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Running head: ITEM FORMAT AND QUESTION TYPE ON MATH ACHIEVEMENT 1

The Effect of Item Format, Question Type, Personal Interest, and Gender on Algebra

Achievement on a Computer-Based Assessment

Michael Mazzarella

George Mason University

Fairfax, Virginia

ITEM FORMAT AND QUESTION TYPE ON MATH ACHIEVEMENT 2

Abstract

Previous research shows that item format, question type, interest, and gender have effects

on math achievement, but few studies have focused on these variables together on a computer-

based assessment. The current study will analyze the responses of 225 high school Algebra II

students on a computer-based math assessment with different question types and item formats, as

well as a survey measuring their personal math interest (gender?). The test results will be

analyzed using Classical Test Theory (CTT) and Item Response Theory (IRT) statistics, while

other comparisons will be made using inferential statistics, such as correlation and ANOVA.

Keywords: item format, technology-enhanced, interest, attainment value, perceived task

difficulty, knowledge transfer, information processing.


The Effect of Item Format, Question Type, Personal Interest, and Gender on Algebra

Achievement on a Computer-Based Assessment

Within the last decade, many schools and school districts across the country have begun

administering end-of-the-year tests and other standardized assessments on the computer. Taking

these exams on the computer can impact how students perform on tests, even when the content is

the same as that of a paper-and-pencil test (Scherer & Siddiq, 2015). This change can drastically

impact student achievement, especially for high-stakes assessments. For example, in the state of

Virginia, the Standards of Learning (SOL) Assessment has been well-known by teachers,

students, and parents alike. Passing this assessment in almost all of the core high school subjects

is required for graduation (Virginia Department of Education, 2012). In the 2011-2012 school

year, the state of Virginia changed the format of all of the SOL exams in order to make them

more technology-based. All math SOL assessments now include fill-in-the-blank, drag-and-drop,

and graph plotting questions, instead of only multiple choice questions. In the first year, passing

rates for all math SOL exams significantly dropped. Many who are familiar with the test,

however, wonder whether this drop can be attributed to a change in item format, the introduction

to computer-based testing, or an increase in difficulty of the exam (source?).

Information Processing Theory

The cognitive processes that students undergo while taking assessments can be partially

explained by the information processing theory (IPT). According to Mayer (2012), IPT can be

defined as humans creating mental representations and applying cognitive processes to them.

Martin (2004) distinguished between two interpretations of information processing: literal, which

is the processing of information, and constructivist, which is the construction of knowledge. In

an earlier work, Mayer (1995) introduces the metaphor of a computer to explain IPT: Human

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To strengthen the introduction, briefly summarize information processing theory, cognition, and assessment forms.


minds are like processing systems, which have memory storage and control processes. Figure 1,

found in Appendix A, illustrates the basic model of information processing. The model shows

how sensory, working, and long-term memory work together to select, organize, and integrate

information. In the context of assessments, the goal of creating a good assessment is to properly

test what students know. A test will be more reliable when it is based on what is known about

human information processing (Mayer, 2011).

Several studies have related the IPT to assessments and mathematics. Raghubar, Barnes,

and Hecht (2010) reviewed the prior research relating working memory and mathematics. They

found that working memory is involved in arithmetic, but the amount of working memory used

during math processing may vary depending on age or strategy use. Furthermore, the way that

the task is presented to the individual is also related to working memory (Raghubar, Barnes, &

Hecht, 2010). This conclusion holds true for computer-based assessments, and it is also worthy

to note that working memory and math processing is also impacted by the task difficulty and

question type (Goldhammer, Naumann, Stelter, Toth, & Rolke, 2014). These findings are

relevant to the current study because the study will analyze computer-based math problems of

varying types and formats.

Assessments: Item Format

In the present study, item format refers to the ways in which students can respond to the

prompts. Some item formats include multiple choice, true or false, selecting multiple correct

answers, and fill-in-the-blank. Many research studies have been conducted regarding the

relationship between item format and achievement. Ozuru, Best, Bell, Witherspoon, and

McNamara (2010) measured achievement on a reading assessment. Items were separated into

multiple choice and open ended questions. Overall, students scored the multiple choice questions

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Expand on this idea.

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Include a figure you designed which incorporates information processing theory within the context of assessments.

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correctly more often than the open ended questions. The average score for the multiple choice

section without and with available text was 68% and 79%, respectively, while the average score

for the open ended section without and with available text was 48% and 60%, respectively

(Ozuru, Best, Bell, Witherspoon, & McNamara, 2010). The large gap between the scores of the

multiple choice and open ended questions suggests that students think about each type of

question differently, which affects achievement on assessments.

Not only can different item formats produce different achievement scores, but they can

result in different strategies used. Katz, Bennett, and Berger (2000) had students record the

strategies used for each item on an assessment with multiple item formats. Traditional strategies

included using formulas and solving algebraic equations, while nontraditional strategies included

estimation and guess-and-check. Results showed that while item format for some questions

changed their levels of difficulty, the strategies used for different questions did not affect the

achievement (Katz, Bennett, & Berger, 2000).

Item format is particularly important for computer-based exams. Jodoin (2003) studied

responses on an engineering exam that used multiple choice and “innovative” items, such as

drag-and-drop and selecting multiple answers. Results showed that examinees answered multiple

choice items with more accuracy, even when items of different formats were asking about the

same subject (Jodoin, 2003).

