKS Math Scale Score 1 251.344 .000 .066

Group Assignment 1 .552 .457 .000

Table 6. Two-way Analysis of Covariance of 2011 Mathematics Achievement of RM and Control-group Students

Source df F p Partial Eta Square

2011 TAKS Math Scale Score 1 1.41 .236 .000

Stanford Math NCEs 1 16.94 .000 .005


13

A one-way multivariate analysis of variance (Table 6) was performed to investigate group differences

in mathematics performance based on both 2011 TAKS mathematics vertical scales and Stanford 10

mathematics NCEs. The independent variable was group assignment. Preliminary assumptions were

checked and revealed no serious violations. There was a statistically significant difference between RM

and control-group students on the combined dependent variables: F(1, 3349)=8.687, p=.000; Wilks‘

Lambda=.995, partial eta squared=.005. When the results for the dependent variable were considered

separately, the only difference to reach statistical significance was Stanford NCE performance: F(1,

3349)=16.94, p=.000, partial eta squared=.005. In summary, the RM group performed significantly better

than the control group on Stanford 10 (M=40.25, SD=30.19 vs. M=35.86, SD=29.37). On TAKS, the

RM group also performed better, but the results were not statistically different (M=677.81, SD=169.28 vs.

M=670.56, SD=170.70). It should be noted that these findings are based on the performance of students

with both TAKS and Stanford 10 results.

What were students’ perceptions of RM and how were their attitudes and interests in mathematics


Fourth-grade students were surveyed to gather their perceptions of RM, particularly to assess

whether their interests and attitudes about mathematics were influenced following participation in the

program. Table 7 depicts the survey results, including the total number of respondents on each item and

the proportion of students who replied ‗yes,‘ ‗maybe,‘ or ‗no‘ to the items.

General Perceptions of RM

The majority of student respondents were, generally, positive about the program. Some of the most

notable findings were indicated by the high percentage of students that enjoyed the class (88.9 percent)

Table 7: RM Students Perceptions of RM, Attitudes and Interests in Mathematics, 2010–2011

Yes Maybe No

General Perceptions of RM N % % %

Reasoning Mind helps me understand math better. 952 87.2 11.0 1.8

I enjoy my Reasoning Mind class. 947 88.9 8.8 2.3

Reasoning Mind meakes me better at helping others solve math problems. 949 77.3 17.9 4.7

Reasoning Math makes it easier to solve hard math problems without help. 949 70.3 24.1 5.6

Guided Study helps me learn math. 952 89.0 9.8 1.3

The game room helps me get faster at math. 944 68.9 21.1 10.1

E-mailing the Genie and getting e-mail from the Genie makes me more excited to learn math. 953 52.9 30.2 16.9

Shopping in the Mall and decorating . 954 81.2 10.2 8.6

Reasoning Mind is easier than my regular math class. 943 66.1 26.9 7.0

I like Reasoning Mind more than my regular math class 950 59.3 28.9 11.8

I use Reasoning Mind outside of school. 947 48.7 19.3 32.0

Attitudes and Interests about Math

I would like to do more math in my life. 958 62.3 33.6 4.1

Math will help me become more successful in the future. 954 80.2 18.2 1.6

Math is harder for me than for many of my classmates 956 16.8 28.6 54.6

I am using math in my everyday life (at the grocery store, etc.). 947 55.5 25.9 18.6

I am just not good at math. 947 20.0 20.3 59.8

I like math. 944 80.6 12.7 6.7

I enjoy learning math. 945 82.2 14.4 3.4


14

and expressed that RM helped them understand math better (87.2 percent). A higher percentage of

students saw the benefits of Guided Study in helping them learn math (89.0 percent) compared to

shopping in the Mall and decorating (81.2 percent), or communicating with the Genie (52.9 percent). (The

Mall is a virtual experience, where students spend earned points to purchase virtual items.) On the other

hand, there was a high percentage of uncertainty reflected in the Genie‘s ability to make them more

excited to learn math (30.2 percent). The high proportion of students that did not use the program outside

of school (32.0 percent) may be related to students‘ lack of access to computers at home.

Attitudes and Interests in Math

Table 7 also provides information regarding

students‘ attitudes and interests in mathematics.

Specifically, students consistently indicated that

they liked math and enjoyed learning math (80.6

percent and 82.2 percent). However, there was a

high degree of uncertainty on items that measured

students‘ ability to perform math. Specifically, 16.8

percent of students indicated that math was harder

for them than for many of their classmates, but 28.6

percent replied ‗maybe‘ to this item. In addition,

about 40 percent of respondents expressed ‗yes‘ or

‗maybe‘ on just not being good at math (20.0 and

20.3 percent, respectively). The majority of students revealed that they would like to do more math in

their life (62.3 percent); however, 33.6 percent replied ‗maybe‘ on this item.

