Abstract

The focus of this research project is to identify best practices in eighth-grade mathematics teaching and learning. Our methodology is to identify school systems who face high poverty, yet whose students reach high levels of achievement as indicated by the Georgia Milestone Assessment System (GMAS). Within the 29 Georgia counties with the highest poverty rates in the state, we identified four counties with the highest percentage of students performing proficient and above on the GMAS. Teacher survey results at the high-performing middle schools in these counties reveal the importance of continuous assessment, grouping strategies, high expectations, technology use, strong curriculum, and a variety of instructional methods. In addition, the surveys indicate that in order to meet the specific needs of students in poverty, schools need to: (1) address students' nutritional needs, (2) provide supplies to students, (3) seek out families in need and immediately provide help, (4) demonstrate to students that you care about them, (5) increase the curriculum at school in order to decrease homework expectations, and (6) obtain external technology grant.

From 2003 to 2015, the state of Georgia has continuously closed the gap with the nation in 8th-grade math performance as measured by the National Assessment of Educational Progress (NAEP). During the past 2 years, this improvement has stalled. So, how can we start narrowing the performance gap again?

One way of improving overall performance is to identify low performing groups of students and determine how to better reach them. Children living in poverty are more at risk of underperforming when compared to their counterparts not living in poverty. Research conducted by the NAEP showed nationally that only 18% of 8th grade math students who were eligible for the National School Lunch Program reached the level of at or above proficient, while the overall percentage of 8th grade math students in the nation who reached the level of at or above proficient was 32% (NAEP Report Cards). In Georgia, only 15% of 8th-grade math students eligible for the National School Lunch Program performed at the level of at or above proficient, while the overall percentage of 8th-grade math students in Georgia who reached the level of at or above proficient was 28% (NAEP Report Cards). Clearly, poverty is a major impediment to success in mathematics.

Is it possible that the performance gap between Georgia and the nation could be narrowed again if more students in poverty began to perform at a proficient level? By identifying high performing schools in high-poverty areas, we can determine the reasons for this high performance, in order to better reach math students in Georgia who live in poverty.

Methodology

In the U.S. Quick Facts: Persons in Poverty, the U.S. Census Bureau divides the counties of Georgia into five categories based on the percentage of people living in poverty with the lowest percentage category of 5.7-14.9% and highest percentage category of 26.8-39.2%. There are 30 Georgia counties in the category with the highest level of poverty. According to the Quick Facts, Clarke County is a high poverty county. However, research indicates that poverty rates are over-reported in towns near a large university, as in Clarke County's case, University of Georgia. Therefore, we excluded Clarke County from our study (Benson & Bishaw).

NAEP assessment data does not break down scores by county. Therefore, to identify which of the 29 counties have high-performing schools, we studied the Georgia Milestone Assessment System (GMAS) from the Georgia Department of Education, which publishes the results of the GMAS by county. In order to select the high-performing counties, we chose counties with at least 40% of students scoring at or above proficient on the GMAS. We chose this minimum value as it is significantly higher than the overall state's percentage of 34.5% (Georgia Department of Education). According to the 2016-2017 Georgia Milestones Statewide Scores Spring 2017 School Summaries, there are four counties of the 29 high-poverty counties which significantly exceeded the state of Georgia's percentage of students at or above proficient (Georgia Department of Education). See the table below.

The Georgia Department of Education also provides assessment data for all the schools within these high-performing counties. The Spring 2017 Georgia Milestones End-of-Grade Assessment for these schools is shown in Table 2.  

Table 2- Georgia Milestone High-Performing Schools

We emailed the survey below to the eleven 8th grade math teachers at these schools.

If we did not receive a response, we repeated the request two more times. After sending the survey request three times, five of the eleven teachers responded.

Results of the Surveys

When asked about instructional methods or other aspects that the teachers deemed important to their students' success, we found that most of the teachers stressed the importance of assessments, grouping strategies, high expectations, and technology. Some also referenced their curriculum and actual instructional methods.

