# Reflections on Project-Based Learning (PBL) and Developing Girls’ Mathematics Identity

##### Posted on May 11, 2017

*An Interview with Lorraine Howard, Mathematics Professor and 21st Century Teaching and Learning Instructional Coach and Trainer, Wilkes University and Consultant, Pennsylvania Department of Education, Curriculum, Instruction and Assessment *

*By Caitlin Fritz *

Throughout my first year at PHENND the words, Project-Based Learning (PBL), have come up frequently when discussing teacher education, afterschool programing, and model university-school partnerships. To say that PBL is the new trend in education is an understatement, but what really is PBL? Over the summer I was able to sit in on a PBL workshop by Lorraine Howard, a long-time friend of PHENND’s and an avid promoter of PBL. I sat down with Lorraine to get her reflections on PBL, which in many ways are influenced by her own personal journey.

*Caitlin: Project-Based Learning. It seems pretty straight forward, but what does this really involve?*

Lorraine: In short, project-based learning, or PBL, is a systematic instructional method that engages students in learning important content knowledge through an extended, student-influenced inquiry process, structured around complex, authentic questions. I emphasize the word “authentic” because a PBL experience should involve a real world context, student voice, reflections and time for feedback. PBLs should also incorporate opportunities for students to develop 21^{st} century competencies and skills in critical thinking, creativity, communication and collaboration; and the PBL framework should also include some sort of final presentation to an authentic audience, usually beyond the classroom.

*Caitlin: What is the value of PBL?*

Lorraine: PBL empowers students to develop deeper understanding and connections because the learning is made relevant and is applied to real world issues. A particular passion of mine is how PBL can help strengthen one’s mathematics identity, especially pertaining to girls. Indeed, research confirms that PBL helps to empower, engage and build the confidence of girls, because it requires a different mindset. We need to stop girls and their parents, from saying “I can’t do math,” or “I wasn’t good at math.” Even if it were true in the parents’ learning experiences, these types of statements foster a negative mindset which needs to be dispelled. To do this we need more mentors for girls and more opportunities for them to “do” mathematics in an authentic learning context.

*Caitlin: So how did you develop this passion for PBL and empowering girls in math?*

Lorraine: With an exceptional mathematics learning experience throughout elementary, middle and high school, I competed and won a nationally competitive Boeing Aircraft Scholarship in Mathematics to Wichita State University, Kansas where I began my undergraduate studies. Between my sophomore and junior year, and as a Boeing Scholar, I was afforded the awesome opportunity to intern with the Boeing Aircraft Company’s VERTOL (VERtical Take-Off and Landing) Helicopter Division in Ridley Park. I’ve always loved math since my kindergarten days; but it was while working on the VERTOL helicopter “projects” that my ‘aha’ moment came and math really came alive for me. Thus, this experience, coupled with falling in love with the “bright lights and big city” of Philadelphia was a no brainer for my transferring to the University of Pennsylvania where I earned my B.A. in Mathematics, later completing my MBA/Ph.D. work in Finance and Policy Analysis from Wharton.

*Caitlin: You mentioned math identity earlier. Exactly, what is math identity and why is it important for math performance and achievement?*

Lorraine: Mathematics identity refers to a person’s beliefs, attitudes, emotions, and dispositions about mathematics and their resulting motivation and approach to learning and using mathematics knowledge. It involves the ways students think about themselves in relation to mathematics and the extent to which they have developed a commitment to, are engaged in, and see value in mathematics. It is through social processes and shared experiences that individuals develop identity and gain a sense of self and meaning. Students learn to engage in practices through communities and develop a sense of self in relation to the practices and communities in which they learn. A math identity is especially key to girls’ math success.

*Caitlin: Why is math identity key to girls’ math success?*

Lorraine: I believe that there are two major pillars of mathematics: –the belief that you can do math and the belief that you belong. Girls’ math identity is about girls’ math beliefs, dispositions and attitudes about their own abilities in mathematics and it is these beliefs, dispositions and attitudes that really affect girls’ later decisions about careers and education.

There was a very interesting study where hundreds of students were given feedback on a test. A random number of these students were given an additional feedback statement of, “I’m giving you this feedback because I believe in you.” A year later, the difference between the achievements rates of the students who got that sentence and the students who didn’t get that sentence was extraordinary.