Reasoning Mind students were instructed to reflect on their fourth-grade experiences in regular math

class. The results for related items are depicted in Figure 7. The sample size for this section of the survey

represented between 894 and 953 students among the total survey respondents. The majority of students

expressed that their grades are better, math is easier, and they need less help completing their math

homework this year than last year. Again, there was a high level of uncertainty in their abilities during

fourth grade as indicated by the large proportion of students who replied ‗maybe‘ to these items. Most

notably, nearly 30.0 percent of surveyed students expressed ‗maybe‘ that their grades are better this year

in math than last year.

To what extent did teachers’ RM training, skills, and instructional delivery practices contribute

toward students’ mathematics achievement?

A survey was administered to RM teachers to gather information on the extent that professional

development, skills, and instructional time influenced students‘ performance in math. A total of 32

teachers completed some portions of the Reasoning Mind Teacher Survey. Teachers at 16 of the 21 RM

campuses (76.2 percent) openly identified their campus.

Preparedness to Provide RM Instruction

RM teachers were asked how prepared they were after attending the RM introductory training session

in 2010–2011 to use the program. Among the 24 teacher respondents, 70.8 percent indicated that they

were very well prepared to teach students to use the RM ‗student‘ interface and manage the computer lab

classroom environment. In addition, 65.2 percent of the respondents replied that they were very well

prepared to use the RM ‗teacher‘ interface. The highest proportion of teachers indicated that they were

very well prepared in classroom management (75.0 percent).

Figure 7. Reflection on math experiences of RM students,

2010–2011

57.7 57.1 55.765.5

29.1 23.7 23.726.6

13.2 19.2 20.67.8

0

20

40

60

80

100

My grades are better

this year than last

year.

Math is easier for

me this year than

last year.

I need less help

completing my math

homework this year

than last year.

I usually do well in

math.

Yes Maybe No


15

Twenty-two teachers responded to the survey item related to estimating the total number of hours

trained in math workshops and in-services during the 2010–2011 academic year. The largest proportion of

teachers indicated that they participated in 1-10 hours of on-site RM training on qualification courses,

curriculum study sessions, and best practices (36.4 percent). Morover, 59.1 percent of respondents

designated 1-10 hours of training related to remote curriculum study and/or curriculum study assessments.

Training support provided directly to them by RM, such as classroom observations and one-on-one

meetings with the program coordinator were indicated by 63.6 percent of respondents, while other

professional development that dealth with math or teaching math and reading books or professional

journals related to math were indicated by 68.2 and 59.1 percent, respectively.

Instructional Delivery

RM teachers were asked to estimate the number of hours spent providing RM instruction during

school hours as well as before or after school. In addition, teachers were asked the length of time they

provided regular math instruction aside from RM. The findings are depicted in Table 8.

Among the 22 RM teacher respondents, the largest percentage spent between two to three hours

providing RM instruction during school hours. Five teachers (22.7 percent) indicated having spent more

than six hours providing RM instruction. Table 8 also shows that nearly 55.0 percent of RM teachers

provided RM instruction before and after school, with the highest percentage spending one to two hours

engaging in this task.

The length of time that RM teachers provided regular math instruction aside from RM varied from

zero to more than 90 minutes each day. Responses indicated that teachers were more likely to spend 46 to

60 minutes or 76-90 minutes providing daily regular math instruction to students (27.3 percent for both

groups). These times are within the HISD policy guidelines for providing regular mathematics instruction

at the elementary-school level.

Other Comments

RM teachers were asked to share additional comments/concerns about the implementation of RM

during the 2010–2011 academic year at their campus. Fifteen RM teachers provided comments. In

general, respondents typically perceived RM as improving the math skills of their students. However, one

concern expressed by a teacher was related to scheduling, specifically, students missing other instruction

because they are participating in RM. Two of the consistantly positive comments were:

It is a great program for the students to be exposed to technology as well as further their

Table 8: Length of RM Instruction and Regular Math Instruction for RM Teacher Sample, 2010–2011

Length of Time

Providing RM Instruction

During School Hours

Length of Time

Providing RM

Instruction Before and

After School

Length of Time Providing

Regular Math Instruction

aside from RM

Hours/Day N % N % Minutes/Day N %

0 0 0 10 45.5 0 2 9.1

1 to 2 7 31.8 11 50.0 <=30 0 0.0

2 to 3 10 45.5 1 4.5 31 to 45 4 18.2

3 to 6 0 0.0 46 to 60 6 27.3

>6 5 22.7 61 to 75 1 4.5

76-90 6 27.3

> 90 3 13.6

Total 22 100.0 22 100.0

Total 22 100.0


16

knowledge in math. The kids are very excited to collect points in RM City to get rewards in

return. From a teacher‘s perspective, RM City is beneficial because it lets every student work at

their own pace, and it also allows them to learn new objectives to where they can gain prior

knowledge before a teacher covers those particular objectives.