The first main focus was assessments, mainly formative assessments. These formative assessments varied in timing at different locations in the lesson. For example, Mauri Jarrard, an 8th-grade math teacher at Telfair County Middle School, uses an informal or formal assessment prior to covering new content. This enables her to determine the student's background knowledge and fill in any missing skills. Sabrina Rentz, another 8th-grade math teacher at Telfair County Middle School, utilizes formative assessments during the lesson. Rentz stated, "Students have numerous opportunities to show what they know during the lesson by utilizing an array of assessments, such as stick-its, whiteboards, thumbs-up/down, agree/disagree, Socrative app, and Quizizz. These results are used to gauge my students' understanding of the content and adjust instruction." Eighth-grade math teacher, Siterro Wheeler, mentioned another opportunity to use formative assessment. After exposing her students to the new content one day, the next day Wheeler uses a formative assessment to determine daily grouping for students. This enables the students to practice the new ideas learned on the first day of the lesson. Another location of formative assessment use is at the end of the class. Not only does Jarrard begin the new content with an assessment, she also ends each day with one in order to assess the students' learning of the content introduced that day. Some of her practical examples are: ticket out the door, think-pair-share, writing assignment to explain their learning for the day, and demonstrating understanding of the content via a hands-on activity.

Not only are teachers at the high-performing schools conducting formative assessments, they are also continuously assessing informally during the lesson. Wheeler is constantly rotating throughout the classroom. This allows her to be able to assist any student as needed while they complete their independent practice. She also repeats and asks questions about the topic throughout the lesson. Additionally, Wheeler has students summarize the main vocabulary terms and main concepts as a class. Likewise, Rentz informally assesses while students work in groups together. Informal assessment allows both of these teachers to determine what their students know or where they are lacking understanding so they can adjust as needed.

Secondly, the teachers heavily utilize grouping strategies. The surveyed teachers use formatives assessment to group students. Rentz said, "All groups are created with a purpose. Sometimes I utilize heterogeneous groups to allow for peer tutors and at other times I use homogenous groups with leveled work that matches their abilities." This method allows the grouping to be fluid and benefit all students. Wheeler also describes her use of formative assessment for grouping as, "A formative assessment is given to the students to determine daily grouping. Based on the formative assessment, students either work independently on a rigorous assignment or they work in a small group led by me to strengthen their understanding of the concept."

Thirdly, the teachers attributed their students' success to high expectations. Rentz stated, "It is my belief that another major impact on my students is the high expectations that I hold for them regardless of their ability levels. My classes are grouped based on ability and my lower achieving class is exposed to everything my other classes are. They are expected to be able to succeed with the same content as everyone else. I use the assessments to see what parts of it I need to differentiate, but I never decrease work amount as differentiation. The type of differentiation that I utilize has students learning the same material and practicing on the same material, but maybe in different ways. I require them to dig deeper into the content and expand on that. High expectations play a tremendous part in student success. They are going to perform to the expectations you have for them." A teacher, who asked to remain anonymous, echoed Rentz by saying, "Students must be held to a high standard. Expect every student to excel." Not only should individual teachers convey high expectations, the whole school should also hold each student to a high standard. Wheeler praised her school for conducting a major school-wide initiative that "raised the bar for all students." This included implementing PBIS school-wide and having teachers create lessons that are "rigorous and challenging while meeting the needs of every student." From reading the teacher responses, communicating clear and high expectations to the students is a major key to their success.

The fourth major aspect of student success mentioned by many of the teachers is the use of technology. Technology is a way to keep students engaged. Additionally, technology is very mobile and versatile. Walker uses it for students to practice tests online through the academic software Study Island. Rentz and Jarrard stress the importance of giving every student access to some form of technology. "We expose our students to various forms of technology. Our students have access to Chromebooks, iPads, SmartBoards, and calculators. The SmartBoard is used almost daily to provide instruction and occasionally used for student activities. Each math teacher has a class set of iPads that can be used for assessment and activities", stated Jarrard. Likewise, Rentz expresses, "We use technology on a daily basis in the classroom to increase student success. The iPads are used for different performance tasks, review activities, and assessments. By incorporating technology, we are able to reach more of our students and keep them actively engaged."

