Sunday, January 8, 2017


STEM and Inspiration

Thinking back a few years, I wrote this letter to Annie Kuster....

RE: H.R. 4515. To amend the Elementary and Secondary Education Act of 1965 to provide grants to eligible local educational agencies to encourage female students to pursue studies and careers in science, mathematics, engineering, and technology.

Dear Representative Kuster:

As a middle school mathematics teacher as well as a doctoral student at the University of New England, I am writing to gain further insight into Getting into Researching, Learning & Studying of STEM Act of 2014 or the Girls-STEM ACT of 2014 (Bill H.R. 4515).

The goal of supporting girls in STEM is one which is dear to my heart. The intent to encourage the ongoing interest of female students in careers requiring skills in STEM and to prepare female students to pursue industry-recognized credentials needed to pursue a career in the STEM related fields is one which I hope to see our nation support whole-heartedly. I can see myself taking full advantage of said grants so as to serve underrepresented or low-income students, and to establish or implement programs to ultimately support girls in the area of STEM.

Reviewing H.R. 4515 initially, I supported it 100%. The intent of supporting girls in science, technology, engineering and mathematics is one which is dear to my heart. However, after viewing Public Policy and the Power of Networks (Thersaorg, 2010), I began to look at the details of this bill differently; through the lenses of value, facts and myths.
The potential awarding of grants via H.R. 4515 is based on the assumption that the suggested actions will encourage the ongoing interest of female students in STEM careers and prepare female students to pursue credentials needed for a STEM career. The actions suggested are mythical in the sense that there is no support that they will indeed have a direct impact on the intended of encouragement and preparation.
H.R. 4515 fails to define the current levels of interest of female students in STEM careers and also fails to discuss the current levels at which females pursue STEM careers. Women have made great strides in the STEM fields since the passing of Title IX of 1972. According to Women and Girls in Science, Technology, Engineering, and Math (STEM) from the Executive Office the President (2012), women currently earn 41% of PhDs in STEM fields. Women have made huge gains in life sciences and social sciences with approximately 49% of the workforce in life and biological sciences being female according to the National Coalition for Women and Girls in Education (NCWGE). There has even been a report of a 50% increase in these fields over the past two decades by the NCWGE (2012). Where does the current problem lie?
Women, however, remain under represented in the fields of computer science and engineering. Despite being nearly equal in high school engineering classes, women represent 18% of engineering undergraduate degrees and about 11% of the engineering workforce (NCWGE, 2012). What additional verifiable information can be used to support the actions noted within this bill?
Considering this limited data, are the suggested actions of H.R. 4515 diagnostic in nature? How might the implementation of fewer clarified actions have a direct and/or greater impact on girls and STEM? Ideally it would be supportive in nature to see additional facts that support the causal claims intertwined within this bill to have a greater impact on girls and STEM. As a teacher, I can make speculations but I would like to see data which defines the specific needs so as to better determine if H.R. 45415 is aimed at meeting these needs.
H.R. 4515 defines the intended value it would like to invoke on the education and future of girls in our nation but is lacking in quantitative measures. Title IX at 40: Working to Ensure Gender Equity in Education (2012) states that “federal science agencies, which are responsible for ensuring that academic institutions 
to which they offer grants comply with Title IX, have an uneven track record in monitoring compliance. How will the implementation of this bill be different? As it is written its intent is to support local agencies but who and how will these local agencies be monitored? I would be interested to learn about the quantitative measures which will be used to determine growth and/or success as well as the plans for monitoring proposed actions.
How would the passing of H.R. 4515 would impact the effect the taxpayer financially? This is an important factor to consider with all policy considerations.

The Girls-STEM Act of 2014 lends itself towards positive improvements for girls in the area of STEM. However, I am concerned that the actions proposed are not backed by facts and/or data. More important is the fact that there are no measurable outcomes proposed and the intended actions are diagnostic in nature. Bardach (2011) addresses in A practical guide for policy analysis: The eight fold path to more effective problem solving as reasons for being skeptical in examining problems. 
As a strong advocate of women in STEM, I see the positive goals and intentions of H.R. 4515. To support this bill, I would need to know about the quantitative measures that would be used to determine success, growth and/or progress of awarded grants. Additionally, data which support the intended actions would prove to be beneficial as well as how a clear definition as to how the awardees may be determined. Such provisions would move the mythical aspects of this bill to facts and value which support the intended expenditures.

Thank you for your time and interest. I look forward to hearing back from you so I can learn more about the Girls-STEM Act of 2014 and advocate for increased support.


Katrina Hall 

At the time I had an opinion, but now I feel as if girls and STEM has become a part of me.  I continue to work and advocate for the future of our young women in these fields.  This is not to say that I have pushed aside the relationship of boys in STEM but I feel as if the girls need more attention in the situation until there is some level of equality for all.  All should have a fair chance.

I have worked at various angles to bring about specific opportunities to inspire our future female leaders. I have specifically enjoyed connecting groups of middle school girls with the NH High Tech Council and Tech Women | Tech Girls

We have had the chance to hear from inspirational female leaders who have reached beyond the glass ceiling to achieve their goals as well as meet with other leaders in the STEM fields at the Ambassador Week hosted by Nashua North High School. 

My next phase reaches beyond girls and STEM.  After learning of the STEM Docent opportunity offered through the UNH Extension, I felt I could reach out to no only girls in my classroom, but also to boys and girls in community...even the state.  I have taken to heart what "Bill Gates, Neil de Grasse Tyson and Jane Goodall have all had at least on their careers".....Inspiration.

What have you taken on to Inspire our youth?

Friday, July 22, 2016

One Good Thing....Thanks #MTBos

Well, school is out and summer has definitely arrived. Having "free" days one would assume that there is plenty of time to smell the roses. I, however, feel as if the summer days are just as busy as school days. For this reason, taking the time to acknowledge the good things that happen in a day came along at a perfect time.

