Integrated Assignment By: Hannah Summitt, Nicole Hilbig, and Andrew Davis

1. Integrated Assignment By: Hannah Summitt, Nicole Hilbig, and Andrew Davis Integrated AssignmentBy: Hannah Summitt, Nicole Hilbig, and Andrew Davis

2. Case Study #1: Alexis Case Study #1: Alexis

3. 30 25 20 Alexis ’ s trend - line 15 Digits Correct in 2 Minutes 10 X 5 Alexis ’ s goal - line X 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Weeks of Instruction Analyzing Alexis’s Problem What do you notice about Alexis’ progress with math computation?

4. Computation Progress Graph Analysis • Alexis’s progress is at a much lower slope than the slope of her goal line • She is approximately 6 digits behind where she needs to be to meet her end of the year progress goal • After 8 weeks of monitoring her teacher as determined there is a definite discrepancy between actual progress and her goal line • An instructional change must be made as of week 8

5. Computation Skills Profile Analysis • In what areas is Alexis struggling?

6. Computation Skills Profile Analysis Shows Significant Progress in this area: A1 , S1, F1, F2 Shows Less than Significant Progress in this area: M1 , M2, D1 Shows Definite Lack of Progress in this area- Cause for Concern: M3, D2, D3

7. Computation Skills Profile Analysis: Continued • Alexis is progressing satisfactorily in A1, S1, F1, and F2. • Here is a brief description of these categories in which Alexis is doing well: • A1: multidigit addition with regrouping • S1: multidigit subtraction with regrouping • F1: add and subtract simple fractions with like denominators • F2: add and subtract whole numbers and mixed numbers • Alexis is progressing less than satisfactorily in M1, M2, and D1. • Here is a brief description of these categories in which Alexis is progressing • slightly below the desired level: • M1: multiplication facts, factors to 9 • M2:multiply a two digit number by a one digit number • D1: Division facts, factors to 9 Shows Significant Progress in this area: A1 , S1, F1, F2 Shows Less than Significant Progress in this area: M1, M2 , D1 Shows Definite Lack of Progress in this area- Cause for Concern: M3, D2, D3

8. Computation Skills Profile Analysis: Continued • Alexis’ progress is severely lacking and indicates cause for concern in these categories: M3, D2, D3 • Here is a brief description of these categories in which Alexis struggling: • M3: multiply a two digit number by a two digit number • D2: Divide 2-digit numbers by a 1-digit number • D3: Divide 3-digit numbers by a 1- digit number Shows Significant Progress in this area: A1 , S1, F1, F2 Shows Less than Significant Progress in this area: M1, M2 , D1 Shows Definite Lack of Progress in this area- Cause for Concern: M3, D2, D3

9. How Areas of Concern Correlate to NCSCOS Standards The areas in which Alexis is struggling correlate to the standards specified in the North Carolina Standard Course of Study as described below:

10. Notes on Home Environment Information gathered from forms filled out by parents at the beginning of school year: • Transportation Home: Rides bus home after school each day • Homework Environment: Alexis’ parents indicated that she would be doing her homework when she arrived home each afternoon Information gathered from parent teacher conference for 1st six weeks: • Alexis stays home alone while parents are at work each afternoon • Parents make sure Alexis has completed homework but do not review answers • There is not an adult or sibling at home whom Alexis get ask for help while doing homework in the afternoon • Parents feel Alexis is most likely struggling during homework and doesn’t want to bother them by asking for help when they get home from work

11. What Conclusions Can You Draw Concerning Alexis’ Situation? • What might be causing Alexis to struggle in these areas: • M3: multiply a two digit number by a two digit number • D2: Divide 2-digit numbers by a 1-digit number • D3: Divide 3-digit numbers by a 1- digit number How might Alexis’ homework environment be contributing to her problem?