Fifth, the teachers stressed the importance of a strong curriculum. When discussing curriculum, every teacher varied in his or her response. Some use only the Georgia Performance Standards and supplement with various resources. One teacher mentions, "When looking for resources, the focus is to solidify the understanding of the content and to provide appropriate rigor." Similarly, another teacher revealed that she uses the Georgia Performance Standards and the Engage New York (ENY) curriculum. "I really like the ENY approach because it is more rigorous, and the methods are mathematically sound. The curriculum is based on the deep understanding of mathematical concepts rather than just procedures," she said. On the other hand, one uses Glencoe Math by McGraw-Hill as her main math curriculum. She states, "It helps me as a teacher to be better prepared to differentiate my instruction, which in turn will help the students achieve success." After reading all of these responses, there was another aspect that was intriguing. Bethune Middle School has created two math classes for the 8th graders. Walker states, "Our principal made a crucial decision in 2014-2015, he added a support math class to 8th grade during the first year of GMAS, so 8th graders had two math classes. In one class, students learn the standards through units. The support math class is used to reinforce concepts and do extra practice. In my opinion, the addition of the second math class has been the reason for our higher than the state's percentages in the proficient and exceeding levels of the mathematics GMAS. I really believe the reinforcement during the 2nd math class in addition to the extra hour of practice has made the biggest difference in the scores."

Lastly, the teachers reported using a variety of instructional methods to meet the needs of their students, such as:

(1) Direct instruction.

(2) Interactive notebooks.

(3) Discovery of patterns to aid in the development of algorithms.

(4) Modeling procedures.

(5) Thinking maps.

(6) Manipulatives

(7) Constant review

Addressing the Needs of Students Living In Poverty

In order to address the needs of students living in poverty, the high-performing schools, oftentimes in collaboration with their school systems, seek and utilize external partners and consider the special needs of students living in poverty. In particular, the respondents credit the following for impacting student learning and success at their schools:

(1) Providing for the nutritional needs of their students.
All respondents stressed the importance of meeting the nutritional needs of their students. Students are provided a free breakfast and lunch. According to Rentz, "Students living in poverty may only receive a warm meal at school. By providing students with the nutrition that their bodies need, we are helping fuel their brains and increase focus and memory retention in the classroom." Some schools provide food beyond the regular work week to ensure their students are not in want. Wheeler states, "Several students are given sack lunches to take home on the weekends because of lack of food within their homes."

(2) Providing supplies to students.
In partnership with members of the community, employees of the Telfair County schools host a beginning of the year kick-off event at the county recreational department. At this event, parents receive the supplies their child will need for the school year. In addition, Jarrard shares, "Our school has a supply room with supplies provided by various local churches, businesses, and people throughout the community. Our students have access to these supplies whenever they are needed."

(3) Seeking out families in need and immediately providing help.
At Johnson County Middle School, Wheeler states, "All faculty and staff go above and beyond to ensure that students are learning and succeeding. If there is an issue, we quickly act upon it by contacting the necessary people to help find a solution to the issue. We have a representative that seeks out families in need and she makes sure those students needs are taken care of immediately."

(4) Demonstrating to your students that you care about them.
One teacher stressed that "you must have empathy for what your students go through every day. Students must know that you care about them and understand that you expect them to excel" in order to break the poverty cycle.

(5) Increasing the curriculum at school in order to decrease the homework expectations based on the situation at home.
One teacher states, "I rarely give homework because most of the time there is no help at home." At Bethune Middle School, Walker states, "the factor that has had the major impact on test scores besides sound math instruction is the extra math class. The higher rigor of common core math requires students to spend more structured time using and applying what they learned. Before, students had to find time at home to review, but most parents are unable to help their children in this new math."

