Computation Skills & HS Outcomes

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Research Proposal

The Impact of Math Computation Skills on High School Achievement

Sue Hendrickson Barb Olson Christine Osthus Tim White

Purpose

The general purpose of this research is to determine if a correlation exists between math computation skills and specific academic outcomes. The measurement of academic achievement can be found in such things as achievement test scores, ACT scores, GPA, class rank, and graduation rate. Each of the four members of our research team is a high school teacher. We often see students who cannot do simple mathematical computations without using a calculator, and who do not know their mutiplication facts. It seems to us that this deficit impacts their ability to perform higher level tasks, as well. During informal talks with elementary teachers, we have found nearly each one of them says that they have received a message, either implicitly or explicitly, from curriculum specialists or professors that basic skills and computational abilities should not be stressed, and they have the sense that they are doing the "wrong thing" by asking and/or insisting that students memorize basic mamultiplication facts and become proficient at basic computation. The emphasis, they are told, is to on "higher order thinking skills." However, we think that the ability to do "higher order thinking skills" is impaired if the knowledge base -- which includes basic computational abilities -- is deficient. Therefore, we would like to query grade school teachers about their beliefs and practices concerning math computation in their classrooms. We would also like to determine if a lack of computational ability negatively impacts a student's career in math, and indeed in high school as a whole. If we find that deficient computational abilities are a significant handicap, we intend to publish the information as a useful tool for curriculum specialists and other aducators.

Definitions

Basic operations: Multiplication, division, addition, and subtraction.

Computational skills: The ability to perform the four basic operations of arithmetic on whoe numbers, integers, fractions, decimals, and percents.

Problem-solving: Synthesizing, analyzing, and applying mathematical strategies to real-life situations.

Constructivist learning: A learning theory that advocates the learner relating new knowledge to what is already known, constructing his/her own understanding, and making his/her own meanings.

Bloom's Taxonomy: A hierarchical list developed by ......Bloom, listing six levels of cognitive thinking: 1) Knowledge: The ability to recall facts, concepts or principles. 2) Comprehension: The ability to translate or interpret information. A grasp of meaning, intent, and relationship is demonstrated in oral, written, or non-verbal communication. 3) Application: The ability to apply previously acquired knowledge of information to a new or concrete situation. 4) Analysis: The ability to break material down into its components so that organizational structure may be understood. 5) Synthesis: The ability to analyze the parts and put them together to form a whole. 6) Evaluation: The ability to make judgements based on evidence and determine the value of material based on definite criteria.

Higher-order thinking skills: This phrase frequently refers to levels 4, 5, and 6 of Bloom's Taxonomy.

Prior Research

A nation at risk (1983). Washington, DC: Department of Education This report was commissioned by the then-Secretary of Education, T.H. Bell. It warned of declining academic performance in the United States, and warned that this situation was the reason for a decline in economic productivity. This report is often cited as the catalyst that started the "standards-based" education movement.

Creech, Joseph D. (1996). High school graduation standards: What we expect and what we get. Goals for Education: Educational Benchmarks. The author states that the current trend of raising high school graduation standards has not necessarily resulted in higher achievement. Employers are still complaining that high school graduates do not have the skills needed in the workplace, and that 30% of new college students need remediation in language arts or mathematics or both. He says that core curriculum must be linked to prior learning, and that each grade level needs curriculum frameworks and clear guides and objectives.

Kerka, Sandra (1995). Not just a number: Critical numeracy for adults. Ms. Kerka says that numeracy is the type of math skills needed to function in everyday life. Low levels of numeracy can limit access to jobs, education, and training; and can lead to low productivity on a job. She contends that numeracy is practical, procedural math that is perceived as less important and prestigious as theoretical and analytical mathematics. However, adults with functional numeracy skills can participate fully in civic life.

Murnane, Richard J. and Levy, Frank (1996). Teaching the new basic skills. New York: Free Press. Mr. Murnane and Mr. Levy contend that mastery of basic math skills has a big impact on earnings. Many employment tests that are mentioned in their book measure skills taught no later than junior high, such as manipulation of and conversion among fractions, decimals, and percents; and interpreting line and bar graphs.

Steen, Lynn A. (2997). What employers and educators test: The mathematics that really counts. Northfield, MN: St. Olaf College. Ms. Steen points out the importance of basic math skills in various employability tests and college entrance exams. She asserts that the level of ability tested is usually no higher than the eighth or ninth grade level. She says that there is a huge gulf between employment tests and education tests and the skills of "mathematical power" promoted by MCTM, which includes such skills as communicating, reasoning, and connecting.