12. Conclusions Drawn from Alexis’ Situation Conclusions related to category M3: • Alexis is progressing slightly below desired level for M1 and M2, she is most likely not ready to be successful with 2-digit by 2-digit multiplication and needs some additional practice with 1-digit by 1-digit and 2-digit by 2-digit • Should be gradually moved up to 2-digit by 2-digit multiplication Conclusions related to category D2: • Alexis is making progress with simple division (D1), but may not yet have sufficient fluency with division facts and factors 1-9 to be successful with 2-digit multiplication- needs more practice with simple division • Considering Alexis’ similar difficulty with 2-digit multiplication, she may be struggling with using the standard algorithm (i.e. lining numbers up in place value columns)

13. Conclusions Drawn from Alexis’ Situation Conclusions related to category D3: • Until Alexis is successful with 2-digit division (D2) she is not ready to be successful with 3-digit division • Lack of proficiency with simple division and using the standard algorithm are most likely sources of difficulty. Conclusions related to lack of homework help: • Alexis is struggling with division and multiplication problems during homework, and has no one present to help her in the afternoons. • This difficulty with homework is causing her to fall behind even more due to lack of successful practice in solving multiplication and division problems. • Alexis may not be retaining knowledge of simple multiplication and division as well as desired because difficulty with homework is causing her to devote less time and attention to the simple review problems included in each night’s homework

14. Alexis- Specific Learning Disabilities • M3 – She struggled some with M1 & M2 which • shows she might not be ready to multiply 2 by • 2 digits yet. • Needs more practice with 1 by 1 and 2 by 1 multiplication problems • D2 - Alexis is making progress with basic division • but does not have enough understanding with 1-9 division facts to compute 2 digits. • May struggle with lining up the problems • D3- She has difficulty with dividing with 2 digit numbers which will lead to difficulty with 3 digits.

15. What are some instructional changes that could be made for M3?M3: multiply a two digit number by a two digit number

16. M3 • Differentiate worksheets, quizzes, word problems until Alexis has mastered 1 by 1 and 2 by 1 multiplication problems • Has one-on-one help with teacher • During whole class instruction, do think alouds that does not assume everyone knows 1 by 1 or 2 by 1 facts • When lining up or collecting papers, ask a quick multiplication fact • When Alexis finishes early or comes in early, let her play computer games that involve simple multiplication facts

17. What are some instructional changes that could be made for D2?D2: Divide 2-digit numbers by a 1-digit number

18. D2 • Use some of the same changes used for multiplication • Show/model using the algorithm more ( large and clear problems on the board) • Use the virtual manipulative website either at home or in the mornings http://nlvm.usu.edu/en/nav/vlibrary.html • Give Alexis her own manipulative set to work on problems and on homework • Give her fewer problems but have her draw out how she did the problem with the manipulatives

19. What are some instructional changes that could be made for D3?D3: Divide 3-digit numbers by a 1- digit number

20. D3 • Let Alexis use manipulatives on tests and quizzes • Use the manipulatives place value column chart to help understand traditional algorithms • Give problems on columned paper to help her transition to common algorithms

22. What advice do you have about the homework situation?

23. Homework Help • Conference with parents to mention afterschool program and coming before school to review on the computer • Send home tips and manipulatives to use on homework • Flashcards

24. Case Study #2: Brandon

25. Analyzing Brandon’s Problem Brandon’s Goal Line What do you notice about Alexis’ progress with math concepts and applications?

26. Concepts and Applications Progress Graph Analysis • Brandon’s actual progress is significantly below his goal line • He is approximately 4 digits behind where he needs to be to meet his end of the year progress goal • After 8 weeks of monitoring his teacher as determined there is a discrepancy between actual progress and his goal line • An instructional change must be made as of week 8

27. Concepts and Applications Skills Profile Analysis In what areas is Brandon struggling? A1 S1 M1 M2 M3 D1 D2 D3 F1 F2

28. Computation Progress Profile Analysis A1 S1 M1 M2 M3 D1 D2 D3 F1 F2 Shows Significant Progress in this area: A1, S1, M1, M2, M3, D1 Shows Less than Significant Progress in this area: D2, D3 Shows Definite Lack of Progress in this area- Cause for Concern: F1, F2

