Ubiquitous wireless laptops in upper elementary mathematics
Roy B. Clariana
Abstract
This quasi-experimental investigation considers the second year of implementation of wireless laptops (1:1 ratio) in three 6th grade mathematics classrooms in one school compared to non-laptop classrooms (5:1 ratio) in seven other schools in the district. Comprehensive mathematics software from CompassLearning delivered via the internet was structured by the teacher to align to state standards and replaced the print-based textbook. The seven non-laptop schools accessed the same software using desktop computers in the classroom and lab. In the laptop classrooms, students moved at their own pace, students assumed responsibility for their own learning, the teacher’s role shifted substantially towards one-on-one interaction with each student, there was increased record-keeping to monitor student’s progress, and the teacher was more willing to give responsibility for learning to the student. Analysis of achievement data showed that the laptop students significantly out-scored the non-laptop students on the four Quarterly Benchmark examinations (effect sizes ranged from 0.47 to 0.90), but not on the state examination, though the laptop school’s relative rank in the district improved. The relationship between required benchmark testing and state tests is discussed and recommendations for future implementation are provided.
(note: On march 5, 2008, this manuscript was accepted for publication in the
Journal of Computers in Mathematics and Science Education)
Ubiquitous wireless laptops in upper elementary mathematics
Arecent nation-wide survey (ADS, 2007) reports that in 2006, 31% of superintendents in the U.S.were implementing a 1:1 project (one computer per studentor ubiquitous computing) in at least one classroom in their district. This commitment to ubiquitous computing is consistent with a longer term trend. Anderson and Ronnkvist (1999) reviewed K-12 instructional computer use survey data from 1983 through 1998 (see Figure 1).
Figure 1. The historical trend of student to computer ratio in U.S. schools (Anderson & Ronnkvist, 1999).
Extrapolation of their data suggests that schools would reach a ratio of one computer for each student by 2002, though more recent data indicates that the student to computer ratio has flattened outat 3.8 students per computer nationally in 2006, and for internet connected computers, the ratio is 3.7:1 (Technology Counts, 2007). In addition, in 2006 in the U.S., 19.4% of schools’ instructional technologywere mobile devices (i.e., mainly wireless laptop computers) and that percentage is estimated to grow in 5 years to 52.1% (ADS, 2007).
Why level off at four to one now? Internal factors(e.g., costs, logistics, support, and infrastructure) and external factors (e.g., parents, community expectations, national bench marks, and other districts’ practices) drive local decisions. Also computer lab versus classroom access is a touchy issue. For both pragmatic scheduling reasons and for reasons related to teacher pedagogical beliefs, there has been a preference for placing computers in the classroom rather than in a lab. Today, when you visit a typical elementary classroom you will see three to five desktop computers lined up side-by-side along the back or side wall of the classroom.
But even if there is a will at the district level to place more computers into classrooms, there is usually not enough physical space, table space, or electrical outlets in most classrooms to accommodate more than five desktop computers. Because of size and infrastructure, it is impractical to use desktop computers in the central instructional area of the classroom. The bulk and form factor precludes desk space for working on other instructional materials or even clearly seeing the teacher in the front of the room. Thus infrastructure relegates desktop computers to a supporting role, at most, in our classrooms. Wireless laptops can overcome the classroom infrastructure problem (Lowther, Ross, & Morrison, 2003).
Recent investigations support the decades old findings of ACOT (2005) that 1:1 computers in the classroom influences a shift in teachers’ and students’ roles and responsibility. A report funded by Microsoft Corporation (Rockman, Chessler, & Walker, 1998) listed the following changes in1:1 laptop classrooms: (1) Teachers become facilitators, spending more time consulting and conferencing with individuals and groups of students (relative to the non-laptop ‘shadow schools’). Teacher surveysreflect this role change from a director of learning to a facilitator of learning.Teachers spend less time lecturing, 21% of classroom time compared to 34% in non-laptop classrooms,and laptop teachers commented that their classrooms were more student-centered. (2) Students become collaborators, the laptop students spend more time collaborating with their peers than non-laptop students.(3) Students direct their own learning and teachers felt that the laptop students were more able to work independently and to direct their own learning, with teachers assisting students as needed. And (4) laptop students report a greater reliance on active learning strategiesand used computers to accomplish complex school tasks.However, Windschitl and Sahl (2002) report that laptops alone are not sufficient to transform classroom practice, but can be a catalyst to enable teachers with constructivist leanings to move away from teacher-centered practice and towards more collaborative and student-centered learning tasks.