SCANS Report for America 2000 (1991). What work requires of schools. Washington, DC: Department of Labor. The report by this commission explains the importance of basic competencies and fundamental skills necessary for new employees in today's work force.

Hypothesis

Deficient math computational skills in grade school adversely affect many aspects of a child's education, including problem-solving ability, performance and advancement in mathematics classes throughout schooling, class rank, graduation rate, and college entrance tests.

Population

An ideal population would be students from high schools across the nation. The lack of available resources, and common testing instruments, however, will force our population to be more localized in the Duluth and Superior area.

Sampling

We intend to examine records of the entire senior class from both Superior Senior High School in Superior, MN; and Denfeld Senior High School in Duluth, MN.

Instrumentation

As part of our information-gathering, we will distribute a questionnaire to a random sample of elementary school teachers, middle school teachers, and high school teachers. We intend to gain insight into the teacher's perception of the level of computational skilll of her/his students; the perceived effect from a lack of computational skills; and the ways in which the teacher deals with students' computational deficiencies. We shall also access data from achievement test scores in Duluth and Superior. We shall pull records from the senior class (1998) of Denfeld High and Superior Senior High, and record math computation scores in grades 5, 8, 10, and 12; math courses taken and completed; final overall GPA and class rank; ACT scores (where available); and the number of students who graduated on time.

The predictor variable is the computation score on achievement tests in 5th grade. The criterion variables are problem-solving scores, class rank, the type of math courses taken in high school, the performance in these classes, and ACT scores (if available). We should be able to obtain a prediction equation that will enable us to use the 5th grade score to predict high school outcomes, as described above. We will be able to compare the equations obtained from two different schools. We will enter scores on a spreadsheet for each student in the senior class of the two high schools. The spreadsheet will look something like this: Subject O1 O2 O3 O4 O5 etc. where

O1 = Gender O2 = Race O3 = Free or Reduced Lunch O4 = Special Education or other special services O5 = Computation Score on 5th Grade Test O6 = Problem-Solving Score on 5th Grade Test O7 = Computation Score on 8th Grade Test O8 = Problem-Solving Score on 8th Grade Test O9 = Computation Score on 10th Grade Test O10 = Problem-Solving Score on 10th Grade Test O11 = Computation Score on 12th Grade Test O12 = Problem-Solving Score on 12th Grade Test O13 = Class Rank O14 = ACT O15 = Graduate or Not O16 = 9th Grade Math Course O17 = 9th Grade Course Grade O18 = 10th Grade Math Course O19 = 10th Grade Course Grade O20 = 11th Grade Math Course O21 = 11th Grade Course Grade O22 = 12th Grade Math Course O23 = 12th Grade Course Grade

Our questionnaire to teachers will be along these lines: 1. What grade level do you teach? (Or, in the case of high school teachers, what math courses do you teach?) 2. How long have you taught?

For the following questions, answer with a 1, 2, 3, 4, or 5. The scores mean as follows: 1 = Strongly agree 2 = Mildly agree 3 = I don't know 4 = Mildly disagree 5 = Strongly disagree

1. It is important that students have multiplication facts memorized. 2. It is unimportant for students to memorize multiplication facts, because they can use a calculator. 3. It is important that students understand the meaning of fractions. 4. It is important that students can compute with fractions without a calculator. 5. It is unimportant that students can do fractional computation without a calculator. 6. It is important that students understand the meaning of decimal numbers. 7. It is important that students can compute with decimals without a calculator. 8. It is unimportant that students can compute with decimals without a calculator. 9. It is important that students understand the meaning of percents. 10. It is important that students can compute with percents without the use of a calculator. 11. It is unimportant that students can compute with percents without a calculator. 12. Problem-solving ability is more important than computation ability. 13. Computational skills of my current students are less than they were a few years ago. 14. Computaitonal skills of my current students are better than they were a few years ago. 15. Problem-solving skills of my current students are less than they were a few years ago. 16. Problem-solving skills of my current students are better than they were a few kyears ago. 17. Deficient computational skills harms problem-solving skills. 18. Deficient problem-solving skills harms computational skills. 19. I spend more time in the classroom on computational skills than I did a few years ago. 20. I spend more time in the classroom on problem-solving skills than I did a few years ago.