It is important to note that measures with different item formats can threaten validity in

several ways. For example, in one of the first articles looking at computer-based assessments

with different formats, Martinez and Bennett (1992) analyzed several types of math skills (e.g.

algebraic reasoning, computer science) that were tested using different item formats.

Psychometric analysis determined that there was little discrepancy between computerized raters

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Expand to transition to this section on validity.


and human raters, but in some cases, scores differed by up to 1.2 points on a 16-point scale

(Martinez & Bennett, 1992). Because of this small difference, computerized grading gained more

trust; nevertheless, even a small difference such as this highlights the importance of calculating

validity and reliability of computer-based assessments.

In a similar article, Pomplun and Omar (1997) outlined four different threats to the

validity of an assessment: lack of familiarity of the item format, omitting alternatives,

dependency among alternatives, and guessing. In their study, two specific types of item formats

used were “multiple mark” (a multiple choice question with more than one correct answer) and a

“multiple true-false question” (similar to multiple mark, but only with T/F as possible choices).

The results of this article stated that omitting answers or not following directions did not

seriously threaten validity, but students tended to leave choices blank instead of guessing

(Pomplun & Omar, 1997).

Assessments: Question Type

Assessing mathematics knowledge is a broad idea that can be categorized into multiple

aspects. Thus, it is important to study differences in the ways that questions are asked on math

assessments. In particular, two such types of math problems are computational (i.e.

straightforward) problems and word problems. Fuchs et al. (2008) studied whether or not

different aspects of cognition (e.g. language, concept formation, and working memory) were

used in different types of problems. Results showed that correlations between computational and

problem-solving skill was only moderate. Cognitively, processing speed was highly correlated

with computational skill, but not with problem-solving skill. Working memory, on the other

hand, was more highly correlated with problem-solving skill than with computational skill

(Fuchs et al., 2008). The same study also compared demographics to achievement on different


question types. For example, poverty and race had little effect on difficulty with computational

problems, but those who had difficulty with solving word problems were poorer and more likely

to be African-American (Fuchs et al., 2008). Therefore, it is certainly worthwhile to study

question type as it relates to math achievement.

When studying question type, one must take into consideration the construct of

knowledge transfer. Knowledge transfer can be defined as the ability to relay knowledge that

students learned one way to a task presented in a different way (Belenky & Nokes-Malach,

2013). In the present study, knowledge transfer is relevant regarding question type because

students may have learned a math procedure in a straightforward manner, but may not be able to

apply that knowledge to a word problem, for example. Knowledge transfer also relates to

assessments from an information processing viewpoint. Working memory is necessary for

students to be able to transfer, organize, and apply their knowledge to a given task (Belenky &

Nokes-Malach, 2013). Day and Goldstone (2012) state that despite cognitive load or item

difficulty, student transfer is high when students are shown several examples of the problem.

They go on to claim the following: “Contextual similarity between the situations themselves

seems to play a much larger role in determining whether transfer will actually occur” (Day &

Goldstone, 2012, p. 155).

Kramarski, Weiss, and Sharon (2013) experimented with an intervention that attempted

to increase students’ transfer abilities among math tasks by increasing self-regulation. The

researchers gave students a survey measuring three aspects of self-regulation (planning,

monitoring, and evaluation), procedural knowledge algebra tasks, and verbal algebra problem

solving tasks, which they classified as “long-term transfer to novel tasks.” The results showed

that while there was no significant difference between the two learning approaches for the


procedural knowledge tasks, there were significant differences between the two learning

approaches for the problem-solving tasks, including all three specific types of mathematical

categories (algebraic, number sense, and visualization; Kramarski, Weiss, & Sharon, 2013). In

terms of self-regulation, those who were part of the intervention group tended to be higher in

self-regulation, which led to high scores on mathematical tasks that were classified as “far

transfer” tasks (number sense and visualization; Kramarski et al., 2013). Overall, knowledge

transfer is another construct to consider in all aspects of assessments, especially question type

and item format.

Computer-Based Assessment

As mentioned, many standardized tests are now computer-based, which prompts research

on the effects of technology on assessments, especially those in mathematics. In addition to the

studies mentioned previous regarding item format and question type, other studies focus on the

effects of computer-based assessments. Burns, Klingbeil, and Ysseldyke (2010) looked at the

effects of a technology-enhanced formative evaluation (TEFE) system on elementary school

math scores in four states. Results shows that schools that had been using the TEFE system for

more than five years reported higher math scores than schools that had been using it for between

one and four years; schools who had been using it for between one and four years scores higher

than schools who did not have a TEFE system (Burns et al., 2010).

Threlfall, Pool, Homer, and Swinnerton (2007) created a study in England that compared

student achievement on math assessments on paper-and-pencil to student achievement on

mathematics assessments on a computer using the same exact questions. Results showed that out

of seven mathematical categories, students who took the computerized version of the exam

scored higher on five of them. The authors attribute this difference in scores to the interactive


tools that students could use on the computer (i.e. moving items across the screen; Threlfall et

al., 2007). A similar study compared the results of a paper-and-pencil test to those of a computer-

based test in an American elementary school classroom. The researchers found that some

computer-based measures tended to be significantly less reliable than their paper-and-pencil

counterparts. Furthermore, there were inconsistencies between the multiple computer-based

measures (Shapiro & Gebhardt, 2012). This suggests that changing an assessment from paper-

and-pencil to computer-based requires analysis to ensure that the validity is still strong, even if

the same paper-and-pencil test was found to be valid and reliable.