Per usual, my day started off with a cup of coffee.  Unlike the hectic school days where I start the Keurig and run out the door or stand in line at the local DD along with others looking for their morning jolt, coffee this morning was served by my awesome husband....straight from the French press. This was a good thing!

Unlike my hectic school morning, this morning I had the chance to snuggle with my Boston Terrier, Brick. On a typical morning, I take Brick outside in the morning, feed him breakfast and scoot out the door. As I am leaving, I get the big puppy eyes. He loves the morning snuggle time! Today, I had my cup of coffee and had the relaxing snuggle time with Brick. This was a good thing!

Next, I hear steps coming down stairs.  I look up to see my oldest son holding my grandson. I hear more footsteps.  It is my favorite daughter....Okay, she is my only daughter. Kicking off the morning with smiles from these three is a good thing! 

Today, I have my grandson for the day. We head off to do some planting with my best friend. A bit of an emotional planting as she has offered to plant flowers and bushes at my mother and brother's gravesite. A feeling of peace is a good thing this morning!

A quick lunch and then off for a walk with my grandson and daughter. We walk on path where we see turtles, flowers, birds and LOTS of grasshoppers. Even the snake wasn't so bad. Taking the time to simply walk and talk without the rush of cars and hurried people was a good this on this morning!

As I head home, my youngest son has finally risen from the sleeping world.  The teenage life. When did he get so tall?  A senior this year and getting ready for college applications. In a few months, he will be an official adult. Taking the time to appreciate having all my kids home.....a good thing!

In walks my husband....need I say more?  A good thing!

Taking the time smell the roses means taking the time to appreciate all the things that I rush by each morning, afternoon and night. Makes me realize that I need to take the time to smell the roses every day.

Thanks #MTBos !

Wednesday, November 11, 2015


As I have embarked on the research portion of my doctoral studies, I recognized the fact that I needed an online survey tool that went beyond the average commonly used tools so frequently used.  Not only did I need a tool that was easy to use, efficient, secure and cost effective online survey tool quickly but also one that was going be effective when it came to data analysis.

After much searching and a comparison of tools, I came across SoGoSurvey. There were several aspects that lured me to SoGoSurvey.

First the cost for SoGoSurvey was right up my alley. As a student, keeping costs low is a goal.  With SoGoSurvey the free option certainly drew my eye.  However, this was an option available with many of the other options.  SoGoSurvey, however, has a wonderful option for students. SoGoSurvey offers upgrades to the professional edition for academics and  students. This certainly drew me in.

SoGoSurvey offers a professional looking survey.  This was especially important to me.  I really wanted an online tool that was appealing to the eye, looked professional and allowed me to add my personal touch. The choice of fonts, header and footer text, the addition of images and the variety of themes is perfect.

I also needed a survey tool that was going to be easily shared with others. SoGoSurvey offers a variety of tools to make this easy. There are options to upload contacts, to send the survey via email, embed it into a website and share on a multitude of social media sites included FaceBook, LinkedIn, Google+ and even Twitter.

Knowing that surveys were going to be used with students, it was also important to find a tool free of third party ads.  SoGoSurvey has that option. SoGoSurvey also offers secure and encrypted data.

SoGoSurvey offers unlimited responses!!!  

Registration was super easy and I was immediately impressed with the team at SoGoSurvey. They have reached out via email with support options but have not flooded my mailbox like many online tools choose to do.

I am excited to continue with SoGoSurvey and use their easy to use platform to create my surveys.  

Thank you SoGoSurvey!

Friday, March 13, 2015

Self-Care: Avoiding Burnout #fried

"Yes, that is me."

Reading Fried (2011), I had a hard time putting it down. I found myself saying, "Yes, that is me" over and over again. According to the results of the Kiersey’s temperament assessment (2010), my temperament is that of a 40%-45% of the population, the Inspector. Inspectors' needs lend to complaints of being tired, drained and stressed. Inspectors can take actions to avoid stressors, gain back control of their emotions and avoid the preventable disease of burnout via self-care.

There is not a one size fits all technique for reducing stress but yoga, mediation, retreats and other non-medical forms of self-care as techniques for training one's attention and awareness to help bring thoughts under control (Guttenberg, 2013). Disengaging from the external factors and looking internally to develop feelings, beliefs and actions, which benefit the body’s growth, are ways to develop as a healthy leader but more importantly to develop a healthy soul. To reduce stress and focus on a healthy body, I will practice yoga, chiropractic care and acupuncture a minimum of three times a week.

Edenfield and Saeed (2012) state that mindfulness, the act of bringing external and internal factors to one's attention, has been shown to effect stress reduction and reduce negative mood states, and improve the emotional well-being of individuals with chronic physical illnesses. " Improving attention, awareness, acceptance, and compassion may facilitate more flexible and adaptive responses to stress" thereby improving the health, life satisfaction, well-being and overall quality of life (Edenfield & Saeed, 2012). To focus on mindfulness and reduce negativity, I will not only incorporate my yoga practice back into my schedule but also use my compassion meditation app on my iPhone a minimum of three times a week.

Finding the balance of giving to others and giving to oneself is not an easy task, especially for the idealists who take on more and more. In essence, the appearance of selflessness is an individual’s search to be right, feel accepted and be rewarded; ego fulfillment. It is this energy draining, idealistic, ego fulfilling vision in life that lends to burnout. The ideal is to move from serving one's own ego to recognizing the limits of life and serving one's soul. To transition from the stressed idealistic woman, I am going to set out a block of time daily where I focus on me. Time where I rest, eat a healthy meal, spend time alone, avoid social media and simply focus on myself. The goal is to “put the oxygen mask on” and transition from ego fulfilling to "selfish" actions.