Caitlin, it’s not that any of us intentionally give the wrong message to children nor do we intentionally want them not to do well. But it’s almost seamless in a child’s life from the time they’re born up to the time they can begin to make decisions about what they want to do with their life that these messages are coming in all the time. Therefore, it takes a conscious, explicit effort to counteract them. We need to change the messages children receive as to who belongs, we need to change the messages children receive about innate abilities and we REALLY need to change the way math is taught and we need to start these processes very early. Students need to have inquiry-based, project-based mathematics learning experiences. Indeed, a deeper, sustaining mathematics learning experience and enjoyment come from actually “doing the mathematics” — applying the concepts to an authentic, relevant, real world context, similar to the experience that I had at Boeing.

*Caitlin: When and where did you get your initial math identity?*

Lorraine: Caitlin, I was born and raised in Shreveport, Louisiana and have been extremely fortunate and lucky with my mathematics experience. I attended segregated elementary public schools until my parents transferred my twin brother, younger sister and I to a parochial school during middle school from where we all graduated. I’ve always had a “love and knack” for numbers, so much so, that at a very early age, with a pencil and pad, I used to go house to house in my neighborhood and simply record the number of the street addresses. I didn’t know it was called “math identity”, but I knew then that I could ‘do’ math and that I ‘belonged.’ I had encouraging parents and extraordinary teachers in all academic subjects, especially in mathematics and I usually placed first in state mathematics competitions during my high school years. These experiences solidified my math identity.

*Caitlin: You mentioned that a strong math identity informs education and career choices. Has this been the case for you?*

Lorraine: Absolutely, it has, Caitlin. After completing my undergraduate studies at Penn, I was asked to continue my graduate studies in mathematics and was offered a Ph.D. graduate fellowship. Some will say that I defected from the mathematics “union”; but after much reflection, I opted to accept the Ph.D. offer from the Wharton School. At the time, Penn’s graduate mathematics curriculum was significantly theory and research based and I certainly would have gotten an even deeper grounding in the discipline. However, both my personality and interest were more geared to an applied problem-based approach. So, the Wharton experience, indeed, turned out to be an ideal balance of applied mathematics, economic theory and problem-solving for me.

*Caitlin: So where did this Wharton experience initially take you?*

Lorraine: Well, I decided to test the lights of another “big city” when a headhunter recruited me for a newly created Division Controller position at Columbia University in New York City. Here my mathematics and finance learning, training and experience really came together. Of course, I later went full speed ahead and worked several years with an investment firm on Wall Street, again using my mathematics and finance learning and training.

*Caitlin: So now it seems you’ve come full circle around to the education environment?*

Lorraine: Each investment or financial client is a specialized educational “project”; so, in a sense, I’ve always been involved in the education arena. But, yes, after serving on the university finance and education faculties at Wharton, the University of Tennessee, Knoxville, Drexel and Temple, I felt it important to bring these experiences to bear on today’s 21^{st} century educators and students, especially in seeking to incorporate the much needed project-based learning approach at the secondary level.

*Caitlin: So, as the incoming president of the **Women and Mathematics Education organization** (WME), is this the reason you have chosen “Strengthening Girls’ Math Identity” as the 2017-18 theme for the organization?*

Lorraine: Absolutely!

*Caitlin: Can you share the vision you have for this Girls’ Math Identity initiative?*

Lorraine: First of all, I am deeply honored and privileged to have been selected by my fellow board members to serve as President of WME, an international and intentional network of 250 (and still growing) teacher educators, researchers and practitioners dedicated to excellence in the teaching, learning and leading of mathematics. Our goal is to make change and especially in helping to solve the problem of girls not having a strong, positive math identity.

WME will celebrate its 40^{th} year Anniversary next year; and during my WME presidency over the next two years, I hope to lead the organization in becoming more vigilant and intentional in setting up partner networks and opportunities for teachers and students to connect and collaborate with businesses and community organizations in solving mathematical-oriented real world problems through project-based learning experiences.

I look forward in continuing my relationship with PHENND and connecting with partners in initiating PBL opportunities. This has great potential for empowering and engaging educators and students for 21^{st} century learning and career exploration.

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