Information About Circles and Pairs





People



Organizers


Dr. Mark Tomforde
UCCS



Dr. Lauren Nelsen
Colorado College





Facilitators and Tutors


Sam Caro, Colorado College (Thursdays)
Ella Engel, Colorado College (Thursdays)
Kristen Gearhart, UCCS (Tuesdays and Thursdays)
Lauren Nelsen, Colorado College (Thursdays)
Jonathan Thompson, UCCS (Tuesdays and Thursdays)
Mark Tomforde, UCCS (Tuesdays)
River VanIwaarden, UCCS (Tuesdays and Thursdays)
Yvonne Zino, Colorado College (Thursdays)







 





Schools

Circles and Pairs is currently working with Galileo Middle School, a middle school located in Colorado Springs.






 





Activities

There are two primary components to Circles and Pairs: Math Circles and One-On-One Tutoring. In both components, Circles and Pairs puts students into direct contact with professors, graduate students, and undergraduates, all of whom serve as teachers and mentors.


Math Circles: Math Circles are group problem solving activities that emphasize creativity, collaboration, and discovery-based learning. The topics introduced are designed to generate excitement, expose students to mathematics they often do not see in the classroom, and encourage the students to study more mathematics in middle school, high school, and college. The lessons are designed to foster interaction through hands-on activities and discovery-based learning. Students frequently break into groups of 2 or 3 to work on problems and explore topics, and there are several professors, UCCS graduate students, and UCCS undergraduate who serve as facilitators to help with the activities. We also encourage students to explain their solutions to others and to develop effective communication skills when talking about technical subjects.

The mathematics problems we give in Math Circles are designed to provide challenging, enriching experiences for students, while simultaneously building critical thinking skills. Often the problems we give seem more like puzzles or games than traditional math problems.

Some sample problems:
  1. If 10 people at a party each shake hands with every other person, how many handshakes occur?
  2. Is it possible to cover a chessboard with rectangles of size 3x1?
  3. If a disease infects 1 in 10,000 people, and you test positive for the disease using a test that is 99% accurate, what is the probability you actually have the disease? (Hint: It is not 99%.)

Math Tutoring: Circles and Pairs provides one-on-one tutoring during which the students can work on their math homework, prepare for exams, or do enrichment problems. Tutoring is staffed by volunteers who are undergraduate and graduate students at UCCS.




 




Mission


Fact: Mathematics ability is distributed uniformly throughout the population.

In particular, a person's gender, race, and socioeconomic status have no effect on innate mathematical ability or potential to do well in mathematics or mathematically-related disciplines.


Problem: Women, minorities, and low-income students are vastly underrepresented in all areas of mathematics, science, engineering, and technology.

Since many women, minorities, and low-income students do not get the opportunity to develop their potential in math and science, the talent of many people is squandered. This loss of potential results in fewer discoveries, overlooked innovations, and delayed development of science and technology. When only a fraction of the population is free to contribute, we all miss out.

The lack of qualified workers in mathematically-related fields has become a critical national issue. Despite decades of effort and millions of government dollars spent to change this situation, women, minorities, and low-income students remain vastly underrepresented in science and math-related fields.


What We Believe: Every student deserves access to a top-notch education and the ability to pursue that education unhindered. Moreover, society will be more innovative and prosperous if everyone has equal opportunities to pursue mathematics and science.


Our Mission: The Circles and Pairs mission is to address the critical issue of underrepresentation in math and science, and create pathways for underserved students to become mathematicians, scientists, engineers, and programmers.


What We Do: We provide Math Circle lessons and tutoring each week. More details on can be found in our Activities Section.


Goals of Circles and Pairs: You can find details in our Goals Section.


Why Math? Since Circles and Pairs wishes to encourage students to pursue STEM fields, you may wonder why we focus on mathematics. The primary reason is that mathematics is a prerequisite to all STEM fields. A solid foundation in mathematics is necessary in all areas of science, engineerings, and technology, and without it many doors remain closed. Indeed, many college students who wish to be doctors or engineers end up leaving their major due not to bad grades in their major, but rather difficulty with the required mathematics for their major classes. Mathematics is ubiquitous and necessary in the study of subjects relevant in our modern, technology-driven world.

There are also several additional benefits to teaching mathematics in Circles and Pairs.

(1) Students must often pass certain standardized tests in order to advance grade levels and graduate from high school. For most struggling students it is the math portion of the exam (as opposed to other sections, such as science or english) where the students have the lowest scores. Consequently, lack of mathematics knowledge is often the number one obstruction for a student to graduate from high school. This problem is exacerbated in struggling or underserved high schools, where the discrepancies between scores in math and other subjects are even greater. In a nutshell, quality math education is a serious need in many schools, particularly in underserved communities.

(2) Mathematics is a prerequisite for any college-level study of science, engineering, technology, computer science, medicine, or several other subjects. This is why almost everyone in college is required to take one math class, and many majors require multiple. It's also one reason why the SAT focuses on two areas: English and Math. Mathematics is fundamental, and knowledge of mathematics provides opportunities. A good mathematical background can substantially improve a student's scores on college entrance exams, helping the student to get into a better school or to receive more scholarships. Mathematics opens the doors to college.

(3) In addition to the technical topics taught in math courses, mathematics can also be used to teach critical reasoning, problem solving, logic, and general quantitative literacy. Mathematics provides useful skills and leads to clarity of thought. It can also inspire curiosity and creativity. It helps students to understand how to think and how to learn, and its skills are useful and transferable to many other situations.

(4) Mathematics can be taught without expensive equipment, computers, labs, or materials. It is easy to give quality math education with very little funding, and what we do in Circles and Pairs can also be replicated by teachers or administrators in the partnering schools without requiring them to spend money or purchase additional resources.