Mama Gena is quoted in Fried (2011) as saying, "You don't revive from burnout by thinking about it and reflecting on your problems." Instead individuals should focus on changing their minds and feelings; cognitive-behavior therapy (CBT) (Borysenko, 2011). Through strategies such as self-talking and writing about feelings, thoughts, beliefs and actions, individuals can use CBT to transform their frame of mind, the way they feel and their action despite a lack of change in external factors. With this in mind, I have set a goal of journaling at least three times a week, using the Day One application, to write about my feelings, thoughts and beliefs with the intent of changing negative feelings, actions and stress to a positive sense of being.

"Learning to care for yourself is an art" (Borysenko, 2011, p. 116). Much of this contributes to the fact that the speed of life certainly has changed. As life progresses there appears to be less and less time. Keeping up with the Joneses is not an easy task and one which sets individuals up for failure and even burnout. Instead take the time to keep up with yourself and understand that "When you come to the end of the rope, tie a knot and start climbing" (Borysenko, 2011 p. 144).


Borysenko, J. (2011). Fried: Why you burn out and how to revive. Carlsbad, CA: Hay House.

Edenfield, T. M., & Saeed, S. A. (2012). An update on mindfulness meditation as a self-help treatment for anxiety and depression. Psychology research and behavior management, 5, 131.

Guttenberg, K. (2013, May22). Yoga, meditation benefit both brain and body [Blog post]. Retrieved from

Personality Test - Keirsey Temperament Website. (2010). Personality Test - Keirsey Temperament Website. Retrieved July 25, 2014, from

Friday, March 6, 2015

Quantitative Analysis: Perspective as a Researcher and Scholar

According to Creswell (2012), the quantitative researcher describes a research problem through a description of trends or a need for an explanation of the relationship among variables. Initially the researcher relies greatly on the literary reviews so as to develop a strong backing as to why the research is important and necessary. Quantitative researchers create questions and look to find the answers to these questions. Once the necessity of the research is developed it is these researchers who rely on standardized methodologies of data collection to create statistical models where numeric data can be analyzed and correlations can be identified amongst variables.

One of the challenges for a practicing researcher is the background knowledge and skill one must have to effectively use the quantitative method. A thorough understanding of statistical knowledge and the process by which statistical data needs to be analyzed is not necessarily a skill mastered by a practicing researcher. This makes me wonder where I will be in terms of my research having had no practice with the methods learned within this course other than the practice within the course itself. Will I be prepared?

In the beginning, the terminology, the software and the APA formatting were unknowns; I had a great deal of work to accomplish before meeting any of the learning outcomes or course objectives. Right from the very beginning with the basics of SPSS and the management of data, my learning expanded. Follow that with the descriptive analyses, correlational analyses and the studying of hypotheses and one can say my researching skills went from null to ready to practice. However, the evaluation of the CRISS Project made me realize I have so much more to learn. Will my research results be at this level? Will I be able to handle the variations, which I encounter?

As I began the initial work with this course, the statistical software and the readings by Creswell, I was certain the quantitative work was not going to be a good fit for my research as it relates to students and education. Even in my initial epistemology paper, I noted that the quantitative researcher purely focused on numerical data with the objective of testing theories and hypotheses; refraining from personal interactions or descriptive analyses. This just did not seem to be the right fit for me; students are more than numbers and statistical data.

As the final weeks of learning related to quantitative analyses arrived, my mindset began to change as I studied the various philosophies associated with the style of research. One specific philosophy which helped me to realize quantitative research does not rely on absolution of numbers if that of post-positivism which is described as “A deterministic philosophy in which causes probably determine effects or outcomes. Thus, the problems studied by post-positivists reflect a need to examine causes that influence outcomes, such as issues examined in experiments ”(Creswell, 2012, p. 7). Good research within this paradigm is described by Mertens (2009, p. 12, as cited in Christians, 2005, p. 159) as “Intellectual honesty, the suppression of personal bias, careful collection and accurate reporting of data, and candid admission of the limits of the scientific reliability of empirical studies.” Post-positivistic researchers make major assumptions regarding reality and truth which develop from reading literacy as a variable of interest and use a quantitative measure of that variable, awareness of the need to eliminate alternative explanations and he application of statistics to data to support claim within a certain level of probability (Mertens, 2009, p. 14). The post-positivists concur that a reality does exist, but argue it can be known only imperfectly because of the researcher’s human limitations. Quantitative researchers can discover “reality” within a certain of probability. They cannot “prove” a theory, but they can make a stronger case by eliminating alternative explanations (Mertens, 2009). A realization for me that quantitative research is recognized as having limits in social sciences.

Knowing the limitations the quantitative research, I think back on my initial epistemology paper where researchers Johnson and Onwuegbuzie (2004) suggest taking a non-purist approach, specifically in the area of educational research. It is these researchers who recognize the mixed method of research as the perfect balance in overcoming the individual weaknesses of quantitative and qualitative methodologies. I look forward to studying the qualitative methodologies and philosophies to see how they may balance the limitations of the quantitative research. Will the qualitative research bring the human connection to my research and provide me with the perfect mix?

Quantitative research, although it did not appear to be the “right” method for me turned out to be more of a match than expected. Having a math background, I enjoy the number aspect of this method. Looking at data and the story, which can be developed from the analyses, is a mathematicians joy. However, the teacher in me also knows that behind this data is reality and truth; there is always another side to the data which must be considered. As a researcher and scholar, I think it is important that these two various views be recognized in research. In the end I have appreciated learning about all aspects of quantitative research, however, I look forward to developing as a well-rounded researcher who is aware of all methodologies and philosophies to provide sound research to education.


Creswell, J.W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research. (4th ed.). Boston, MA: Pearson.

Johnson, R. B., & Onwuegbuzie, A. J. (2004). "Mixed methods research: A research paradigm whose time has come." Educational Researcher, 33(7), 14-26.

