Description
The lesson in review was designed for third grade students participating in an after school program. Students selected for the program demonstrated need for intervention in the areas of both mathematics and literacy. The program coordinator admitted students to the program based on reading level and GMADE scores. Homogeneous student groups consisted of up to twelve students who attend four forty-five minute sessions divided between two days. The intended standards addressed in the lesson from the MA Curriculum Framework included:
· “Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.” (P.42)
· Fluently add within 1000 using strategies and algorithms based on place value.” (P.46)
The lesson design incorporated the use of two specific technology programs. The Base Blocks Addition applet intended to allow students a visual representation of the addition process. The applet selected provided a picture explaining commonly used terminology such as carrying to the next place value. The second program, IXL, offered students an opportunity to apply the addition process illustrated with the Base Blocks Addition applet. Additionally, IXL collected data on student performance recording the amount of time spent working on problems, the number of problems answered both correctly and incorrectly, and student responses to specific questions. The lesson plan allotted time for whole-group and individual time to demonstrate and investigate the Base Block Addition applet. Students used IXL individually and the data collected by the program used to assess student understanding of the indicated standards. No changes were made to the original lesson plan prior to implementation.
Narrative
The initial two student groups who participated in the lesson described above comprised students with the lowest reading level and GMADE scores of all the student groups. The lesson and objectives were introduced to the group using the SMART Board to demonstrate the applet and discuss place value and addition strategies using place value. Students expressed interest in the applet and all wanted an opportunity to use the manipulative on the SMART Board. Students were selected throughout the demonstration of how the applet worked to both explain the next step in the process and perform the described step using the SMART Board. After seeing student interest in using the applet with the SMART Board, the decision to modify the original plan was made. Instead of sending students to individual computers to investigate the Base Blocks Addition applet, the group remained together taking turns explaining steps of the addition process and using the manipulative. After modeling the features of the applet and students collectively demonstrating how to use the applet to model and solve addition problems, students proceeded to individual computers and began applying the strategies for solving addition problems. Allocating more time for the introduction of the applet as a whole group, the lesson ended with student work on IXL. The closing discussion described in the original lesson plan was rescheduled to begin the next lesson before allowing additional time for students to complete problems using IXL.
Reflection
The intended objectives for the lesson included: modeling numbers with three digits using base blocks, modeling and solving addition problems with numbers up to three digits, and explaining how place value can be used to solve addition problems. Underlying assumptions about knowledge involved connecting representations to help develop concepts. Affordances and constraints of the knowledge presented are discussed in conjunction with the benefits and drawbacks of selected technologies in a following paragraph. The planned demonstrations of both Base Blocks Addition and IXL represented information processing. Although student led, the group discussion falls into the information processing category. Constructivism was evidenced as students investigated the Base Blocks Addition applet individually and figured out how to use the tool to solve addition problems.
The lesson designed was used as an intervention for low-achieving students. The lesson’s objectives and goals align with those specified in the curriculum for third grade mathematics. Student differences in learning were addressed offering the option of using the Base Blocks Addition manipulative to solve problems. IXL also differentiates difficulty level by increasing difficulty as students correctly solve problems. The virtual manipulative also addressed differences in learning styles by including numeric and visual representations. The significance of the tool remains in that the applet highlights the connection between the numeric and visual representation offering insight into the addition process.
The class discussion provides an opportunity for instructors to gauge student understanding of place value and the process of adding numbers with up to three digits in addition to the feedback individualized IXL reports offer. To be successful, IXL reports would demonstrate increased progress toward mastering the skill and students could explain mathematical ideas such as grouping, carrying, and decomposing numbers.
The technology identified for the lesson on addition of two numbers up to three digits served a variety of purposes. First, the virtual manipulative played a critical role in helping students develop an understanding of the addition process by connecting common numeric representations with a visual representation. The visual representation additionally offered students an image to refer to when explaining or discussing addition problems. The applet communicated the content visually for students and allowed student manipulation of the blocks, both of which an advantage. One disadvantage of the applet related to grouping or decomposing blocks. Students were intrigued by this feature of the applet yet the feature remains limited. For example, students wanted to move a block from the thousands place to the ones place; the applet only decomposed blocks one place-value lower. The design of the blocks which represented specific place values were also advantageous for helping define each place value. Many students referred to blocks in the tens column as “longs.” When asked how long those blocks were, students could count the unit block markings to help develop an understanding of place-value name meanings.
Second, IXL offered a platform for students to apply the strategies using grouping for addition problems as well as an assessment tool for the instructor. Affordances of IXL included individualized problem sets which progress in difficulty based on student performance. Additionally, the program provided a variety of reports for analysis of student progress indicating information such as incorrect responses and mastery of skills. One drawback of coupling the Base Blocks Addition applet and IXL involved the reporting feature. Creating and solving the given problem with the applet increased the amount of time taken on each problem. IXL uses length of time to solve a problem as an indicator of student progress toward mastering a skill. Looking forward, the Base Block Addition applet may be better used early on in presenting grouping strategies for addition and encouraging students to rely less on the tool as their understanding develops.
Second, IXL offered a platform for students to apply the strategies using grouping for addition problems as well as an assessment tool for the instructor. Affordances of IXL included individualized problem sets which progress in difficulty based on student performance. Additionally, the program provided a variety of reports for analysis of student progress indicating information such as incorrect responses and mastery of skills. One drawback of coupling the Base Blocks Addition applet and IXL involved the reporting feature. Creating and solving the given problem with the applet increased the amount of time taken on each problem. IXL uses length of time to solve a problem as an indicator of student progress toward mastering a skill. Looking forward, the Base Block Addition applet may be better used early on in presenting grouping strategies for addition and encouraging students to rely less on the tool as their understanding develops.
The lesson also included other technologies such as the internet and SMART Board. The SMART Board enabled an interactive demonstration of the applet’s features and the internet integral with the use of web-based technologies; however, the applet could have been demonstrated without the SMART Board. Both SMART Board and internet were technologies used as a medium to access the applet and IXL but were not intended to significantly impact learning. The most unique and significant contribution of the selected technologies remained the connections between numeric and visual representations for modeling addition.
Students were excited to use the Base Blocks Addition applet. The applet helped facilitate a whole-group discussion about place value and the addition process. Student questions predominantly hinged upon features of the applet. For the student who wanted to decompose the thousand-block, I asked how many blocks would be in each of the remaining columns to redirect and help connect how many groups of ones, tens, and hundreds make a thousand.