Reasoning Mind has helped the students, of course, with their math. I[t] has also allowed them

to stretch their minds in the computation of word problems that Reasoning Mind entails. Even

though we started in January 2011 with Reasoning Mind, I, as a teacher, can see an

improvement in the students‘ academic level [in] math.

A respondent that expressed concerns about the instructional delivery time at their campus wrote:

Since this is a lab, I have the students for math only during the week and have had success in

moving the students forward. I have noticed that many students miss opportunities to improve

because they are pulled from the classroom for other things. This usually falls on many of the

lowest performing students and so they get further behind.

In summary, the majority of teachers who attended RM training were prepared to provide instruction

to students using the program. Teachers indicated that classroom support was provided to them by RM

staff through observations and individually-scheduled meetings. The time allotted to supplement RM within the regular mathematics curriculum was within the HISD guidelines.

Discussion

Reasoning Mind is a technology-based program, designed to teach mathematics and develop logical

reasoning skills. The program engages students with interactive content, animations, and games and offers

individualized instruction as students encounter more challenging content in mathematics. The program

diagnoses weaknesses in students‘ knowledge and offers instructional solutions. RM also provides

teachers with continuous feedback on how students are performing. The feedback model applied in RM

has been supported in the literature. Specifically, a study conducted by Baker, Gersten, and Lee (2002)

found that providing teachers and low achieving students with specific information on how each student

is performing consistently enhances achievement.

This study examined the performance of fourth-grade students who participated in RM during the

2010–2011 academic year. It should be noted that some students may have had previous experience with

the program; however, data were not collected on this variable. Some of the more notable findings

included the increase in the proportion of RM students who met TAKS passing standards and who tested

commended by 2011. The increases were significantly higher for RM students compared to control group

students. Improvements were also noted on the Stanford 10 mathematics tests; however, control-group

students made slightly higher gains on the test. Moreover, there was a reduction in the gap between

economically-disadvantaged and non-economically-disadvantaged students in their TAKS mathematics

passing rates over the two-year study period, but an increase in the gap on commended rates. In addition,

the gap between African American and Hispanic students relative to the percent of students who met

passing standards was reduced from 2010 to 2011, while the gap between these ethnic groups and White

students increased over the same period. Notably, the gap between the percentage of African American

and White students who tested commended on the TAKS mathematics test was reduced from 2010 to

2011, while the gap between Hispanic and White students increased, in favor of Hispanic students.

Students were, generally, positive about the program regarding its ability to help them learn

mathematics and increase their interests in mathematics. Teachers indicated benefits of RM training and


17

the positive impact of the program toward improving mathematics achievement. It is essential that the program adapts to future modifications of state testing requirements in mathematics.

Recommendations

1. Gains in the mathematics performance, particularly among historically underperforming student

groups in mathematics provide evidence of the benefits of the program. Continued support for these

students in mathematics might continue to contribute toward closing the achievement gaps.

2. Students and teachers were overwhelmingly positive concerning the benefits of RM toward

improving mathematics achievement. Thus, an extension of the program might enhance benefits

beyond fourth grade and to students at other schools.

3. HISD administrators should continue to work with RM administrators to ensure that scheduling of

students for mathematics instruction includes both core and supplemental instruction.

4. RM administrators should continue to ensure that mathematics concepts delivered through the

program meet state standards and are aligned with Student Expectations (SE) in the Texas Essential

Knowledge and Skills (TEKS).


18

References

Agodini, R., Deke, J., Atkins-Burnett, S., Harris, B., and Murphy, R. Design for the Evaluation of Early

Elementary School Mathematics Curricula (2008).Mathematica Policy Research, Inc. Retrieved from,

http://www.mathematica-mpr.com/publications/pdfs/mathcurriculadsgnrpt.pdf.

Fleming, N. (2011). Web-Based Russian Math Curriculum Shows Positive Results. Education Week.

Retrieved from http://www.edweek.org/ew/articles/2011/03/17/25math.

Houston Independent School District (2008). Exxonmobil Gives $1.2 Million to Houston A+ Challenge

for Area Schools: Funds will improve math education in elementary and middle Schools. Retrieved

from, http://www.houstonisd.org/portal/site/HISDArchives/

National Center for Education Statistics (2009). The Nation's Report Card: Mathematics 2009 (NCES

2010–451). National Center for Education Statistics, Institute of Education Sciences, U.S.

Department of Education, Washington, D.C. Retrieved from,

http://nces.ed.gov/nationsreportcard/pdf/main2009/2010451.pdf

National Education Technology Trends (2007).State Strategies and Practices for Educational Technology:

Volume II—Supporting Mathematics Instruction with Educational. Office of Planning, Evaluation

and Policy Development,U.S. Department of Education, Washington, D.C. Retrieved from

www.ed.gov/about/offices/list/opepd/ppss/reports.html.