Mertens, D.M. (2009). Research and Evaluation in Education and Psychology: Integrating Diversity With Quantitative, Qualitative, and Mixed Methods. Retrieved from:

Pole, K., (2007). "Mixed method designs: A review of strategies for blending quantitative and qualitative methodologies." Mid-Western Educational Researcher, 20(4), 35-38.

Sunday, March 1, 2015

Reflecting on the Week

What Inspires You?

As I sit today wondering how to inspire readers, I find my mind straying away from the task at hand. I should be writing about the upcoming NCTM Annual Meeting coming to Boston, the anxiety teachers are feeling in regards to the Smarter Balanced Assessment, the continuing pressure on the continuance of the CCSSM, the middle school math contest, the recent state STEM task force report, and the question of whether STEM should become STEAM. Dr. Magnus provided so many suggestions but I just can’t focus on these topics. My mind keeps reflecting on the lessons of the week.

Eighth grade classes have been discussing relations and functions. They have ventured into determining if a relation is a function from a set of ordered pairs, and even via the vertical line test. A quick assessment and yes, they are getting it. We move on to identifying domain and range. A quick assessment and yes, they are getting this too. Continuous and discrete graphs? That’s a piece of cake too! These children are mathematical wizzes but then we move onto evaluating functions and they fizzle. Why? Students continue to struggle with the order of operations and manipulating integers. Even with the use of a calculator students struggle. How does one move on from this gap in understanding so as to lead the student towards success at the next level? A lack of mastery of previous content has become our roadblock.

Moving on, I reflect on the Algebra students. As a collaborative project, students are working on the case of the missing student. The excitement in their eyes as they encountered the mystery and learned of this assessment. “This is so much better than a quiz.” As I watched my students scattered throughout the room, I see their excitement in using math to solve the mystery. Students are collaborating, working cooperatively and managing themselves just as they would in a real-world task. As the teacher, I find myself walking around the room listening to conversations and smiling. Is this what STEAM is all about?

The week of teaching and learning had its highs and lows. Of course, I love the highs but I wouldn’t change the lows. As an educator, I take the lows as the opportunity to extend my learning as a teacher of mathematics. I reflect and look for ways to not only make the learning experience stronger for my students but also better understand the gaps in their learning. It is the gaps that provide me with the opportunity to create new lessons and bring about the “aha” moments in the classroom. Yes, the highs are wonderful and I love the adrenaline it creates but the lows inspire me to be more. What inspires you?

Monday, February 16, 2015

Attitude, Self-Concept & Achievement in Middle School Mathematics

Getting Started on a Literature Review 

Mathematics self-concept, attitude and achievement are emphasized as motivational factors in science, technology, engineering, and mathematics (STEM) fields. The purpose of this review was to gain a better understanding of these factors as they relate to middle school students.

With no mention of theory, Obgunotyinbo (2012) reports on the low mathematical achievement seen in the United States. The main proposals for the United States’ inability to perform globally in the area of mathematics include poor teaching training, a hyper-focus on standardized testing, the lack of diversity amongst teachers and on the failures to focus on reasoning and sense making in mathematics. In summary, Obgunotyinbo (2012) uses the voice of mathematical scholars to disperse a lack of inspiration and challenge in the secondary schools as the reason for the lack of U.S presentation in the math arena. Research by Yilmaz, Altun and Olkun (2010) states that a successful student has a positive attitude. However, Bouhlila (2011) found some of the highest scoring countries with the greatest number of negative attitudes in mathematics. Differing in views, attitude appears as a popular theme.

In mathematics education, research on attitude has been motivated by the belief that it plays a crucial role in learning mathematics. Ma and Kishor (1997) define one’s attitude towards mathematics “as an aggregated measure of liking or disliking of mathematics, a tendency to engage in or avoid mathematical activities, a believe that one is good or bad at mathematics, and a belief that mathematics is useful or useless” (p. 27). Neal (1969) defines attitude towards mathematics as “an aggregated liking or of disliking mathematics, a tendency engage in or avoid mathematical activities, a belief that one is good or bad at mathematics, and a belief that mathematic is useful or useless"(p. 632). Mathematical attitude where behaviors do not appear explicitly are defined as a pattern of beliefs and emotions associated with mathematics (Daskalogianni & Simpson, 2000). Thus leading from a motivation view to one, which based on self-concept; a student’s perception or belief in ability.

Self-concept of ability is commonly discussed as having a direct impact on a student’s attitude and achievement (Möller, Pohlmann, Köller & Marsh, 2009; Marsh, Trautwein, Lüdtke, Köller, & Baumert, 2005; Wilkins, 2004). Using commonly found theoretical models, studies have found elements that effect self-concept of ability and directly impact student achievement. Research by Wang, Osterlind, and Bergin (2012) further emphasizes self-concept of ability as one of the major predictors of achievement making it an essential concept in the field of mathematics education.

As students progress in years of schooling negative attitudes towards mathematics increase, and self-concept of ability in mathematics decrease (Wilkins, 2004). This happens to coincide with the dip in mathematical achievement seen at the middle school level. A reason why the three constructs have been researched in depth for several years. Further reasoning as to why social-cognitive models and theories emphasize attitude and self-concept as impacting factors on mathematics achievement.

In the U.S. negativity towards mathematics becomes prominent around the middle school years. According Hassan, Ching, and Hamizah (2012), interventions such as teacher support, cooperative learning, classroom materials, modeling, and self-efficacy have direct effects on the intrinsic motivation; related to the attitudes of students. With such interventions having an impact on attitude, one can consider these interventions to further have an impact on self-concept and achievement. However, this is unclear.

The mathematical performance of students is regularly compared. One particular study is that of Bouhlila (2011) which considers factors that effect the mathematics education in the Middle East and North Africa (MENA). Factors connected to low performance in mathematics include language fluency, homework, mathematical content and cognitive domains set by curriculum, family background, socioeconomic status and attitudes towards mathematics. According to the data analyzed by Bouhlila (2011), MENA countries rank high in attitude and self-concept however mathematical performance is low. Conversely, countries such as Japan, Korea and China who ranked low in positive attitudes, and self-concept are some of the higher scoring countries in mathematics. However, there is no mention of how a positive or negative student perception is developed nor is there mention of the relations found in United States.