(6) Obtaining external technology grants.
Telfair County Middle School was awarded a technology grant that provided each math classroom with a SmartBoard and a classroom set of iPads. According to Rentz, "Most students who live in poverty are not fortunate enough to have access to this type of technology.

Conclusion

By studying schools in high-poverty areas that have achieved high levels of student success, we have found the following key components of success: continuous assessment, grouping strategies, high expectations, technology use, strong curriculum, and a variety of teaching methods. We believe that all students at all schools in Georgia will benefit from these components of success. Further, all schools have at least some students who live in poverty. In order to address their specific needs, our study found that schools and school systems need to: (1) address students' nutritional needs, (2) provide supplies to students, (3) seek out families in need and immediately provide help, (4) demonstrate to students that you care about them, (5) increase the curriculum at school in order to decrease homework expectations, and (6) obtain external technology grant.

Acknowledgments: We wish to thank the 8th-grade math teachers Mauri Jarrard and Sabrina Rentz at Telfair County Middle School, Suraya Walker at Bethune Middle School, Siterro Wheeler, and an anonymous teacher for both their dedication to their students as well as their willingness to take the time to provide well-thought-out responses to our survey. We also thank the principals Danny McCoy at Bethune Middle School, Christopher Ellis at Telfair County Middle School, and Elaine Merritt for connecting us with these excellent teachers.

References

Benson, C., & Bishaw, A. (2017, December 07). Examining the Effect of Off-Campus College Students on Poverty Rates. Retrieved April 09, 2018, from https://www.census.gov/data/tables/2017/demo/income-poverty/acs5yrs.html

Georgia Department of Education. (2017, July 20). Georgia Milestones 2016-2017 Statewide Scores. Retrieved February 19, 2018, from http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Pages/Georgia-Milestones-2016-2017-Statewide-Scores.aspx

The Nation's Report Card. (n.d.). NAEP Mathematics. Retrieved February 10, 2018, from https://www.nationsreportcard.gov/math_2017/#states/scores?grade=8

United States Census Bureau. (n.d.). U.S. Census Bureau QuickFacts: United States. Retrieved March 01, 2018, from https://www.census.gov/quickfacts/fact/map/US/IPE120216#viewtop

Dr. Gregory Harrell is a Professor in the Department of Mathematics at Valdosta State University. He is interested in facilitating success for all mathematics students from kindergarten to college graduation. He earned his M.A. in Mathematics at the University of Georgia and Ph.D. in Instruction & Curriculum with a specialty in Mathematics Education from the University of Florida.

Anna Joy Holton is currently attending Valdosta State University. She is pursuing a bachelor's degree in Middle Grades Education with concentrations in Mathematics and Social Studies. She is currently completing her student teaching in an 8th grade Pre-Algebra class and will graduate with Honors in December of 2018.

A new school year always brings with it the excitement of a new group of students and renewed energy to plan and teach engaging lessons that not only meet the standards but also prepare students for their life after high school. Teaching the traditional "Three R's", Reading, Writing, and Arithmetic, leaves students lacking the skills they need for the 21st century. In addition to subject matter knowledge, today's students must be skilled in critical thinking, communication, collaboration, and creativity (the "Four Cs") (National Education Association, 2010). Educators must complement their subject matter content with the "Four Cs" to prepare young people for citizenship and the global workforce (National Education Association, 2010). The "Four Cs" can be incorporated into any classroom, but it requires educators to be intentional and purposeful in their planning. If students are going to be equipped with 21st-century skills when they graduate high school, they must have been provided opportunities to develop these skills throughout their schooling.

Unfortunately, there is not a single resource that educators can implement in their classroom that will address all of the 21st century needs of their students. The flood of technology resources provided for educators is vast. Sorting through the plethora of resources in order to find the perfect combination that will address all of the "Four Cs" in one lesson will most likely leave the educator feeling defeated and overwhelmed. However, the skills students need for the 21st century, critical thinking, communication, collaboration, and creativity, can be addressed by taking advantage of technology, utilizing group activities, assigning project- and problem-based learning, and most importantly, sharing resources.