While there is much research about computer-based instruction, less research exists about

the effects of computer-based delivery of an assessment on student achievement. The current

study hopes to extend this research and understand whether or not technology is an effective tool

in math assessment delivery.

Interest

While knowledge transfer and information processing relate to the cognitive processes

that students undergo while taking assessments, other psychological constructs also influence

students’ learning processes and achievement. Personal interest in a certain subject is one such

factor in predicting achievement. Dewey (1913) defined interest as an object, subject, or idea that

becomes an accompanying part of one’s identity. Mitchell (1993) specifies educational interest

as interest directly tied to the content of instruction. The present study will use the same

definition as that of Mitchell (1993).

Students’ interest may also differ based on the different types of problems. Renninger,

Ewen, and Lasher (2002) studied three cases of students with varying levels of math interest and

analyzed how that interest related to math word problems. The researchers found that even when

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Revise for clarity.

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Save this until the end of the literature review.


word problems are personalized to students’ math abilities, high interest resulted in higher

achievement. Furthermore, higher interest can also result in students rereading problems to

understand their contexts or checking their answers to make sure that they makes sense in the

contexts of the problems (Renninger, Ewen, & Lasher, 2002).

Trautwein, Ludtke, Marsh, Koller, and Baumert (2006) measured interest in ninth grade

students on different mathematics tracks. The researchers found that interest in math is

significantly higher in students in the upper track, but there was little difference in interest for

students in the middle or lower tracks. Interest was also found to be significantly correlated to

both individual achievement on standardized mathematics tests and the overall school

achievement on the same standardized tests (Trautwein, Ludtke, Marsh, Koller, & Baumert,

2006). The same researchers also found marginally significant results stating that there were

reciprocal effects on math interest and self-concept; in other words, rather than one construct

impacting the other, both interest and self-concept impact each other. These results were also

found to be generalizable across gender (Marsh, Trautwein, Ludtke, Koller, and Baumert, 2005).

Other studies have also found personal interest to be related to other psychological constructs.

Ozyurek (2005) found statistically significant correlations between interest in a math class and

self-efficacy, subject preference, previous math performance, and class expectations. These

results were also consistent for undergraduate students who were mathematics majors and not

mathematics majors (Ozyurek, 2005). Therefore, may factors contribute to one’s personal

interest, including math achievement, which is a variable to be used in the current study.

Gender

Gender differences are also important to analyze when it comes to math assessments and

motivation. Much research has been done on how males and females perform on math tests,


particularly standardized assessments. Liu and Wilson (2009) state that on many large-scale

math assessments, such as the SAT exam, males typically outperform females. However, their

research of the Programme of International Student Assessment (PISA) data in 2000 and 2003

showed that there was no strong correlation between gender and achievement on certain question

types (Liu & Wilson, 2009). Hoffman and Sparatiu (2008) also studied math problem solving

using undergraduate students. They found no significant differences between males and females

in terms of problem solving accuracy and efficiency (Hoffman & Sparatiu, 2008).

Other studies claim that there are significant differences in math achievement between

males and females. A study by Keller (2012) looks at the relationship between gender and

achievement on the SAT and ACT exams, which are nationally used college entrance exams.

Between 1997 and 2010, although the test scores of both males and females slightly increased

over time, males consistently scored higher than females (Keller, 2012). Kaufman, Kaufman,

Liu, and Johnson (2009) found that males scored significantly higher than females in math

achievement on a standardized test, despite the fact that there was no significant difference

between genders regarding fluid or crystallized intelligence. Technology can play a role in both

achievement and motivation between genders. Barkatsas, Kasimatis, and Gialamas (2009) used

the Mathematics and Technology Attitudes Scale (MTAS) to track motivation and attitudes

toward performing math using technology. The study found that students who are comfortable

with technology perform better on classwork and other math assignments. Furthermore, the

results also distinguished between genders. Males were more likely to be on either end of the

motivation and achievement spectrum than females. All students, however, were open to using

technology, and the discussion concluded that technology is a positive mathematical tool

(Barkatsas, Kasimatis, & Gialamas, 2009). Research has even shown that there are differences


in the strategies that males and females use in different item formats. Katz et al. (2000) examined

the different strategies used for multiple choice and constructed response math items. In this

study, constructed response questions were identical to the multiple choice questions with the

only difference being that there were no choices. Results showed that while item format changed

the difficulty of some questions, the strategies used for different questions did not affect the

achievement. In terms of gender, females tended to use more traditional strategies and scored

better on multiple choice items than constructed response items. Males, on the other hand, used

more nontraditional strategies, but scored about the same on both item formats (Katz et al.,

2000).

Gaps in the Literature

Despite previous research on these topics, there are several gaps in the literature. First,

although Renninger, Ewen, and Lasher (2002) claim that math interest can impact achievement

on different question types, their study was done using a paper-and-pencil assessment. For that

reason, it is worthwhile to study whether similar results will occur with a computer-based

assessment. Second, while there is much research on item format and question type individually

as they relate to achievement on a computer-based test, there is little research comparing the

effects of the interactions between item format and question type on achievement on a computer-

based test. Finally, there is minimal research comparing the relationships among item format,

question type, personal mathematics interest, and gender. As a result, this study will address

several unanswered questions in the literature and attempt to fill the aforementioned gaps.

Research Questions

The following research questions hope to address the gaps in the literature regarding

computer-based math assessments, math interest, and gender:

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Check for word redundancy.