The goal is to look globally for factors and influences, which have a positive effect on middle school students’ mathematical attitudes and self-concept to provide supports and interventions. The hierarchal and/or causal relations of the social supports and the role which they play in the development of self-concept in the middle school mathematic student is an area which is lacking.

The Constructs of Self-Concept, Attitude and Achievement

Self -Concept

Self-concept is defined as “an individual’s perception or belief in their ability to do well in an academic domain” (Wang et al., 2012, p. 1215). Self-concept explains an individual’s belief to learn and do well in mathematics. Research endorses the importance of a positive self-concept to achievement, emphasizing self-concept enhancement (McInerney, Cheng, Mok, & Lam, 2012). Self-concept has an important effect on the way student’s “feel about themselves, their accomplishments, persistence and educational decisions” (Möller et al., 2009, p. 1130).

In defining self-concept two separate areas, academic and non-academic, must be defined. Academic self-concept of ability consists of an individual’s belief to perform well in subject specific domains, such as math, science or English. The non-academic area consists of the physical, social, and emotional aspects of an individual.

Academic self-concept of ability is of significance in understanding mathematics achievement defined as an explanatory variable in mathematics achievement and as a controlling variable in initial achievement (Valentine, Dubois & Cooper, 2004; Wang et al., 2012). Academic self-concept is one of the strongest predictors of mathematics achievement in both the near and distant future of students (Valentine et al., 2004). This advances self-concept as a fundamental attribute in understanding the mathematical achievement in students.

Internal/External Frame of Reference Model.

Academic self-concept is recognized as impacting academic achievement across subject domains. There are high positive correlations between math and verbal achievements as well as math and science achievements. Studies of self-concept should be redefined on a domain specific level based on the high subjectivity of this construct (Möller et al., 2009).

According to the internal/external frame of reference model, students compare their abilities using two frames. The external frame of reference is modeled by students who makes social comparisons such as comparing math performance to their peers. The internal frame of reference refers to instances when students compare their achievement in one subject to that of another subject. These external and internal elements are considered crucial in the development of self-concept. Based on the external frame students who are comparatively low in the area of mathematics achievement are expected to have low levels of self-concept. Using the internal frame, students who are low achievers in the area of mathematics are expected to have higher levels of self-concept in subjects such as English. Few studies have used the I/E model to investigate mathematics and non-verbal subjects. This leaves room for researchers to expand the application of the I/E model and the study of self-concept to areas other than math and the verbal domains.


A simple definition of mathematical attitude is the learned tendency or predisposition to respond in a consistently negative or positive manner towards mathematics; a positive or negative emotional disposition toward mathematics. Interestingly related to attitudinal studies by researchers is the direct correlation between achievement and attitude (Lipnevich, MacCann, Krumm, Burrus, & Roberts, 2011).

A common assumption is students with a negative attitude towards mathematics are low achievers. This conversely, students with positive attitudes tend to be those with high levels of achievement. Disputing this common assumption are results shared by Bouhlila (2011) and Riegle-Crumb, Moore, and Ramos-Wada (2011).

The expectancy-value model is a model that concentrates on students’ beliefs in their own ability and competence (Denissen et al., 2007). According to this model there are two key predictors of achievement; self-concept of ability and subjective task values. Subjective task values are strong predictor of future choices (Wilkins, 2004; Wang et al., 2012). Where as, self-concept of ability is a stronger predictor of achievement of self-concept (Wilkins, 2004; Wang et al., 2012). This model tends to put a focus on self-concept for those concerned with immediate achievement. However, the work of Marsh, Trautwein, Lüdtke, Köller, and Baumert (2005) confirms the relationship between academic self-concept and achievement but extends the relationship to include academic interest adding a new branch when considering achievement.

Authors Riegle-Crumb et al. (2011), refute the expectancy-value model dispelling that African American female are just as likely to strive for careers in mathematics due to the enjoyment of the subject; despite low levels of self-concept. Such research guides the creation of positive, intriguing and enjoyable classroom experiences. Providing enjoyable experiences is not a predictable factor of achievement but a predictor of positive attitudes and interest in mathematics. Self-concept and achievement may be low, however, the existence of a positive attitude is attainable via the design of proper classroom environmental factors. Positive experiences can lead to positive attitudes in mathematics. In summary, failing to focus on one factor diminishes the relationship and directly impacts the other factors (Marsh et al., 2005).

Self-Concept and Achievement

There is validity in self-concept as a key factor in understanding the levels of math achievement. Breaking from motivational constructs, Wang et al. (2012) confirms that self-concept as “the only identical pattern of prediction of eighth grade students’ mathematics achievement across four countries” (p. 1231). Relying on the expectancy-value model, self-concept of ability is defined as a strong predictor in achievement having a positive relationship with mathematics achievement in various countries.

Self-concept is of particular importance in understanding mathematics achievement. Despite being studied in conjunction with other constructs such as task value and other subjects such as science, math self-concept has a stronger relation to math achievement than other constructs. Self-concept in mathematics has a greater magnitude of variance in math achievement over subjects such as science and English. Self-concept also aligns itself better with predicting achievement over task value, which has been aligned as a predictor of course choice.

Self-concept affects achievement and achievement affects self-concept (McInerney et al., 2012). According to the self-enhancement model, academic self-concept is a strong predictor of achievement. The inverse is believed to be true through the skills development model that implies that self-concept is a result of achievement. Other models suggest the existence of a reciprocal model where self-concept predicts future achievement and prior achievement affects self-concept (Valentine, Dubois, & Cooper, 2004). The dispute lies in whether one can predict the other.