29. Computation Skills Profile Analysis: Continued • Brandon is progressing satisfactorily in A1, S1, M1, M2, M3, D1. • Here is a brief description of these categories in which Brandon is doing well: • A1: multidigit addition with regrouping • S1: multidigit subtraction with regrouping • M1: multiplication facts, factors to 9 • M2:multiply a two digit number by a one digit number • M3:multiply a two digit number by a two digit number • D1: Division facts, factors to 9 • Brandon is progressing less than satisfactorily in D2, D3. • Here is a brief description of these categories in which Brandon is progressing • slightly below the desired level: • D2: Divide 2-digit numbers by a 1-digit number • D3: Divide 3-digit numbers by a 1- digit number • *Note that this lack in desired progress is very slight and not a major cause for • concern Shows Significant Progress in this area: A1, S1, M1, M2, M3, D1 Shows Less than Significant Progress in this area: D2, D3 Shows Definite Lack of Progress in this area- Cause for Concern: F1, F2

30. Computation Skills Profile Analysis: Continued • Brandon’s progress is severely lacking and indicates cause for concern in these categories: F1, F2 • Here is a brief description of these categories in which Brandon is struggling: • F1: add and subtract simple fractions with like denominators • F2: add and subtract whole numbers and mixed numbers Shows Significant Progress in this area: A1, S1, M1, M2, M3, D1 Shows Less than Significant Progress in this area: D2, D3 Shows Definite Lack of Progress in this area- Cause for Concern: F1, F2

31. How Areas of Concern Correlate to NCSCOS Standards The areas in which Brandon is struggling correlate to the standards specified in the North Carolina Standard Course of Study as described below:

32. Notes on Home Environment • Information gathered from forms filled out by parents at the beginning of school year: • Transportation Home: Grandmother picks Brandon up after school each day • Homework Environment: Brandon’s parents indicated that he would be doing his homework each afternoon while staying at his grandmother’s house , and that grandmother would supervise homework completion • Information gathered from parent teacher conference for 1st six weeks: • Brandon is doing homework at grandmother’s each afternoon • Grandmother informed parents that she makes sure Brandon completes homework but does not review answers • Grandmother also informed parents that Brandon does not request homework help • Parents feel Brandon is most likely struggling during homework and simply doubts his grandmother can help him.

33. Anecdotal Notes Taken During 8 Week Progress Monitoring • Week 3: September 16th I watched Brandon attempting to solve the following fraction problem: 1/3 + 1/2 = Brandon made facial expressions indicating that he was struggling. I asked Brandon “How is this problem going Brandon?” He replied “I just don’t get these fractions. They just aren’t making sense to me.” I assisted Brandon in solving this problem by walking him through reviewing and correcting his model. Interpretation of Situation: Brandon is significantly frustrated by this unit on fractions. (note- this is an interpretation, not fact.)

34. What Conclusions Can You Draw Concerning Brandon’s Situation? • What might be causing Brandon to struggle in these areas: • F1: add and subtract simple fractions with like denominators • F2: add and subtract whole numbers and mixed numbers How might Brandon’s homework environment be contributing to his problem? How might Brandon’s frustration be contributing to his problem?

35. Conclusions Drawn from Brandon's Situation General Conclusions : • Brandon typically does well in math and is doing well in math and his difficulty with fractions is being worsened by the resulting frustration he is experiencing • Fractions are just not “clicking” with Brandon, some change in instruction must take place to allow Brandon to grasp and succeed with fractions at the level he grasps and succeeds with other math concepts Conclusions related to categories F1 and F2 : • Due to the fact that other math concepts have come easily for Brandon, and that he was successful with division which contains the basic concept of dividing amounts equally that is essential to understanding fractions, the problem most likely lies in the type of models and algorithms Brandon is being shown • Brandon’s frustration and negative opinions of fractions is another significant obstacle which can only be overcome by providing Brandon with positive experiences working with fractions