1. To what extent do item format (multiple choice or technology-enhanced), question type

(straightforward or word problem), and personal math interest impact algebra

achievement on a computer-based assessment?

2. Are there differences in these effects based on gender?

These research questions will address issues regarding information processing and

knowledge transfer because as students complete a math assessment with different item formats

and question types, they may be required to apply different cognitive processes for each type of

question. If significant differences are found, it may suggest that some question types require

students to use working memory in different ways.

The author hypothesizes that both item format and question type will have an effect on

math achievement, but item format will have a more significant impact. Furthermore, because

the test is computer-based, the researcher hypothesizes that males will have a higher

achievement. This is based on the previous research by Barkatsas, Kasimatis, and Gialamas

(2009). Finally, it is hypothesized that there will be no interaction effect between item format

and gender or between question type and gender.

Method

Participants

The purpose of this study is to examine the relationships between item format, question

type, interest, and gender on math achievement on a computer-based assessment. The

participants of this study will be 225 high school students (n = 225) currently enrolled in an on-

level Algebra II course in a large suburban school district during the 2014-2015 school year.

These students will be selected based on availability and convenience of the researcher. Students

who participate in the study will be enrolled in the high school at which the researcher currently

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You may want to move this sentence before participants. Also, include a sentence describing the research design.

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Good job on the first section.


teaches. The 225 students will come from a total of nine on-level Algebra II classes, four of

which are taught by the researcher and five of which are taught by other teachers in the same

school. As an incentive, the researcher will randomly select four students who participated in the

study to receive a $25 Target gift card.

The sample will consist of 113 females (n = 113) and 112 males (n = 112). The ages of

the students at the time of the study will range from fifteen years to nineteen years. The mean

age of the students will be 16.34, and the standard deviation will be 0.76. The ethnicity of the

students is expected to be similar to that of the school demographic: About 33% of students will

be Hispanic, 25% of students will be Asian, 24% of students will be white (not of Hispanic

origin), 18% of students will be African-American (not of Hispanic origin), and 2% of students

will be listed as “other.” Approximately twenty students will be categorized as limited English

proficiency. About 55% of students will receive free or reduced lunch on a daily basis.

Approximately 5% of students will be categorized as special education.

Procedures

All students participating in the study will first take a survey in which they self-report

their levels of personal interest in mathematics. The survey consists of four Likert-scale items

and will take approximately one minute to complete. In addition to the Likert-scale items,

students will also record their gender, grade level, and age on the survey. The items of this

survey can be found at the end of this document in Appendix B.

One class period after taking the self-report survey, students will take a measure of math

achievement. Students will have one full class period (90 minutes) to complete this test. Classes

will be randomly assigned to take one of four versions of the math measure: Test A, Test B, Test

C, or Test D. Test A and Test B have the same prompts in the same order. On Test A, the odd

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This section is well done.


numbered questions will be multiple choice questions, and the even numbered questions will be

technology-enhanced questions (either fill-in-the-blank or selecting multiple correct answers).

On Test B, the even numbered questions will be multiple choice questions, and the odd

numbered questions will be technology-enhanced questions. Test questions are staggered this

way so that data will be collected for every prompt as both a multiple choice and technology-

enhanced format. On both Test A and Test B, there will be twenty straightforward math

problems (ten multiple choice and ten technology-enhanced) and ten word problem or real-world

application problems (five multiple choice and five technology-enhanced). Creating the

assessments in this way yields four categories: straightforward multiple choice, straightforward

technology-enhanced, word problem multiple choice, and word problem technology-enhanced.

Both tests have the same amount of questions in each category. These tests were created in this

way because the data collected will provide a comparison of the same prompts with different

item formats, as well as a comparison between straightforward questions and word problems.

The items in Test A and Test B can be found at the end of this document in Appendix C.

Test C will have the same exact questions and formats as Test A, but the questions will

be in reverse order. Test D will have the same exact questions and formats as Test B, but the

questions will be in reverse order. Test C and Test D were created to account for test fatigue.

Tyrrell and colleagues (1995) support that visual and mental fatigue can occur as students take

assessments, especially when the assessments are taken on the computer. As students work

through throughout the thirty-question math measure, some may become less motivated or

energized toward the end of the test. Thus, if this occurs, it is important to test whether or not this

occurs in the measure before drawing conclusions about specific test questions or overall

achievement.

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This is a good explanation.

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Include a transition to here to improve readability.


The results of the tests will be available online to the teacher once the test is complete.

Results will include the number of correct answers and the responses to each multiple choice and

technology-enhanced question.

Measures

Math achievement (Mazzarella, 2015). Students will be given a set of thirty math items

on the computer through the program Horizon, which is a commonly used computer-based

assessment program in the county in which the present study will be being conducted. This

program allows teachers to create items of different formats, and teachers will receive the

students’ results for each question when the assessment is complete.

The curriculum used to create these math items aligns with the standards set forth by the

county in which this study will be conducted. These standards also match the standards used to

create the end-of-year state assessment that students in Algebra II are required to take. Some

examples of standards included in the math measure are solving radical, absolute value, and

rational equations, finding the domain and range of various functions, simplifying rational and

radical expressions, identifying properties of a normal distribution, and recognizing and solving

permutations and combinations. According to the state in which the study is taking place, there

are four strands (i.e. standards) that categorize Algebra II test questions: Expressions and

Operations, Equations and Inequalities, Functions, and Statistics (Virginia Department of

Education, 2012). It is also worthwhile to note that students in the county are required to

complete and pass Algebra II in order to graduate. This is important to keep in mind because it

implies that students with a variety of skill levels will be measured in the present study, rather

than only students who choose to enroll in an Algebra II course without it being required.