Cultural Implications.

Utilizing an internal-frame-of reference effect, academic self-concept achievement shares a reciprocal relationship. Wilkins (2004) addresses the relationship between self-concept and achievement from an international perspective that is lacking in the field. The international and global comparison of Wilkins (2004) shows students worldwide tend to have a relatively positive view about their mathematics performance. On a student level, students with positive self-concepts had higher levels of achievement and vice versa (Wilkins, 2004). Differing from this view is that at the country level where higher achieving countries, particularly Asian and Eastern European countries have lower levels of self-concept despite high levels of achievement (Wilkins, 2004). This defines Wilkins proposal that that cultural differences may impact individual countries’ self-concept.

Cultural differences between countries could mediate the relationship between math self-concept and math achievement. The research of Yoshino examines the relationship between eighth-grade students’ math self-concepts and achievements via the TIMMS 2007 data. The results indicate a positive relationship between a student’s self-concept and mathematics achievement. Yoshino extended this study beyond the United States into Japan so as to examine the impact of culture on these two constructs. Self-concept is found to be lower in Japan despite the level of mathematics achievement signifying cultural differences as impacting self-concept.

The work of Yoshino (2012) confirms a strong interaction between math self-concept and country as well as a positive connection between math self-concept and math achievement irrespective of the country. Thus implying the existence of cultural aspects that impact the math self-concept and achievement of these students. Whether these aspects include racial differences is unknown.

The discussion of the I/E model provides insight to self-concept of mathematics ability and culture. For instance, students in Japan are more likely to compare their scores to other students who performed at higher levels thus decreasing their perception of mathematics abilities. Such findings are pertinent to educators in understanding the affects culture and comparison has on the self-concept of the mathematics students as well as their perception of achievement. Differing from other research, Wilkins (2004) shared additional research laying claim that there is wide range in self-concept amongst boys and girls amongst cultures. Consideration of cultural variances as it pertains to self-concept is a factor to examine.

Attitude and Achievement

For over thirty years, student attitudes and achievement have been themes in educational research. Such research has proven there to be a strong relationship between positive attitudes and academic success.

A common belief, whether factual or not, is that students have a more negative attitude towards math and science in comparison to other academic areas; a reason for researchers to delve into the studies of attitude and achievement (Rice et al., 2013). Of importance is evidence that suggests attitudes towards science and mathematics follow different paths over adolescence (Rice et al., 2013). Such evidence backs the need to differentiate mathematics from other subjects as achievement is being studied.

Within a multi-variant study on achievement, Lipnevich et al. (2011), expose the existence of a relationship between mathematical achievement and attitudes towards mathematics via a theory of planned behavior. The results of the Lipenvich et al. (2011) study show a strong correlation between a student’s mathematics attitude and achievement. The study also shares a minimal difference in the mathematical attitudes across the two cultures. The strongest implication of this study is the use of interventions designed to improve student attitudes have a direct impact on student grades. Such interventions include increased teacher support, collaborative work, and the use of manipulatives and technology.

Consistent with findings from earlier research, Rice et al. (2013) suggest that students who receive social support for math and science from teachers, peers and parents have better attitudes towards the subject and a better self-concept. This may be the reason why Lipenvich et al. (2011) noted that attitudes are the most important predictor for students’ mathematical achievement. The findings from the study of Rice et al. (2013) coincide with the value of social supports as successful interventions.

Of interest is the suggestion that interventions designed to influence a student’s attitude may directly impact the student’s achievement. Suggested interventions include teacher support, classroom interventions and modeling by peers, parents and teachers. With interventions having a direct impact on the attitude of students, the question that rears its head is whether the also interventions have a direct impact on self-concept.

External Factors

Social Support

The social-cognitive model relies on social agents such as parents, teacher and friends. Social agents are to influence academic achievement directly through elements such as self-concept of ability and attitude (Rice et al., 2013). Students who have the perception of social support from parents, teachers and peers tend to have more positive attitudes and self-concept of ability (Rice et al., 2013). As a result of such studies, parents, teachers and peers are all identified as important social agents in establishing positive self-concept across math.

Gender and Stereotypes

According to research aligned with social cognitive models and the expectancy-value model, gender has a direct impact on self-concept and achievement (Bleeker & Jacobs, 2004; 2004, Else-Quest, Mineo & Higgins, 2013). The research of Wang et al. (2011) helps to differentiate gender as it is related to self-concept and achievement by clearly stating that “no gender differences between boys’ and girls’ mathematics achievement” is found in the four countries studied (p. 1229). This steers one in the direction of self-concept.

Self-concept of ability is a psychological paradigm where individuals base their future academic abilities on past experiences (Jones, Irvin & Kibe, 2012). Evidence shows that prior academic self-concept does predict academic achievement. Despite lower math self-concepts in girls, the positive effect of high math self-concept on subsequent math achievement is similar amongst boys and girls. Therefore, diminishing the effect of gender differences in prior achievement.


Parents’ perceptions of their children’s abilities and their expectations are related to the children’s’ development of self (Bleeker & Jacobs, 2004). Gender-dependent self-concepts are shared by Hergovich et al. (2004) where parents’ have more positive views of their sons’ abilities in mathematics over their daughters’. This is found to be true despite the achievement levels of the girls, therefore supporting the reputation parent’s play in student achievement.