Threats to Validity

All of these things pose threats to validity: ability level of students; the socioeconomic make-up of the class; the racial and ethnic make-up of the class; placement in special education classes or other specially funded programs. We believe that we can control for the ability level, and special services. Another threat to validity will be the lack of records of students who have dropped out prior to the end of their senior year. The subjects who are "lost" are likely to have poor scores. Thus, the loss of these subjects can be expected to reduce the correlation between 5th grade scores and subsequent high school achievement.

Data Analysis

By the use of scatter plots, we shall see if a positive correlation exists. We will generate a prediction equation, and compare the predicted results with actual results. Also, we will compare the results and prediction equations of the two different schools.

Research Proposal

The Impact of Math Computation Skills on High School Achievement

Sue Hendrickson Barb Olson Christine Osthus Tim White

Purpose

The general purpose of this research is to determine if a correlation exists between math computation skills and specific academic outcomes. The measurement of academic achievement can be found in such things as achievement test scores, ACT scores, GPA, class rank, and graduation rate. Each of the four members of our research team is a high school teacher. We often see students who cannot do simple mathematical computations without using a calculator, and who do not know their mutiplication facts. It seems to us that this deficit impacts their ability to perform higher level tasks, as well. During informal talks with elementary teachers, we have found nearly each one of them says that they have received a message, either implicitly or explicitly, from curriculum specialists or professors that basic skills and computational abilities should not be stressed, and they have the sense that they are doing the "wrong thing" by asking and/or insisting that students memorize basic mamultiplication facts and become proficient at basic computation. The emphasis, they are told, is to on "higher order thinking skills." However, we think that the ability to do "higher order thinking skills" is impaired if the knowledge base -- which includes basic computational abilities -- is deficient. Therefore, we would like to query grade school teachers about their beliefs and practices concerning math computation in their classrooms. We would also like to determine if a lack of computational ability negatively impacts a student's career in math, and indeed in high school as a whole. If we find that deficient computational abilities are a significant handicap, we intend to publish the information as a useful tool for curriculum specialists and other aducators.

Definitions

Basic operations: Multiplication, division, addition, and subtraction.

Computational skills: The ability to perform the four basic operations of arithmetic on whoe numbers, integers, fractions, decimals, and percents.

Problem-solving: Synthesizing, analyzing, and applying mathematical strategies to real-life situations.

Constructivist learning: A learning theory that advocates the learner relating new knowledge to what is already known, constructing his/her own understanding, and making his/her own meanings.

Bloom's Taxonomy: A hierarchical list developed by ......Bloom, listing six levels of cognitive thinking: 1) Knowledge: The ability to recall facts, concepts or principles. 2) Comprehension: The ability to translate or interpret information. A grasp of meaning, intent, and relationship is demonstrated in oral, written, or non-verbal communication. 3) Application: The ability to apply previously acquired knowledge of information to a new or concrete situation. 4) Analysis: The ability to break material down into its components so that organizational structure may be understood. 5) Synthesis: The ability to analyze the parts and put them together to form a whole. 6) Evaluation: The ability to make judgements based on evidence and determine the value of material based on definite criteria.

Higher-order thinking skills: This phrase frequently refers to levels 4, 5, and 6 of Bloom's Taxonomy.

Prior Research

A nation at risk (1983). Washington, DC: Department of Education This report was commissioned by the then-Secretary of Education, T.H. Bell. It warned of declining academic performance in the United States, and warned that this situation was the reason for a decline in economic productivity. This report is often cited as the catalyst that started the "standards-based" education movement.

Creech, Joseph D. (1996). High school graduation standards: What we expect and what we get. Goals for Education: Educational Benchmarks. The author states that the current trend of raising high school graduation standards has not necessarily resulted in higher achievement. Employers are still complaining that high school graduates do not have the skills needed in the workplace, and that 30% of new college students need remediation in language arts or mathematics or both. He says that core curriculum must be linked to prior learning, and that each grade level needs curriculum frameworks and clear guides and objectives.

Kerka, Sandra (1995). Not just a number: Critical numeracy for adults. Ms. Kerka says that numeracy is the type of math skills needed to function in everyday life. Low levels of numeracy can limit access to jobs, education, and training; and can lead to low productivity on a job. She contends that numeracy is practical, procedural math that is perceived as less important and prestigious as theoretical and analytical mathematics. However, adults with functional numeracy skills can participate fully in civic life.