Opportunities to think critically and problem solve are essential in the mathematics classroom. These learning experiences push students from "doing" mathematics to "understanding" mathematics. Problem-based learning and project-based learning are great ways for math educators to increase critical thinking in their classroom. These learning opportunities should incorporate inductive and deductive reasoning, require students to interpret information and draw conclusions, and solve unfamiliar problems in both conventional and innovative ways. Robert Kaplinsky's website (https://robertkaplinsky.com) is an excellent source for a list of free real-world problem-based lessons that encourage critical thinking.

Communication represents a variety of interactions in the classroom. "Expressing thoughts clearly, crisply articulating opinions, communicating coherent instructions, motivating others through powerful speech--these skills have always been valued in the workplace and in public life. But in the 21st century, these skills have been transformed and are even more important today" (National Education Association, 2010, p. 13). While important, face-to-face communication is no longer the primary way students interact with each other. They must continue to be taught how to communicate with someone face-to-face, but must also be equipped with the skills to communicate virtually and with people from different backgrounds. In a mathematics classroom, students should be communicating with the educator and other classmates through multiple platforms. These could include email, Google classroom, class website, making individual and group presentations inside and outside of the classroom, creating a blog, and discussing assignments with students in another state or country, to name a few. The G Suite for Education by Google provides numerous ways for students to communicate in and outside of the classroom.

Addressing the "Four Cs" individually can be difficult. Through many of the communication examples listed above, students are engaging in collaboration. In a mathematics classroom, students must be required to work in diverse teams to develop a solution to a real-world problem. Fifty years ago, many jobs could be completed individually. However today, much work is accomplished in teams, and in many cases, global teams (National Education Association, 2010). Through the use of resources similar to Google docs and Padlet, students can collaborate with classmates or students across the world. These learning experiences provide students with the opportunity to strengthen their collaboration skills.

Time constraints often impede the ability to incorporate opportunities to strengthen students' creativity. However, in the math classroom, creativity can easily be integrated into the class by creating an environment where students are encouraged to develop innovative ways of solving a problem and are praised for sharing their original solution. Math educators should incorporate problems into their classroom that can be solved using multiple methods or have multiple solutions. This encourages students to use a wide range of skills and think outside of the box. Students should have access to materials inside the classroom so that they can creatively problem solve. Additionally, students should be encouraged to use a variety of technology resources, such as building a website through Google sites, creating a movie using an iMovie, or comic strip through canva.com.

Integrating the "Four Cs" into the mathematics classroom does take some research and planning, but these efforts will benefit students as they prepare to enter the current workforce. Educators should not feel overwhelmed by attempting to address all of the "Four Cs" in one lesson. Instead, educators should focus on one or two of the "Four Cs" and slowly integrate new technology resources into their classroom. Incorporating technology resources, group activities, project-based, and problem-based learning in the mathematics classroom will help to develop the skills students need to be successful in the 21st century.

References

National Education Association (2010). Preparing 21st Century Students for a Global Society: An Educator's Guide to 'The Four Cs'. [online] Washington DC: National Education Association. Available at: http://www.nea.org/assets/docs/A-Guide-to-Four-Cs.pdf [Accessed 24 Jul. 2018].

Dr. Julie Carter is an assistant professor within the Department of Teacher Education and Social Work at Middle Georgia State University. She has experience teaching high school math. Her research interests include instructional technology and self-efficacy.

Dr. Rhonda Amerson is an assistant professor within the Department of Teacher Education and Social Work at Middle Georgia State University. She has 23 years of classroom experience in grades 2-8, and her research interests include instructional practices, integrated curriculum, and classroom management.

The 59th annual Georgia Mathematics Conference
October 17-19, 2018

GMC 2018 Keynote Speakers