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In the future, , you could have several math teachers review the items as well as examples from each strand.


Personal Math Interest (Mitchell, 1993). The self-report measure will consist of items

measuring personal interest. On this survey, there will be four items measuring personal math

interest. The internal consistency coefficient of this measure was found to be .92, which suggests

that the measure is very reliable (Mitchell, 1993). The survey consists of four Likert-scale items

measuring students’ personal interest in mathematics. One example of an item asks students to

evaluate this statement: “Compared to other subjects, mathematics is exciting to me.” Students

will respond to each item by circling “strongly agree,” “agree,” “slightly agree,” “slightly

disagree,” “disagree,” or “strongly disagree.”

Data Analysis

All data analysis will be conducted using the computer programs SPSS, jMetrik, or

Mplus. The first research question asks: To what extent do item format (multiple choice or

technology-enhanced) and question type (straightforward or word problem) impact students’

math interest and algebra achievement on a computer-based assessment? Several types of

analysis will be used to address this question. First, descriptive statistics will be calculated for

each of the four versions of the mathematics measure. These descriptive statistics, which include

mean and standard deviation, will compare students’ overall achievement on each test. Second,

two separate 2x2 ANOVA tests will be run. The first test will use item format (multiple choice

and technology-enhanced) and question type (straightforward and real-world application) as

independent variables, and math achievement as the dependent variable. The second test will use

the specific technology-enhanced format (fill-in-the-blank and multiple-select) and question type

(straightforward and real-world application) as independent variables, and math achievement as

the dependent variable. For both tests, it is important to consider both the main effects and the

interaction effects.

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Good.

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Good.


The second research question asks: Are there differences in these effects based on

gender? To address this question, descriptive statistics, such as mean and standard deviation, will

be calculated. These statistics will compare overall math achievement, achievement on each

question type, achievement on each item format, and interest based on gender. Additionally,

differential item functioning (DIF) will be run on the math items with respect to gender. DIF

analysis is used to determine whether a question is more likely to be answered correctly by one

of two groups (Dimitrov, 2014). In this case, the groups will be classified as male or female. This

analysis will primarily be used to determine whether a question is strongly biased toward one

group. If one group answers a question significantly more accurately than the other, the item may

be recommended to be altered or removed from the test.

In addition to the data analysis that will be run to answer the research questions, there

will also be item analysis run for each question on the math measure to test the psychometric

features of the tests. First, a confirmatory factor analysis will be run to determine if the items in

the math measure align with the four strands that the state outlined. If these strands are distinct,

then further analysis may be done to determine if significant differences exist among the

different strands. Next, classical test theory (CTT) analysis will be run for the multiple choice

questions. Such descriptors in CTT analysis include reliability, which is defined as the ratio of

true score variance to observed score variance; item difficulty, which is defined as the proportion

of examinees who answered the item correctly; and item discrimination, which is defined as the

difference between the proportion of examinees in the upper group who answered the item

correctly and the proportion of examinees in the lower group who answered the item correctly

(Osterlind, 2010). These CTT analyses will be applied to both individual items and the overall

assessment.

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You may want to run an EFA first. Then re administer to a different group to conduct the CFA.

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Good.


Another method of analysis that will be used is Rasch model analysis. Rasch model

analysis can be used to indicate several characteristics about the assessment scores. One such

characteristic is the fit of individual items. Rasch analysis using the jMetrik program will

identify misfit items, which could be an indication of a poor item in general (item fit) or an

anomaly of examinees’ abilities and the items on which they scored correctly or incorrectly

(person fit). Rasch model analysis using jMetrik will also identify the estimated ability level (θ)

of a student given the number of items that they answered correctly (Dimitrov, 2014).

Limitations and Future Research

There are several limitations in regard to this study. One such limitation is the validity of

a self-report survey. It is important to take into account the validity of each measure when

collecting data. In particular, the measure of interest should be carefully examined. Tracey

(2012) claims that single interest scales contain two types of error: systematic error and general

factor variance. Furthermore, these scales do not take into account bias that can influence

students’ interest. For example, interest is often correlated with students’ math scores, which can

cause a problem with validity (Tracey, 2012). For that reason, it is important to analyze the

results of the interest survey to determine whether any of these problems can compromise the

research questions.

Another limitation of this study is the lack of a variable of prior achievement or grade in

high school mathematics. Literature shows that prior achievement does, in fact, impact

motivation and present achievement (Midgley et al., 1989; Trautwein et al., 2006). However, this

variable will not be included in the present study because Algebra I and Geometry are much less

complex courses than Algebra II, and student achievement may vary drastically across these

courses. Furthermore, classroom test grades were not included because some material that is

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Expand here.

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Great job here!


taught throughout the year-long Algebra II course is not included in the state assessment, and the

aim of this study is to focus on the implications for the end-of-year exam. Nevertheless, this

study could be improved if the researchers determine a practical and relevant measure of

previous grade to include.

Third, the present study is specific in its content and demographics and, therefore, cannot

be generalized across all subjects or grade levels. In addition to a lack of generalizability to other

content areas, this study may be applicable to only on-level Algebra II. As mentioned, Algebra II

is more complex than Algebra I, and thus requires more skills to achieve mastery. Similarly,

achievement in Geometry requires a different mathematical skill set. Furthermore, this study was

conducted with participants in high school only, and the results cannot be generalized to

elementary or middle school students. Further research is needed to determine whether the

results of this study will be similar across these different demographics and subjects.

