Introduction - The intention of this study is to see if some concepts from a Flipped or Inverted classroom may have an impact on a learning issue within two 6th grade mathematics classes.
Individuals Involved in the Case - Myself and the students described below will be the only individuals involved throughout the study. If necessary, the SPED department may assist with the accommodated students during assessments. Also, there is a teaching coach who had been working with some some newly identified students (see rise scholars below) but she was pulled to be a long term substitute. If she becomes available, her input and assistance will be greatly appreciated.
Earlier in the year, I advised the principal of this final course, as well as the Internet-based resources which I found through previous coursework which would be useful within the classroom to support student learning.
School Description and Population - The school setting is in Prince Georges County Public Schools, a suburban Washington, D.C. county in the state of Maryland. Prince Georges county has a total population of 881,138 (U.S. Census, 2014). This majority African American county is one of the most affluent and educated in the country where the median income is over $73,000, with 85.6% of residents being high school graduates or higher, and 29.5% holding a bachelor’s degree or higher.
The school is a Parent Choice Public Charter School with a total enrollment of 444 students from kindergarten through eighth grade. Ninety-five percent of the students are African-American, with the remaining 5 percent considered multiracial (Maryland Report Card, 2014). There are an average of 24 students in each classroom.
School Technology - Though a technology solution will be used to assist the students in gaining understanding of area and perimeter, the resident technology is seriously outdated. There is an onsite computer lab in the library which has limited connectivity during school hours, and there are no specified hours for the classroom teachers to utilize the lab. Within the past two weeks, the staff and families were notified the school will be moving since the technology is inadequate to handle the requirements of the new PARCC assessments being implemented in the State of Maryland.
There are only 5 total classroom computers with inconsistent connectivity to the Internet due to infrastructure issues. These computers are over 10 years old and load very slowly and often have issues with outdated software. The software cannot be upgraded due to either licensing, blocking or hardware issues. Because there is limited access to technology in the classroom, the solution will be based on at-home computer access. If students indicate they do not have access to the Internet, they will be given access to the classroom computers if they are available and functioning.
Specific Student Population - Though the 6th grade population as a whole seems to share at least some aspect of the proposed learning issue which will be studied, within the total group of 51 students there are four IEP students and five 504 students which will be designated with an asterisk (*).
In addition to the students in need of accommodations, there are 7 additional who have been identified through standardized testing as "rising scholars," indicating they need intervention to overcome poor performance in core concepts. There are students who have previously been identified as Talented and Gifted students. Students who work below grade level will be denoted with a minus sign (-) for below, and TAG students will be noted with a plus sign (+) for above grade level.
With respect to the detailed description of this population, there are times when students stay with different family members, and do not have reliable internet connections. This could impact results on assessments also. There are also a number of students who inconsistently submit work, and though given opportunities to make up work and assessments, this opportunity is not taken. The students who have missing work could skew initial findings as well as final results, and will not be included for the purposes of this study. The total number of students remaining following the removal of the 12 students with missing work is 39 students, 20 students from morning class, and 19 students from the afternoon class.
Earlier in the year, I had advised the principal of this final course, as well as the Internet-based resources which I found through previous coursework which would be useful within the classroom to support student learning.
Learning Issue - The learning issue is the students’ inability to consistently find the area and perimeter of polygons. "Consistently," is a keyword here, since the students seem to grasp the concept, but do not retain it on future assessments. At the beginning of the school year, during review and placement testing, a number of students were not able to find either the area of a rectangle, the perimeter of a rectangle or both. More than one student stated “perimeter is addition and area is multiplication.” In fact, during a more recent diagnostic, more than one student stated the same thing with respect to addition and multiplication referring to one but not the other calculation.
The school uses Saxon(c) Math, and is in an accelerated curriculum, where the students are in a 7th grade, course 2 mathematics book in 6th greade. Saxon (c) Math continues to practice learned skills through the school year, rather than introducing a topic, learning the concept, assessing and moving on to a new topic.Surprisingly, the majority of the students have been with one another since kindergarten participating in the Saxon(c) Math program, which presumably, would lend itself to familiarity and consistency of instruction. One would think this would assist the students in maintaining concepts, to be reinforcing them consistently throughout the school year. Under different circumstances, had Saxon (c) Math not been used, the issue may not have presented itself until the topic came up in subsequent lessons or in preparation for testing or end of year exams.
At the beginning of the year, and more recently, students could not come up with the formulas without assistance. Even when the formulas are presented and and then practiced on assessments, many students reverse the required formulas between area and perimeter. Also, if the students are asked to find the area and perimeter of a shape other than a simple rectangle, for example, two adjacent rectangles combined to make an "L" shape, the concept is not applied to a problem which is not exactly like the problems they have learned previously. When demonstrations are given showing perimeter’s additive and multiplicative components, this seemed to confuse rather than clarify, depending on the student.