Mothers who reported high perceptions of their children’s abilities to succeed mathematically during middle school were significantly more likely to have adolescents who had high levels of self-concept though high school (Bleeker & Jacobs, 2004). A mother’s belief about an adolescent’s ability in mathematics is shaped by gender stereotypes that are related to the development of an adolescent’s self-perceptions of ability in mathematics. Mothers who believe that boys are stronger than girls in mathematics indirectly impact the self-concept of ability of both genders despite the grades attained. These beliefs are based on the stereotypes of the mothers, which are affected by culture, family beliefs and upbringing. Such work suggests the importance of positive and unbiased supports to students, as they may not exist in the home environment. A close view as to ways in which parents relay their beliefs is needed as well as a study as to what additional factors beyond parental stereotypes may effect a student’s self-concept of ability. Additionally, looking for ways which non-parental relationships can diminish stereotyping

These findings strengthen the gender-stereotypical differences from the transition to pre-adolescence to adolescence that is consistent with findings of other researchers. Such implications relate to understanding self-concept and achievement in research with a leading direction towards gender stereotypes.


Teacher licensure does not predict achievement, but does have a significant impact on self-concept for students in the United States (Wang et al, 2011). Additional suggestions include the possible relation between a certified mathematics teacher and self-concept as well as self-concept and mathematics achievement. Exploring this relationship could bring about pertinent information to understanding achievement but also in understanding how a student learns. The way in which “teachers deal with frustration and they deal with mistakes may affect students’ self-concept of ability in mathematics directly and mathematics achievement directly/indirectly” (Wang et al, 2011, p. 1234).

To broaden the scope previous studies on students’ mathematical attitudes, Hassan et al. (2012) report high school students’ opinions on what factors influenced their attitudes against mathematics. Building on foundational theories, the authors take a different avenue by involving mathematically gifted Malaysian students in the process of the study; gaining student perspectives over observant data. Students who score high in mathematics rate the materials used during teaching, textbooks, the workload and the teacher’s attitude and personality as their leading factors. Students who score in the average range in mathematics rated the teacher’s attitude and personality, teacher’s knowledge on the topics, workload and textbook use as the leading factors. Low-scoring students rated exams, grades, materials used during teaching and the teacher’s attitude as their leading factors. Personality and attitude of a teacher are key factors in making students dislike mathematics according to this article.

The latent class analyses of Kalder and Lesik (2011) examined the characteristic of pre-service teachers that may be related to positive attitudes and beliefs towards mathematics; making reference to the connection between a teacher’s attitude and a student’s attitude. Findings conclude that teachers with positive attitudes are those who are math majors; both elementary math majors and secondary math majors. Teachers with negative attitudes who are teaching in elementary classrooms directly impact student attitudes towards mathematics. This study sets the stage for the development of positive attitudes in non-math majors with a specific focus on pre-service elementary teachers. A question as to how much of an impact the elementary teachers have on the self-concept of middle school students has risen as well as the what program changes could be put into place to support positive student attitudes.


Peer emulation theory offers a theoretical basis for the relationship amongst peers and academic self-concept of ability and achievement. The peer emulation theory suggests interactions with peers, positive or negative, can affect a student’s academic self-concept (Lee & Shute, 2010). This includes the stereotype of math being for geeks, or not cool.

The work of Jones et al. (2012) relies on behavior. Differing from the peer emulation theory, their study states that the way in which friends interact affects academic self-concept. Research in this area extends this work, claiming that higher achieving friends might diminish academic self-concept. Although limited in examining other variables, such as the role of teachers or culture, the work of Jones et al. (2012) discusses the validity that academic supports such as peer relations are factors to consider in the development of self-concept in mathematics.

Learning Environment

Few researchers have considered the contextual effects associated with classrooms, or schools that may be related to self-concept and achievement (Wilkins, 2004). Current literature suggests educators try to enhance self-concept and skill development simultaneously. According to the meta-analysis of the I/E frame of reference by Möller et al (2009), mathematics achievement is higher when based on test scores instead of grades. Grades in turn have a stronger impact on self-concept. This emphasizes the need for teachers to use grades as a direct form of feedback for students and as a tool for supporting self-concept of ability.

Students who have high levels of self-concept in mathematics are likely to use deep learning strategies. Deep learners are recognized as having higher levels of achievement in mathematics, which is interceded by self-concept, as well as the inverse (McInerney et al., 2012). Students, who use rote or surface level learning strategies, are likely to have lower self-concepts towards mathematics. The successful application of domain specific strategies as they relate to achievement indicates the enhancement of self-concept relies on the segregation of academic domains.

Students are inclined to have distinct self-concepts when it comes to subject domains. Implications of literature advise the separation and focus on the specific domains that are known to directly affect achievement because the correlation between self-concept and achievement is higher for related subjects over non-related subject. English achievement has a positive effect on English self-concept but a negative effect on math self-concept (Chen et al., 2012; McInerney, et al., 2012). Math achievement has a positive effect on math achievement but has no effect on a student’s English self-concept. A lack of reciprocity in domains, lends to the differentiation of mathematics from other domains when studying self-concept and achievement.

Big Fish Little Pond Effect.

The BFLPE lends itself to the internal/external frame-of-reference effect. Through this social construct, the high math self-concept of an individual is impacted negatively when working with an individual of a higher achievement level; external frame-of-reference. The internal frame-of-reference lends to the idea that an individual can only be strong in one subject. A strong mathematical individual cannot be strong in English and vice versa.

The Big Fish Little Pond Effect (BFLPE) proposes that students of equal ability have lower academic self-concept in classes where the average ability or achievement of peers is high and higher academic self-concept in classes where the ability of classmates is low (Marsh et al., 2005; Parker, 2010; Preckel, Gotz, & Frenzel, 2010). The BGLPE suggests gifted students may suffer decreases in academic self-concept when they are grouped with other gifted students (Preckel et al., 2010).

Ability grouping has been shown to affect a student’s self-concept. Data shows that the mathematics self-concept of students, who are grouped by ability, report substantial decreases while students who remain in homogenously grouped classes report no change in self-concept (Precke, et al, 2010). These finding correlate with the BLPE. However, the research of Precke, et al (2010) found the largest decrease in self-concept during the first 10 weeks of class after which no significant decreases were reported. Such findings suggest the need for supports and interventions during the early weeks of classes to offset the negative effects of the BFLPE on self-concept of ability in ability groupings. When ability grouping is not utilized, the impact of supports and interventions remains unknown.