Next, the participant selection of this study is that of a convenient sample. The students

of this study attend the school at which the researcher teaches. Some of the participants are even

the researcher’s students. This can create bias and a potential conflict of interest in the research

because of a personal connection to the researcher. To prevent this, the study should be

replicated using students outside of the researcher’s school.

A final limitation of this study may come from the math measure. Although the measure

was created to replicate the state end-of-year exam, the items in this measure will have yet to be

fully analyzed before their initial use in this study. In order to create the most valid results, it is

recommended that the math tests be taken by a different group of students prior to this study, so

that adjustments can be made to invalid or unfair items. If this is not possible, then this study can

shiller, 05/06/15,

Did this issue come up with IRB? How did you address this concern in your proposal?


act as a pilot study, and an identical study can be run at a later time with the adjusted math

measures.

Further research could add to the findings of this study in several ways. First, including

additional motivational constructs would give an added element to the study. For example,

measuring students’ task value, self-efficacy, and outcome expectations could provide a wealth

of additional information about students’ motivation as it relates to achievement on computer-

based assessments. Second, although the researcher could not determine an appropriate form of

prior achievement or previous grade to include in this study, further research could use several

different types of prior achievement or previous grade (e.g. previous state test scores) to

determine which are more related to achievement and motivation. Third, future research can also

replicate this study in other subjects or demographics. For instance, it would be worthwhile to

determine if the same results would occur with geometry students or in a different school setting

(e.g. rural or urban).

Educational Implications

The present study contains many practical implications for educational psychology and

secondary mathematics education. Overall, this study may bring to light certain aspects of

computer-based testing that have not previously been analyzed. With more counties and states

changing their standardized testing systems from paper-and-pencil to technology-enhanced, it is

important to investigate whether or not these assessments are testing students accurately and

fairly. The present study will not only determine the differences between item format and

question type, but it will also determine how personal interest will impact achievement.

Additionally, the present study will also determine whether gender is a factor on achievement on

different item formats or question types. It is the hope of the researcher that testing companies

shiller, 05/06/15,

Future research is often listed after implications.


will take into consideration the findings of this study and make the necessary adjustments to the

tests so that all students have a fair opportunity to succeed. Furthermore, the data of this study

can also provide valuable information to teaching on how to best prepare their students for these

tests.

Whether it is tailoring instruction to certain types of questions or incorporating

motivational strategies to increase interest, the information gathered from this study can help

teachers of math provide the best personalized education for all students. Overall, this study

hopes to sheds light on the relationships among interest, item format, question type, gender, and

math achievement. Through quantitative analysis, significant results may indicate strong

correlations and possible directions for future research. Despite some limitations in the study, the

results will provide insight into some of the complex relationships that exist within educational

psychology.


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Appendix A: Information Processing Theory Model

Figure 1. Basic model of information processing. Retrieved from Mayer (2012).


Appendix B: Demographics and Interest Measure

Student ID ____________________ DO NOT PUT YOUR NAME ON THIS SURVEY

1. Circle your gender: Male Female

2. Circle your grade: 9 10 11 12

3. Write your age: ___________________

For items 4 – 7, circle the appropriate response based on the statement.

4. Math is enjoyable to me.

Strongly Disagree Disagree Slightly Disagree Slightly Agree Agree Strongly Agree

5. I have always enjoyed studying math in school.


6. Compared to other subjects, I feel relaxed studying math.


7. Compared to other subjects, math is exciting to me.



Appendix C: Math Measure

Test A

Question 1 :What is the solution set for this equation?

A:

B:

C:

D:

Question 2 :Type your answer into the box. You must give your answer in integer form.

The following sequence is given in recursive form.

What is the value of the fourth term of this sequence?

Question 3 :Which of the following situations involves a permutation?

A: Determining how many different groups of 3 employees can be chosen from 9 employees.

B: Determining how many different ways 7 runners can be assigned lanes on a track for a race.

C: Determining how many different ways to choose 10 students to attend a field trip from a group of 25 students.


D: Determining how many different ways 4 cashiers can be chosen to work from a group of 7 cashiers.

Question 4 :Click on a box to choose each y-coordinate you want to select. You must select all correct answers.

What are the y-coordinates for the solution to this system of equations?

A: y = -9

B: y = -3

C: y = -2

D: y = 1

E: y = 2

F: y = 6

G: y = 8

H: y = 9

Question 5 :The number of combinations of 7 objects taken 2 at a time is

A: 3B: 7


C: 21D: 42

Question 6 :Type your answer into the box. You must enter your answer in integer form.

The shoe sizes of a large population are normally distributed with a mean of 8.9 inches and a standard deviation of 0.705 inches. What percentage of the population has a shoe size greater than 9.8 inches? ROUND TO THE NEAREST INTEGER.

Question 7 :

Factor:

A: (2x+3) (3x-7)

B: (2x-3) (3x+7)

C: (3x+2) (2x-7)

D: (3x-2) (2x+7)

Question 8 :Select a box for each correct part of the expression. You must select each correct expression.

Select each part of the simplified expression .

A:

B:

C:


D:

E:

F:

Question 9 :The area of a triangle varies jointly with the product of the base and the height. A triangle has a base of 12 feet, a height of 3 feet, and an area of 18 square feet. What is the base of a triangle with a height of 4 feet and an area of 36 square feet?