Throughout the year, the students have been polled to describe what area and perimeter are in words, or to draw pictures; they seem to have difficulty doing this consistently. For example, area could be described as space taken up by the tiles on the floor, or the amount of sod for grass on a playground. Perimeter could be described as the trim around the outside of the edges of the room, or the distance of the fence around a field. This concept was also used in science, where the students had to develop scaled drawings of their room at home, the classroom and a model playground. The needed to determine the area of the amount of carpet or grass, and the perimeter of the dimensions of the room and the playground area.
Even when students use the correct formula, it seems to be hit or miss whether or not they will persist in getting it correct and choosing the correct formula, on subsequent assessments. With all the diverse approaches to addressing the understanding of area and perimeter, and the persistent re-teaching of the concept, it stands out as a learning issue for this class.
It does not seem to be just one of the three particular learning pathologies Shulman speaks of in the Change article, but rather all three, amnesia, fantasia and inertia (Shulman, 1999). Some students merely forget, as in "amnesia" and once reminded of the formulas, can evaluate a variety of shapes with diverse unknown quantities (Shulman, 1999). Other students demonstrate "fantasia," where they believe they understand this familiar topic, but never really understood it to begin with (Shulman,1999). The student who states "area is multiplication and perimeter is addition" demonstrates this pathology. Finally, a number of student have "inertia" where the area and perimeter are "...not forgotten; nor are they in some intrinsic sense wrong..." as with amnesia and fantasia. The idea of the concept is simply not saved in a coherent fashion related to something the students already know, to be recalled and processed.
Proposed Technology Solution - The proposed solution is to use some aspects of the Flipped or Inverted Classroom and technology-based PBL which the students can access off campus or on school computers if possible.
Background - One of the primary components of a true Flipped or Inverted Classroom is online learning at home.The instruction can be teacher created, or the instructor can assign lessons which are Internet-based. Online discussions can also be an integral part of what takes place outside of the conventional school setting. Time spent in the classroom consists of student-centered projects, discussions or other activities leading to mastery of concepts. In this capacity, the teacher assists and advises rather than leading and instructing (Tucker, 2012).
For the purposes of this study, unlike the model developed by Bergman and Sams, lecture-based instruction will still take place in the classroom since lecture is the current model desired by the school where the study is taking place. However, this study does bear resemblance to the classroom where the flipping was initially conceived, since there is a deficit in student exposure to instruction. In the case of Bergman and Sams, students were missing classroom instruction, and the teachers found it difficult to find the time to reteach and compensate for what was missed. In the case of this study, students are missing engaging instruction due to technology infrastructure issues at the school.
In considering the pathologies of learning mentioned previously, it has been brought to my attention this particular group of students has had consistent and persistent behavior problems in the classroom since kindergarten. Though this may seem unrelated to the learning issue, due to the prevalent behavior problems, there was apparently inconsistency with instruction. Though the teachers were supposed to essentially follow the script as prescribed by the Saxon Math method, some did and some did not. Surprisingly, a number of students and parents indicated the year immediately preceding 6th grade, the mathematics teacher would let them use their books and notes to take tests. The individuals, not surprisingly, were many of the same individuals who are newly identified as not having mastered core concepts for the previous grade.
Solution - The first component of the solution is to use have the students use an online applet, which they can manipulate at their own pace in investigate the difference between area and perimeter. Next students will be assigned specific Learn Zillion (c) instructional videos for homework. Differentiation will be addressed through the self-paces aspect of accessing these resources. The student will be given a certain window for completion taking into account some students may complete them all at one sitting, while others may take a week or more. Additionally, for students who need additional intervention, Videos can be uploaded to ESL Videos, and short multiple choice questions can assess understanding of the core similarities and differences between area perimeter.
Once students are given the conceptual tools to understand area and perimeter, they will create a paperslide video which demonstrates the concept to others. The students have to come up with the "script" of how to solve an area and perimeter problem, write out the script, and describe the background, misconceptions, concepts and processes to others in the form of a video of instructions on paper. Basic length and width forms can be demonstrated, as well as finding missing dimensions, and finding area and perimeter of irregular shapes.
The paperslide videos will be uploaded to ESL videos, and an assessment will be attached to the video with multiple choice questions derived by the students to determine if the viewers understand area and perimeter.
Relative Advantage - The technology solution for the variety of learning pathologies, has to have variety also in order to be effective. Learning for these students cannot be passive, as the passive learning from the text has not been successful. Likewise, the media for the students has been simply books and work sheets, and this methodology is also ineffective. A variety of active, online resources will be used within the objectives to make the learning more effective (Peters, 2009). The idea behind the variety of Internet based presentations of concepts stems from what Brown said about learning on the web. The focus is not so much on the "what" of area and perimeter, but on the "how" students will learn it (Brown & Adler, 2008).