The “Traditional” Teacher-Directed Elementary Mathematics Classroom
Though there are plenty of exceptions, elementary school teachers teach mathematics at the “board”, and in today’s classroom, it is most often a whiteboard or occasionally an overhead projector, and increasingly it is a digital projector or SmartBoard(Beeland, 2002). Teachers use the board to write and solve problems and to direct student activities. Students come to the board to review homework and to work examples and receive feedback in front of the entire class. The teacher introduces a new concept at the board and then students work alone or together on the problems, and students check each others work and/or the teacher collects the work at the end of class to check and assign grades.
For example, Chávez–López (2003) extensively observed three upper elementary mathematics teachers and provides the following estimates of the average percent of class time spent in various activities, in order: first, warm up or homework review (10-20% of class time), then a teacher-directed lesson from the textbook (14-50% of class time), and finally, seatwork practice and homework (0-65% of class time), but also “other” including managerial and non-mathematics instruction (1-33% of class time). Though these teachers used different textbooks and had different philosophies regarding teaching and learning, all three followed what could be described as a “traditional” teacher-directed lesson model.
The primary instructional materials for upper-elementary mathematics in order of prevalence of use are textbooks, worksheets, manipulatives, and workbooks (Dynarski, Honey, & Levin, 2002, p. 15). The textbook serves as a curriculum map, source material, and ‘prop’ (Sosniak & Stodolsky, 1993) that teachers draw on (Freeman & Porter, 1989; Remillard, 2005). Because textbooks are designed for the nation as a whole and for a few large textbook-adoption states, textbook content must cover more than any particular state requires while being constrained by total page length (i.e., cost). Schmidt, McKnight, and Raizen (1997) describe this aspect of textbook content as being “a mile wide and an inch deep” (p.62). But state standards and mandated tests tend to shake-up the status quo (we mean in terms of mathematics content but it also likely supports a somewhat positivist stance). Teachers are forced to look closely at the textbook content and sequence, leaving out chapters and supplementing and re-sequencing other chapters as needed to ‘cover’ the mandated content (Remillard, 2005), a formidable and time-consuming task even for a district-level full-time mathematics education content specialist. During this period of scrutiny and transitionas teachers adopt new standards and evolving benchmarks, some school district leaders have considered replacing costly paper-based textbooks with equally costly laptop computers; for example the Vail Unified School District in Arizona, Henrico County School District in Virginia, and Johnson Elementary school in Dallas, Texas. Bernard (2007) has an active ongoing poll and blog posting internet site on this question, which on March 6, 2008 stands at 52% yes for replacing the textbook with laptops (619 votes) and 48% no (580 votes).
Combining all these trends, this quasi-experimental investigation considers the affects of providing sixth-grade mathematics students with 1:1 wireless laptop access to comprehensive mathematics software lessons from CompassLearning LLCaligned to state standards and to the evolving district benchmark tests. Results of the investigation will be used to inform future instructional and policy decisions.
Method
Participants
All eight elementary schools in one district in north-eastern Pennsylvania were included in this investigation, one school was the 1:1 wireless laptop school and the other seven were the non-laptop controls. The laptop school was chosen from the eight schools because its’ performance on the state test was near the district mean and because this school’s mathematics teacher volunteered to participate in the laptop project. Student participants in the laptop school (n = 66) and the seven non-laptop schools (n = 653) consisted of all of the students in sixth grade in the district.The total elementary school population is predominately white (77%) with 20% Hispanic and 2% black, 52% are male and 48% female, and 43% receive free lunches and 10% receive reduced cost lunches. The laptop school is predominately white (94%) with 4% Hispanic and 2% black, 58% are male and 42% female, and 36% receive free lunches and 15% receive reduced cost lunches. About 8.5% of students in the district are special education and/or assigned individual education plans.
The district implemented this analysis in order to inform future policy and planning related to computer access in the district. The district provided the data for this study “off the shelf” to the researcher and allowed access to observe the classrooms.
Treatments
In the seven control schools, our general impressions are that the day-to-day sixth-grade mathematics instruction corresponded fairly closely to the description given byChávez–López (2003). In general, after initial settling of the students, there was a sustained review of homework problems or of seat work from the previous class, next followed a teacher-directed lesson with a substantial amount of student board work and then students worked independently (usually on worksheets) on the topic covered on the board. Finally, the teacher would assign mathematics homework for next time (see the top portion of Figure 2).Occasionally these non-laptop students moved as a group to the school computer lab to work on CompassLearning mathematics lessons.
In the laptop school there were three sixth-grade subject area teachers (e.g., mathematics, language arts, and science/social studies) and each teacher is the homeroom teacher of about 23 students. Students moved from class to class during the day usually with their homeroom group. Each class period was 85 minutes long. Thus the mathematics teacher saw three separate mathematics classes each day, interacting with about 70 students in total (all of the sixth grade students).