The research of Hergovic et al. (2004) supports a decrease of self-concept early in the school year, with new groups and/or with ability groups. All research being opposite of that concluded by Yilmaz et al. (2010) which suggests the self-concept of successful students will remain high as the love the subject is the deciding factor. Although distant in the beginning a stronger correlation is seen here, however, it is not clear if one predicts the other.

Due to its association with math achievement and self-concept, the BGLPE is frequently referenced in gender and stereotypical views. In understanding this construct one gains an outlook at on leveling classes, ability grouping and the impact they have on the self-concept of students that are commonly used interventions at the middle school level.

Implications for Middle School

Current findings indicate that gender differences in attitudes are present in early adolescence and continue through middle and high school. Gender intensification theory suggests gender-role activities become more important to young adolescents over time as they try to conform to behavioral gender-role stereotypes (Watt, 2004). Perceptions converge as students enter middle school (Booth, 2012; Watt, 2004).

Literature supports decreases in self-concept, attitude and achievement in mathematics through secondary school, with particular changes during transitional years; middle school. In a study done by Watt (2004), students share the perception of seventh grade math as needed less effort than previous years in math. Along with a decline in perceived effort, mathematics self-concept declines in grade seven (Watt, 2004). Watt connects this decline to the person-environment fit model that relies on the effect classroom environment has on self-concept. Other research base declines on the physiological and psychological changes associated with pre-adolescence.

Results show that boys have a higher sense of self-concept than girls in almost all areas. Consistent results show that boys have a higher self-concept than girls in the area of mathematics. The peak difference occurs at the onset of adolescence (Hergovich, Sirsch, & Felinger, 2004). Watt (2004) extends the study to examine gender differences, which shows a decline in girls’ self-concept that are said to rely on prior experiences directly impact a girl’s self-concept in mathematics. In a study done by Watt (2004), girls exhibit more negative change in self-concept than boys through middle school.

Negative effects are commonly found as students enter middle school. In a study completed by Watt (2004), students saw grade seven as a year of review and repetition in mathematics. One consideration is a decline in math achievement results from the belief of students that less effort is needed. The backing for this belief comes from the lack of repetitive content in other subject areas and no other subjects seeing negative effects on achievement.

The importance of inconsistencies that appear in pre-adolescents is highlighted by Riegle-Crumb, Moore, & Ramos-Wada (2011) with a specific focus on how these differences affect self-concept and intrinsic value of mathematics. Social psychological research indicates decisions and preferences individuals develop during adolescence are formative for future choices.

Related indirectly to middle school is the factor of age. In accordance to age is the movement from the elementary structure to that of the middle school. Schools tend to be larger as do the class sizes. Teachers are dealing with a larger number of students on a daily basis and the relationships tend to diverge. Changes in instructional modes, discipline and perceived supports also change for students. At the same time the students at this age are going through physical and psychological changes of their own. The amount of change at this age directly impacts the amount of attainment possible for a student in middle school (Watt, 2004).

The stage-environment/person-environment fit theory suggests that academic outcomes decline after elementary school because middle schools fail to support students’ developmental needs (Attard, 2013; Bicknell & Riley, 2012; Rice et al., 2013). This theory suggests a lack of fit between the middle school environment and the needs of young adolescents, therefore having a negative impact on student self-concept, attitude and achievement.


There exist both cognitive and biological principles as to why students dislike school (Willingham, 2009). Accordingly, the mathematical achievement and learning of a middle school student is impacted by these principles all the time. Willingham provides guiding principles to help teachers in planning as well as providing a balance for the conflicting emotional, social and motivational concerns. However, the implication such principles have on the math attitude, self-concept and achievement of the middle school student lack in definition.

The review of current literature supports the interdependence of attitude, achievement, and self-concept. The relationships are strongly supported by the findings of researchers, and theories however lack causal delineations. However, few studies examine the impact of support and interventions on self-concept of ability. Essentially, the literature fails to discuss collaborative efforts and the potential impacts such efforts could have on a student’s sense of self-concept. Literature suggests a need for teacher and parent awareness in developing attitudes in mathematics (Möller et al., 2009). Excelling a high achieving student in mathematics who does not have a high self-concept can lead to a negative attitude. On the other hand, the proposal of a challenge for a student with a high level of self-concept and a low level of achievement is supportive in the development of a positive attitude. This reference to the I/E model lends to the utilization of the internal frame of reference effectively by both teacher and parents. The encouragement of self-concept as a part of classroom practices is more effective for teachers over separate interventions (Marsh et al., 2005). However, there is little work expressing how this can happen. The differences in self-concept rely on teachers, and parents but there is a lacking in the specifics as to what actions can be taken to promote a positive impact. (Hergovich, et al., 2004). A specific focus on the hierarchical or causal role in which social supports play in the development of a middle school student’s self-concept of ability in mathematics is suggested.

As stated early, there is an apparent negativity towards mathematics that become prominent the middles school years. The general consensus within literature shows a decrease in self-concept as students progress in grade levels. Reasons include a lack of social supports, gender differences, classroom environment and stereotypical views as some of the dominating factors. Such statements propose that the middle school level is a vital time for students. However, little research has been done specifically at this grade level in the area of mathematics achievement. In fact few studies have focused primarily on the one academic domain of mathematics.

With the notion of potential interventions available, one would expect clarity in literature pertaining to said supports. However, this is not the case. Furthermore, there is little indication of what interventions have been deemed successful determinants for middle school aged students worldwide. Currently there are several aspect of literature related to mathematics achievement. However, there is little perspective on specific supports and interventions which have a positive effect on middle school students’ mathematical attitudes and self-concept to provide. The hierarchal or causal relations of supports and the role which they play in the development of self-concept in the middle school mathematic student is an area which is lacking.


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