A: 0.5 feet

B: 9 feet

C: 12 feet

D: 18 feet

Question 10 :Type the answer into the box.The number of permutations of 9 objects taken 3 times is

Question 11 :

Which is a solution of ?

A: x = -5

B:x

= C: x = -


1

D: x = 1

Question 12 :Click on the box to select the value. You must select each correct value.

Two baseballs were thrown on a field as the same time. One ball follows the

path of the function , and the other ball follows the path of

the function , where x is the time in seconds, and f(x) and g(x) are the heights in feet. At what two times, in seconds, are the two balls the same height?

A: 0.7 seconds

B: 1.0 seconds

C: 4.0 seconds

D: 5.14 seconds

E: 5.45 seconds

F: 7.13 seconds

Question 13 :What is the sum of this infinite series?

72 - 36 + 18 - 9 + ...

A: -144

B: -48C: 48


D: 144


Let and , what is ?

Question 15 :A new rollercoaster at an amusement park follows the path of the

function , where x is the time, in seconds, after the rollercoaster begins, and f(x) is the height of the rollercoaster, in yards. Between which two times, in seconds, is the rollercoaster increasing in height?

A:

B:

C:

D:

Question 16 :Select each expression that is equivalent. You must select all correct expressions.

Identify each expression that is equivalent to 1.

A:

B:

C:


D:

E:

F:

G:

H:

Question 17 :

Which of the following describes the end behavior of as x approaches infinity?

A: y approaches negative infinity

B: y approaches -2

C: y approaches 3

D: y approaches infinity


The heights of Galapagos penguins are normally distributed with a mean of 49 cm and a standard deviation of 1.82 cm. If a scientist measures the heights of 300 penguins, how many penguins are expected to be between 48.4 cm and 50.1 cm tall? ROUND YOUR ANSWER TO THE NEAREST INTEGER.

Question 19 :Which is the equation of an asymptote of the graph of the following equation?


A: x = -3

B: y = 3

C: x = 6

D: y = 6

Question 20 :Click on the box to select an interval. You must select each correct interval.

Indicate each intervals where the graph is only increasing.

A:

B:

C:

D:

E:

F:

G:

H:

Question 21 :A math class consists of 10 girls and 8 boys. The teacher wants to


choose 2 girls and 2 boys to go on a trip. How many different groups could the teacher choose?

A: 73

B: 146

C: 1260

D: 5040


If y varies directly with the square root of x, what is the constant of variation if y = 36 when x = 9?

Question 23 :

What are the zeros of the function ?

A: x = -16 and x = 0

B: x = -16, x = -8, and x = 2

C: x = -8 and x = 2

D: x = -2 and x = 8

Question 24 :Click on the box to select the correct equation. You must select each correct equation.

A baseball was thrown by a player, and hit the ground after exactly 5 seconds. If x represents the time in seconds and y represents the height of the ball, which of the following functions could represent the path of the


ball?

A:

B:

C:

D:

E:

F:

Question 25 :A normally distributed set of numbers has a mean of 75 and a standard deviation of 7.97. What percentage of values lies between 70 and 85?

A: 11%B: 37%C: 63%D: 89%

Question 26 :Click on the correct box to select each value. You must select each correct value.

The domain of the function is all real numbers except -

A: -7B: -4C: -3D: 0E: 3


F: 4G: 7

Question 27 :In a school, 12 students are running for 4 class officers- a president, a vice president, a secretary, and a treasurer. If each position is to be held by one person and no person can hold more than one position, in how many ways can those positions be filled?

A: 48

B: 495

C: 11880

D: 20736

Question 28 :Click on each box to select each function. You must select each correct function.

Which of the following functions are in the same family as the

function ?

A:

B:

C:

D:

E:

F:


Question 29 :The steps to simplify an expression are shown below:

Step 1: 4(x+3) - 3x + 1Step 2: 4x + 12 - 3x + 1Step 3: 4x - 3x + 12 + 1Step 4: x + 13

Which of the following properties justifies getting from Step 2 to Step 3?

A: Associative Property

B: Commutative Property

C: Distributive Property

D: Transitive Property

Question 30 :Type your answer into the box. ROUND YOUR ANSWER TO THE NEAREST TENTH.

A baseball player throws a ball from one end of the field to the other. A fan measures the path of the ball and determines that it follows the

function , where x is the time in seconds and f(x) is the height in feet. What is the maximum height of the ball, in feet? ROUND YOUR ANSWER TO THE NEAREST TENTH.

Test B


Question 1 :Type your answer into the box. Enter your answer as a whole number.

What is the solution set for this equation?

Question 2 :The following sequence is given in recursive form.

What is the value of the fourth term of this sequence?

A: 29B: 33C: 61

D: 125

Question 3 :Click on the box to choose the situation. You must select all correct situations.

Which of the following situations involve a permutation?

A: Determining how many different ways to choose 3 employees from a group of 9 employees.

B: Determining how many different ways 7 runners can be assigned lanes on a track for a race.

C: Determining how many different seating charts can be made placing 6 people around a table.

D: Determining how many 5-letter passwords can be made using the


word "graph."

E: Determining how many different groups of 10 students can be chosen to go on a field trip from a group of 25 students.

F: Determining how many different ways 4 cashiers can be chosen to work from a group of 6 cashiers.

Question 4 :What are the y-coordinates for the solutions to this system of equations?