 




Goals


We have three main Outcome Goals for the students in that participate in Circles and Pairs:
  1. Graduate from High School.
  2. Attend College.
  3. Consider Majoring in a STEM field.

Educational Objectives

In addition to the three Outcome Goals above, we want the students in Circles and Pairs to develop qualities that will make them more successful in academic pursuits. This includes (1) acquiring Grit, (2) cultivating a Growth Mindset, (3) developing Positive Attitudes Towards Mathematics, and (4) practicing Habits of Mind that aid in critical thinking.

Grit
Grit is defined as "perseverance and passion for long-term goals". Individuals with high levels of grit are able to remain determined and motivated over long periods of time regardless of obstacles, challenges, or adversity. Over the past decade, research by Dr. Angela Duckworth at the University of Pennsylvania has shown that grit is a much better predictor of success than any of the previously used predictors such as intelligence, family income, innate ability, or scores on standardized achievement tests. Duckworth also developed a short questionnaire to measure grit, and in a study involving thousands of juniors in Chicago public schools, it was found that students with high grit scores on this questionnaire were significantly more likely to graduate. In addition, other studies have established positive relationships between grit and educational attainment, GPA, and retention in college. Duckworth has said that it is still uncertain how to build grit in students, but one of the best ideas she has found involves developing a growth mindset; i.e., the belief that the ability to learn is not fixed.

Here are some resources for learning more about grit.

Growth Mindset
Research has shown that a student's mindset dramatically affects learning and can be used to predict academic trajectories. In a series of studies conducted over 20 years, Dr. Carol Dweck at Stanford University divided people into two groups: those having a "fixed mindset", who believe character, intelligence, and creative ability are static qualities that we cannot change in any meaningful way, and those having a "growth mindset", who believe these qualities can be cultivated and expanded through effort and that people can improve and grow through practice and experience. Dweck's studies showed that people with a growth mindset accomplished more, pushed themselves harder when encountering difficulty, and overall were more successful and happier.

Interestingly, Dweck's work also showed that regardless of what the the facts are regarding the malleability of intelligence and ability, students with a growth mindset (i.e., students who believe that these qualities are malleable) actually perform better. A large component of developing a growth mindset involves informing students that they can change -- for example, telling students that their mental capabilities can grow through practice or experience, that mistakes and failure are opportunities for learning, and that their levels of accomplishment are not predetermined. Likewise, it is important to help students develop Self-Efficacy (i.e., a belief in one's own ability to complete tasks and reach goals). It has also been shown that cultivating a growth mindset is one of the best ways to build grit. This is because students with a growth mindset believe that ability to learn is not fixed and can change with effort. Consequently, they are much more likely to perservere when they encounter challenges because they do not view failure as a permanent condition. Studies have supported this, and shown that telling students that they can grow, improve, and change, or convincing students that success is within their capabilities, can have a dramatic affect on their levels of grit, how hard they work, and their overall performance.

Here are some resources for learning more about growth mindset.

Positive Attitudes Towards Mathematics
Many of the students in Circles and Pairs have had difficulty with mathematics in the past or suffer from math anxiety. We give the students the opportunity to see aspects of mathematics that they typically do not get to experience in their school classroom, and we provide a supportive and welcoming environment for exploring these aspects. We want students to see a side of mathematics they have never encountered before, and to re-evaluate their attitudes towards mathematics.

Even if students do not attend college or major in a STEM field, we want them to understand that in our increasingly technical and scientific world, developing basic quantitative literacy will help them in many aspects of their lives and jobs.


Habits of Mind
We want Circles and Pairs students to become better learners and more effective problem solvers. We accomplish this by having the students practice Habits of Mind that are useful in learning and in thinking.

Practicing these Habits of Mind helps students to be more aware of the process of learning and to take a more active role in their educations.


When tutoring students we use best practices, informed by research on education and cognitive science, to make our efforts as effective as possible. The following handout (created by Nicky Case and dedicated to the public domain) is a nice summary of what cognitive science tells us really works when it comes to learning:

How Do We Learn?


Links to References cited in the handout:


OTHER COMPONENTS

In addition to the Outcome Goals and Educational Objectives listed above, there are several other components to Circles and Pairs and additional purposes we hope the program will serve.


Mentoring Students
By having professors, graduate students, and UCCS undergraduates involved in Circles and Pairs as instructors, facilitators, and tutors, we provide the students in Circles and Pairs with a vertically integrated system of mentoring. The students interact with successful undergraduates in STEM, who are often just a few years older than they are, as well as with graduate students and professors who can provide more experienced advice, guidance, and instruction.

In addition, we provide a great deal of individual attention to the students. We typically have multiple UCCS professors, graduate students, and undergraduates at each lesson. In many of our meetings the ratio of students to instructors and facilitators is 2:1. We also make efforts to get to know the students personally, and provide a great deal of individual instruction, supervision, and feedback. We view mentoring as a critical aspect of the program, and we encourage the students to interact with the instructors and facilitators and engage in dialog on all topics.


Serving the Community and Broadening Access to Education
Part of the mission of the UCCS is to "broaden access to higher education for the benefit of southern Colorado, the state, nation and world." By promoting mathematics education, we are responding to one of the most immediate educational needs of our surrounding community.


Involving Underrepresented Groups in Mathematics
Certain groups are severely underrepresented in mathematics and STEM fields. These include ethnic minorities (e.g., African-Americans, Hispanics, Native Americans and Indigenous Peoples, certain Asians such as Vietnamese and Filipinos), women, and first-generation college students. We believe these populations provide a valuable untapped resource for mathematics and our nation, and that we would all benefit if more individuals from these groups were to become involved in and contribute to mathematics and mathematically-related fields.












Copyright © 2021     Made with by Mark Tomforde.