U.S. Department of Education.SUMMER 2010 EDFactsState Profile-Texas. Retrieved from,

http://www2.ed.gov/about/inits/ed/edfacts/state-profiles/texas.pdf

Drickey, N. (2006). Learning technologies for enhancing student understanding of

Mathematics, International Journal of learning, 13, 109-116.

Frye, N., Dornisch, M. (2007-2008).Teacher technology use and student evaluations: the moderating role

of content area, Journal of Educational Technology Systems, 36(3) 305-317.

National Council of Teachers of Mathematics. (2000). Principles and standards for school Reston, VA

:Author.

McKinney, S., Chappell, S., Berry, R., and Hickman, B. (2009). An examination of the instructional

practices of mathematics teachers in urban schools.Preventing School Failure, 53, 278-284.

The Academy of Medicine, Engineering and Science of Texas. (2006). The Next Frontier: World-Class

Math and Science Education for Texas. Education Committee Report on Texas K-12 Math and

Science Education. Retrieved from

http://www.reasoningmind.org/pdf/RM_Recommendations_for_Schools_and_Policy-makers.pdf.

Tieso, C. (2002). The effects of grouping and curricular practices on intermediate students‘ math

achievement. The National Research Center on the Gifted and Talented, University of Conneticut.

Sutton, J., & Krueger, A. (Eds.). (2002). EDThoughts: What weknow about mathematics teaching and

learning. Aurora, CO:Mid-Continent Research for Education and Learning.


19

Appendix A

Texas Assessment of Knowledge and Skills

Performance Level Descriptors

Mathematics- Grade 4

Did Not Meet the Standard Met the Standard Commended Performance

Unsatisfactory performance; below state

passing standard; insufficient understanding

of the mathematics TEKS curriculum

Satisfactory performance; at or above state

passing standard; sufficient understanding of

the mathematics TEKS curriculum

High academic achievement; considerably

above state passing standard; thorough

understanding of the mathematics TEKS curriculum

Students Who Did Not Meet the Standard Students Who Met the Standard Students Who Achieved Commended Performance

1. Have poor reading skills and a limited math vocabulary

2. Lack persistence, endurance, and stamina

3. Dislike and are uncomfortable with math 4. Rarely retain or apply prior math knowledge

5. Have poor problem-solving skills (e.g., use few

strategies, have difficulty distinguishing between essential and extraneous information, cannot

apply necessary skills, frequently guess, do not

justify answers, have a limited grasp of reasonableness)

6. Operate at a concrete level; require

manipulatives to understand math concepts 7. Are dependent on models of geometric shapes

and solids

8. Have a limited understanding of measurement concepts and tools

9. Make few connections among math concepts

10. Have limited number sense (e.g., estimation,

rounding, place value)

11. Struggle with basic addition, subtraction, multiplication, and division facts and algorithms;

have difficulty computing with accuracy

1. Can read for meaning and detail and have an adequate math vocabulary

2. Often exhibit persistence, endurance, and

stamina 3. Are somewhat comfortable with math

4. Often retain and apply prior math knowledge

5. Have adequate problem-solving skills (e.g., use some strategies, can usually distinguish between

essential and extraneous information, apply

necessary skills, often justify answers and check solutions for reasonableness)

6. Are developing abstract thinking through the

use of models 7. Can usually visualize geometric shapes and

solids

8. Have an adequate understanding of measurement concepts and tools

9. Make some connections among math concepts

10. Have general number sense (e.g., estimation,

rounding, place value)

11. Demonstrate adequate knowledge of basic addition, subtraction, multiplication, and

1. Are fluent readers with a rich math vocabulary 2. Consistently exhibit persistence, endurance, and

stamina

3. Enjoy math and are confident about their math skills

4. Consistently retain and apply prior math

knowledge 5. Have strong problem-solving skills (e.g., use a

variety of strategies, distinguish between essential

and extraneous information, apply necessary skills, consistently justify answers and check

solutions for reasonableness)

6. Are able to think abstractly; can connect operations with concepts

7. Can consistently visualize geometric shapes

and solids 8. Have a thorough understanding of measurement

concepts and tools

9. Make connections among math concepts

10. Have excellent number sense (e.g., estimation,

rounding, place value) 11. Demonstrate thorough knowledge of basic

addition,


20

Appendix B

TAKS Mathematics Vertical Scale Scores

Performance Standard Grade 3 Grade 4

English

Met Standard

500 554

English

Commended

640 698

Spanish

Met Standard

503 555

Spanish

Commended

649 692

Documents

MEMORANDUM - Houston Independent School District · examines the use of Reasoning Mind as a supplemental, fourth-grade computer-based approach to instruction toward improving mathematics