A: y = 1 and y = 9

B: y = -3 and y = -9

C: y = -2 and y = 6

D: y = 2 and y = 8

Question 5 :Type the answer into the box.

The number of combinations of 7 objects taken 2 at a time is

Question 6 :The shoe sizes of a large population are normally distributed with a mean of 8.9 inches and a standard deviation of 0.705 inches. What percentage of the population has a shoe size greater than 9.8 inches? Round to the nearest integer.

A: 5%B: 10%C: 20%


D: 34%

Question 7 :Click on a box for each factor you want to select. You must select all correct factors.

Select all of the factors of:

A: (2x+3)

B: (2x-3)

C: (3x+2)

D: (3x-2)

E: (2x+7)

F: (2x-7)

G: (3x+7)

H: (3x-7)

Question 8 :

Which of the following expressions is equivalent to ?

A:

B:

C:


D:


The area of a triangle varies jointly with the product of the base and the height. A triangle has a base of 12 feet, a height of 3 feet, and an area of 18 square feet. What is the base of a triangle with a height, in feet, of 4 feet and an area of 36 square feet?

Question 10 :The number of permutations of 9 objects taken 3 times is

A: 27B: 84

C: 504

D: 729

Question 11 :Click on each solution to the equation. You must select each correct solution.

Select all the solutions of .

A: x = -5

B:x

=

C: x = -1

D: x = 1


E:x

=

F: x = 5

Question 12 :Two baseballs were thrown on a field as the same time. One ball

follows the path of the function , and the other ball

follows the path of the function , where x is the time in seconds, and f(x) and g(x) are the heights in feet. At what two times, in seconds, are the two balls the same height?

A: 0.70 seconds and 5.45 seconds

B: 7.13 seconds and 5.14 seconds

C: 0.70 seconds and 7.13 seconds

D: 5.14 seconds and 5.45 seconds

Question 13 :Type your answer into the box.

What is the sum of this infinite series?

72 - 36 + 18 - 9 + ...

Question 14 :

Let and . What is ?

A: -29B: 35C: 75


D: 152

Question 15 :Click on the box to select the interval. You must select each correct interval.

A new rollercoaster at an amusement park follows the path of the

function , where x is the time, in seconds, after the rollercoaster begins, and f(x) is the height of the rollercoaster, in yards. Between which two times, in seconds, is the rollercoaster increasing in height?

A:

B:

C:

D:

E:

F:

Question 16 :Which expression is equivalent to 1?

A:

B:

C:

D:


Question 17 :Type your answer into the box. You must give your answer in integer form.

What value does y approach in the function as x approaches infinity?

Question 18 :The heights of Galapagos penguins are normally distributed with a mean of 49 cm and a standard deviation of 1.82 cm. If a scientist measures the heights of 300 penguins, how many penguins are expected to be between 48.4 cm and 50.1 cm tall? Round your answer to the nearest integer.

A: 84

B: 107

C: 168

D: 204

Question 19 :Click on each box to choose each asymptote. You must select all correct asymptotes.

Which are the equations of the asymptotes of the graph of the following function?

A: x = -3

B: y = -3

C: x = 3


D: y = 3

E: x = 6

F: y = 6

Question 20 :

Throughout which of the following intervals is only increasing?

A:

B:

C:

D:


A math class consists of 10 girls and 8 boys. The teacher wants to choose 2 girls and 2 boys to go on a trip. How many different groups could the teacher choose?

Question 22 :If y varies directly as the square root of x, what is the constant of variation if y = 36 and x = 9?

A: 1.5

B: 2C: 4D: 12


Question 23 :Click on the box to select the zeros. You must select each correct zero.

Which of the following are zeros of the function ?

A: x = -16

B: x = -8

C: x = -2

D: x = 0

E: x = 2

F: x = 8

Question 24 :A baseball was thrown by a player, and hit the ground after exactly 5 seconds. If x represents the time in seconds and y represents the height of the ball, which of the following functions could represent the path of the ball?

A:

B:

C:

D:

Question 25 :Type your answer into the box. You must enter your answer in


integer form.

A normally distributed set of numbers has a mean of 75 and a standard deviation of 7.97. What percentage of values lies between 70 and 85? ROUND TO THE NEAREST INTEGER.

Question 26 :

The domain of the function is all real numbers except -

A: -7, -4, 4

B: -7, 4

C: -4, 7

D: 4


In a school, 12 students are running for 4 class officers- a president, a vice president, a secretary, and a treasurer. If each position is to be held by one person and no person can hold more than one position, in how many ways can those positions be filled?

Question 28 :Which of the following is in the same family as the

function ?

A:

B:

C:


D:

Question 29 :Click on the box to select a property. You must select each correct property.

The steps to simplify an expression are shown below:

Step 1: 4(x+3) - 3x + 1Step 2: 4x + 12 - 3x + 1Step 3: 4x - 3x + 12 + 1Step 4: x + 13

Which of the following properties justify Step 2, Step 3, and Step 4?

A: Associative Property

B: Commutative Property

C: Distributive Property

D: Inverse Property

E: Substitution Property

F: Transitive Property

Question 30 :A baseball player throws a ball from one end of the field to the other. A fan measures the path of the ball and determines that it

follows the function , where x is the time in seconds and f(x) is the height in feet. What is the maximum height of the ball, in feet?

A: 2 feet


B: 5.4 feet

C: 6 feet

D: 9.2 feet

mikemazz.weebly.com€¦ · web viewprevious research shows that item format, question type,...

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