Murnane, Richard J. and Levy, Frank (1996). Teaching the new basic skills. New York: Free Press. Mr. Murnane and Mr. Levy contend that mastery of basic math skills has a big impact on earnings. Many employment tests that are mentioned in their book measure skills taught no later than junior high, such as manipulation of and conversion among fractions, decimals, and percents; and interpreting line and bar graphs.

Steen, Lynn A. (2997). What employers and educators test: The mathematics that really counts. Northfield, MN: St. Olaf College. Ms. Steen points out the importance of basic math skills in various employability tests and college entrance exams. She asserts that the level of ability tested is usually no higher than the eighth or ninth grade level. She says that there is a huge gulf between employment tests and education tests and the skills of "mathematical power" promoted by MCTM, which includes such skills as communicating, reasoning, and connecting.

SCANS Report for America 2000 (1991). What work requires of schools. Washington, DC: Department of Labor. The report by this commission explains the importance of basic competencies and fundamental skills necessary for new employees in today's work force.

Hypothesis

Deficient math computational skills in grade school adversely affect many aspects of a child's education, including problem-solving ability, performance and advancement in mathematics classes throughout schooling, class rank, graduation rate, and college entrance tests.

Population

An ideal population would be students from high schools across the nation. The lack of available resources, and common testing instruments, however, will force our population to be more localized in the Duluth and Superior area.

Sampling

We intend to examine records of the entire senior class from both Superior Senior High School in Superior, MN; and Denfeld Senior High School in Duluth, MN.

Instrumentation

As part of our information-gathering, we will distribute a questionnaire to a random sample of elementary school teachers, middle school teachers, and high school teachers. We intend to gain insight into the teacher's perception of the level of computational skilll of her/his students; the perceived effect from a lack of computational skills; and the ways in which the teacher deals with students' computational deficiencies. We shall also access data from achievement test scores in Duluth and Superior. We shall pull records from the senior class (1998) of Denfeld High and Superior Senior High, and record math computation scores in grades 5, 8, 10, and 12; math courses taken and completed; final overall GPA and class rank; ACT scores (where available); and the number of students who graduated on time.

The predictor variable is the computation score on achievement tests in 5th grade. The criterion variables are problem-solving scores, class rank, the type of math courses taken in high school, the performance in these classes, and ACT scores (if available). We should be able to obtain a prediction equation that will enable us to use the 5th grade score to predict high school outcomes, as described above. We will be able to compare the equations obtained from two different schools. We will enter scores on a spreadsheet for each student in the senior class of the two high schools. The spreadsheet will look something like this: Subject O1 O2 O3 O4 O5 etc. where

O1 = Gender O2 = Race O3 = Free or Reduced Lunch O4 = Special Education or other special services O5 = Computation Score on 5th Grade Test O6 = Problem-Solving Score on 5th Grade Test O7 = Computation Score on 8th Grade Test O8 = Problem-Solving Score on 8th Grade Test O9 = Computation Score on 10th Grade Test O10 = Problem-Solving Score on 10th Grade Test O11 = Computation Score on 12th Grade Test O12 = Problem-Solving Score on 12th Grade Test O13 = Class Rank O14 = ACT O15 = Graduate or Not O16 = 9th Grade Math Course O17 = 9th Grade Course Grade O18 = 10th Grade Math Course O19 = 10th Grade Course Grade O20 = 11th Grade Math Course O21 = 11th Grade Course Grade O22 = 12th Grade Math Course O23 = 12th Grade Course Grade

Our questionnaire to teachers will be along these lines: 1. What grade level do you teach? (Or, in the case of high school teachers, what math courses do you teach?) 2. How long have you taught?

For the following questions, answer with a 1, 2, 3, 4, or 5. The scores mean as follows: 1 = Strongly agree 2 = Mildly agree 3 = I don't know 4 = Mildly disagree 5 = Strongly disagree

1. It is important that students have multiplication facts memorized. 2. It is unimportant for students to memorize multiplication facts, because they can use a calculator. 3. It is important that students understand the meaning of fractions. 4. It is important that students can compute with fractions without a calculator. 5. It is unimportant that students can do fractional computation without a calculator. 6. It is important that students understand the meaning of decimal numbers. 7. It is important that students can compute with decimals without a calculator. 8. It is unimportant that students can compute with decimals without a calculator. 9. It is important that students understand the meaning of percents. 10. It is important that students can compute with percents without the use of a calculator. 11. It is unimportant that students can compute with percents without a calculator. 12. Problem-solving ability is more important than computation ability. 13. Computational skills of my current students are less than they were a few years ago. 14. Computaitonal skills of my current students are better than they were a few years ago. 15. Problem-solving skills of my current students are less than they were a few years ago. 16. Problem-solving skills of my current students are better than they were a few kyears ago. 17. Deficient computational skills harms problem-solving skills. 18. Deficient problem-solving skills harms computational skills. 19. I spend more time in the classroom on computational skills than I did a few years ago. 20. I spend more time in the classroom on problem-solving skills than I did a few years ago.