Figure 2. Flowchart depicting “traditional” teacher-directed classrooms (top) and the 1:1 laptop classrooms (bottom). The length of the box represents the relative amount of time spent in each activity.
These 1:1 laptop classrooms were as “teacher-directed” as the more traditional mathematics classroomsmentioned above, but actual classroom activities differed and the teacher’s role was critically and substantially different (see the bottom portion of Figure 2). We observed the following classroom activity on two separate visits. Unlike the control schools, the laptop classrooms did not review mathematics homework as a whole-class activity, so first, after settling in, the teacher taught a 10-minute lesson at the board to the whole class. He selected the lesson topic (i.e., adding fractions and then working with improper fractions) based upon recent common errors that he observed in students’ work during the one-to-one teacher time, but sometimes he may review a past topic that he knows from experience is central or difficult. As an outsider, what I observed next was rather surprising; all of a sudden with barely a comment from the teacher, things began to happen. Students automatically began independent work; some collected a wireless laptop from the charger at the back of the room to use at their desk, some began a worksheet that they collected from a bin file system at the side of the room, some updated their progress chart at the front of the room, some worked on a unit test, some helped others one-to-one with work, and some lined up at the teachers desk. At the teacher’s desk, a small group of students stood in line as the teacher worked one-to-one with each student for about 3-5 minutes each on a paper-based completed worksheet or unit test. The teacher immediately scored the work (or test) in the student’s presence, and if an item was incorrect, he would ask the student to explain the item. (He reported later that if their verbal explanation was conceptually correct, he awarded full credit. If their explanation was incorrect, he would review the topic one-on-one then and there. If the revised explanation now was adequate, the student would receive the grade and check-off that activity on the quarterly progress wall chart; if the responses were still not adequate, the teacher would assign additional work.) Students continued working independently till near the end of class time, when they put away laptops and worksheets and the teacher reviewed accomplishments.
The quarterly progress report wall chart is an important classroom artifact. The wall chart listed students’ names down the first column and listed lesson activities across the top row. Students initialed boxes as they completed each task and so the wall chart looked like a bar chart turned sideways with some students’ bars longer than others. The teacher reported that he had spent a significant amount of personal time in the previous summer establishing a sequence of lesson activities that addressed the state standards. Specifically, here-sequenced CompassLearning software, worksheets, and quizzes to match the four quarterly progress reports, and worksheets and quizzes were duplicated in quantity and filed in classroom bins with the same numbering system and sequence as the quarterly progress report chart.This approach is consistent with the district’s Quarterly Benchmarktesting requirements and the implementation of data-driven decision making. Also, this teacher did not use a textbook at all. Because this teacher designed this intended curriculum, he had great ownership and at the same time, it met the district’s requirements.
Several substantial contrasts between the “traditional”teacher-directed classroomsand this 1:1 laptop classroom were noted. First, the laptop was the primary source of new instruction. The teacher’s day-to-day direct instructionconsisted ofbrief finely targeted whole-class instruction, some small group instruction, and a substantial amount of personal one-to-one instructionand remediation with each student (Pitre, 1999). Note that achievement advantages for the laptop classrooms may be due to this relatively large amount of individualized teacher-studentcontact and not necessarily the laptop. On the other hand, the software freed the teacher from ‘generic’ whole group direct instruction and so allowed for this individualized attention.
Unlike the teacher-directed classroom where students are all working on the same topic at the same time, in this laptop classroom, some students worked much faster than others (Clariana, 1992). Thus the classroom quarterly progress report was essential for maintaining records but also served a motivationalfunction. Essentially, in this environment, accountability for mathematics achievement shifted from the teacher, who must “cover” content, to the student who must learn mathematics. For example, during a one-to-one desk review, I heard a student apologize to the teacher for missing a problem. The teacher replied intentionally in a voice that the whole class could hear, “You don’t need to apologize to me, you’re the one who will be taking the PSSA [state mandated] test.”As an outsider, it seemed to me that the 85-minute periods passedveryquickly (especially relative to visits to traditional classrooms where the class time seems to go by slowly).
Mathematics Online Software
Instructional software licensed from CompassLearningaccessed online through an internet web browserwas selected several years earlier for district-wide implementation. The software package included a comprehensive amount of reading-language arts, writing, and mathematics lessons. In all schools, teachers and district staff worked to align the software lessons to the district benchmarks and state standards. All eight schools had access to the software using 4 or 5 desktop computers in each classroom and also in each school’s computer lab. All labs had sufficient computers so that whole classes could utilize 1:1 access when it was their scheduled time to go to the lab.