36. Conclusions Drawn from Brandon’s Situation Conclusions related to lack of homework help: • Brandon is struggling with fraction problems during homework, and is not requesting help from his grandmother in the afternoons. • This difficulty may be causing him to feel more frustrated and to fall further behind • Brandon may feel his grandmother will not understand or know about the methods and strategies his teacher has taught him to use with fractions, such as modeling

37. Instructional Approaches to Helping Brandon Needs most help with the following learning objectives: F1- Add/subtract simple fractions, like denominators F2 – Add/subtract whole numbers and mixed numbers

38. What are some instructional changes that could be made for Brandon?

39. Instructional Approaches for Brandon • Goal: Find a best approach to overcome his frustration with fractions. • Best approach: Use fun and engaging techniques • Computer Games: A great website for Brandon to use is the following: • http://www.sheppardsoftware.com/mathgames/fractions/fracTut1.htm • It includes a great interactive tutorial, as well as a ton of fun games to play the keep learning fun! • Since Brandon is especially strong in other areas, whenever he finishes early we should let him work on these activities to allow him to get extra practice and make the most of his time.

40. Instructional Approaches Continued • Allowing Brandon to work with partner due to strength in some areas and weaknesses in others • Differentiated homework assignments • Allow Brandon to work on the basics of fractions such as finding common denominators, however include some easier fraction addition problems sprinkled in. • Online virtual manipulative programs • http://nlvm.usu.edu/en/nav/frames_asid_106_g_2_t_1.html?from=category_g_2_t_1.html • After going through the tutorial, the above manipulative game could be a very effective way to reinforce how to find lowest common denominators, then to add the fractions.

41. Additional Instructional Approaches • Brandon might have trouble visualizing fractions so it would be smart to allow him to work with more than just the arithmetic and manipulatives. http://www.sheppardsoftware.com/mathgames/fractions/FruitShootFractionsAddition.htm

42. Additional Instructional Approaches • As with any student, providing them with authentic material that they can relate to is the best way to keep them interested. • Therefore as the teacher it would be wise to find out what Brandon is most interested and develop word problems or diagrams which would keep Brandon as engaged as possible. • 1-on-1 After-School tutoring if possible.

43. References • Cannon, Larry. (2010). Fractions-Adding-NLVM. In Utah State University. Retrieved 12/5/2011, from http://nlvm.usu.edu/en/nav/frames_asid_106_g_2_t_1.html?from=category. • Krech, B. (2000). Math: Model with Manipulatives. Instructor, 109(7), 6. This article discusses the advantages of teaching math with manipulatives. The instructional changes for both of the case studies suggested incorporating manipulatives into the student’s math lessons. Manipulatives are a great way to be hands on and to show exactly how the problem is being solved. Some learners need this type of interaction to fully understand the material. Mark, P. (2009, October 26). ONLINE MATHS IS FUN AND GAMES. Evening Standard. p. 32. Researcher Mark Prigg states that “The secret to online success in education, it seems, lies in the playing of games.” Prigg goes on to explain how this generation of children is extremely drawn to computer games and has an uncanny amount of talent and ability to learn from these types of games. Prigg notes that these games are an incredibly successful teaching tool, especially for mathematics content. The attraction of these math games lies in the competitiveness that is created by the constant need to improve one’s high score and progress to the next level. In all actuality, this type of drive to improve is the heartbeat of education assessment and RTI. For this reason, online games that review and teach concepts about fractions and computing addition and subtraction with fractions are one of the instructional changes our presentation suggests to help Brandon. For students who are frustrated or lack motivation in math, such as Brandon’s situation with fractions, online games are a fresh opportunity to have a positive experience with math content.

44. References Continued NC Standard Course of Study. Public Schools of North Carolina. October 17th, 2011 <http://www.ncpublicschools.org/curriculum/>. Unknown Author. (2010). Fun Kids Online Math Games. In Sheppard Software. Retrieved 12/5/2011, from http://www.sheppardsoftware.com/math.htm#fractions. Unknown Author. (2010). Math Games: Fractions Tutorial. In Sheppard Software. Retrieved 12/5/2011, from http://www.sheppardsoftware.com/mathgames/fractions/fracTut1.htm.