Threats to Validity

All of these things pose threats to validity: ability level of students; the socioeconomic make-up of the class; the racial and ethnic make-up of the class; placement in special education classes or other specially funded programs. We believe that we can control for the ability level, and special services. Another threat to validity will be the lack of records of students who have dropped out prior to the end of their senior year. The subjects who are "lost" are likely to have poor scores. Thus, the loss of these subjects can be expected to reduce the correlation between 5th grade scores and subsequent high school achievement.

Data Analysis

By the use of scatter plots, we shall see if a positive correlation exists. We will generate a prediction equation, and compare the predicted results with actual results. Also, we will compare the results and prediction equations of the two different schools.

Here are some revisions to our paper (and expansion):

Research Proposal

The Impact of Math Computation Skills on High School Achievement

Sue Hendrickson Barb Olson Christine Osthus Tim White

Purpose

The general purpose of this research is to determine if a correlation exists between math computation skills and specific academic outcomes. The measurement of academic achievement can be found in such things as achievement test scores, ACT scores, GPA, class rank, and graduation rate. Each of the four members of our research team is a high school teacher. We often see students who cannot do simple mathematical computations without using a calculator, and who do not know their mutiplication facts. It seems to us that this deficit impacts their ability to perform higher level tasks, as well. During informal talks with elementary teachers, we have found nearly each one of them says that they have received a message, either implicitly or explicitly, from curriculum specialists or professors that basic skills and computational abilities should not be stressed, and they have the sense that they are doing the "wrong thing" by asking and/or insisting that students memorize basic mamultiplication facts and become proficient at basic computation. The emphasis, they are told, is to on "higher order thinking skills." However, we think that the ability to do "higher order thinking skills" is impaired if the knowledge base -- which includes basic computational abilities -- is deficient. Therefore, we would like to query grade school teachers about their beliefs and practices concerning math computation in their classrooms. We would also like to determine if a lack of computational ability negatively impacts a student's career in math, and indeed in high school as a whole. If we find that deficient computational abilities are a significant handicap, we intend to publish the information as a useful tool for curriculum specialists and other aducators.

Definitions

Basic operations: Multiplication, division, addition, and subtraction.

Computational skills: The ability to perform the four basic operations of arithmetic on whoe numbers, integers, fractions, decimals, and percents.

Problem-solving: Synthesizing, analyzing, and applying mathematical strategies to real-life situations.

Constructivist learning: A learning theory that advocates the learner relating new knowledge to what is already known, constructing his/her own understanding, and making his/her own meanings.

Bloom's Taxonomy: A hierarchical list developed by ......Bloom, listing six levels of cognitive thinking: 1) Knowledge: The ability to recall facts, concepts or principles. 2) Comprehension: The ability to translate or interpret information. A grasp of meaning, intent, and relationship is demonstrated in oral, written, or non-verbal communication. 3) Application: The ability to apply previously acquired knowledge of information to a new or concrete situation. 4) Analysis: The ability to break material down into its components so that organizational structure may be understood. 5) Synthesis: The ability to analyze the parts and put them together to form a whole. 6) Evaluation: The ability to make judgements based on evidence and determine the value of material based on definite criteria.

Higher-order thinking skills: This phrase frequently refers to levels 4, 5, and 6 of Bloom's Taxonomy.

Prior Research

A nation at risk (1983). Washington, DC: Department of Education This report was commissioned by the then-Secretary of Education, T.H. Bell. It warned of declining academic performance in the United States, and warned that this situation was the reason for a decline in economic productivity. This report is often cited as the catalyst that started the "standards-based" education movement.

Creech, Joseph D. (1996). High school graduation standards: What we expect and what we get. Goals for Education: Educational Benchmarks. The author states that the current trend of raising high school graduation standards has not necessarily resulted in higher achievement. Employers are still complaining that high school graduates do not have the skills needed in the workplace, and that 30% of new college students need remediation in language arts or mathematics or both. He says that core curriculum must be linked to prior learning, and that each grade level needs curriculum frameworks



-- Anonymous, May 24, 1999


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