Assessment of early arithmetic skills based on a developmental stage - PDF document

Assessment of early arithmetic skills based on a developmental stage model Dominique Arndt, Katleen Sahr, Maria Opfermann, Annemarie Fritz, Detlev Leutner University of Duisburg ‐ Essen Overview •Screening & Marko ‐ D: Sample tasks of all five model stages on both test sets •Empirical results: Reliability & Rasch analysis 2 Theory Tests Current Research

Screening & MARKO ‐ D Screening Stage V Stage IV The ability to distinguish small sets Stage III and to count and enumerate them Marko ‐ D Stage II Stage I 3 Theory Tests Current Research Screening & MARKO ‐ D Screening Stage V Stage IV The ability to: � name predecessor and successor of a given number on a mental number line Stage III � solve addition tasks with small numbers Marko ‐ D by counting or by making use of the Stage II number line Stage I 4 Theory Tests Current Research

Screening & MARKO ‐ D Screening Stage V Stage IV Understanding the connection of number and set in a Stage III cardinal number concept Marko ‐ D Stage II Which number comes right before / after six? Stage I 5 Theory Tests Current Research Screening & MARKO ‐ D Screening Stage V Stage IV � Part ‐ part ‐ whole concept � Organizing the Stage III knowledge of breaking and Marko ‐ D assembling sets Stage II Could you please give me 5 stones? 3 of them shall be red! (Red & blue stones provided to the subject) Stage I 6 Theory Tests Current Research

Screening & MARKO ‐ D Screening Stage V Write the number which is 3 less then 7 on the first line! Stage IV The understanding of congruent intervals Stage III between numbers on the number line Marko ‐ D Stage II Stage I 7 Theory Tests Current Research Empirical results Screening: – Kindergarten subtest: α = .819 (Number of items: 18) – 1st grade subtest: α = .830 (Number of items: 18) – 2nd grade subtest: α = .778 (Number of items: 18) – Test fitted the Rasch model (Weighted Fit MNSQ < 1.2 for 32 items) with person ‐ separation ‐ reliability of .864 Marko ‐ D: – α = .916 (Number of items: 61) – Test fitted the Rasch model (Weighted Fit MNSQ < 1.2 for 61 items) with person ‐ separation ‐ reliability of .945 8 Theory Tests Current Research

Empirical results – Rasch analysis Marko ‐ D Screening Stage V 5 X| | X| X| XX| X| XX| 5 X| 4 XXXX| XX| XXXXXX| XX| XXXXX| XX| XXXXXXXXXX| XXXXXXXXXX| 4 XX| Stage IV XXXX| 3 XXXXXXXXXXXXXXX| XXXX| XXXXXXXXXXXXXXXXXX| XXXXXX| 25 26 XXXXXXXXXXXXXXXXXXXXXX| 43 43 48 49 55 3 XXXXXXX| 20 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 51 XXXXXX| XXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 20 20 47 50 XXXXXXX| 19 2 XXXXXXXXXXXXXXXXXXXXXXXX| 22 2 22 26 2 XXXXXXX| XXXXXXXXXXXXXXXXXXXXXXXXXX| 24 2 24 29 XXXXXXXXX| 30 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 46 46 XXXXXXXXX| 32 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 38 38 XXXXXXXXX| 24 31 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 45 45 53 56 1 XXXXXXXX| 22 22 23 27 28 29 1 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 2 2 30 30 33 33 37 44 44 57 XXXXXXXX| 21 21 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 31 32 42 32 42 Stage III XXXXXXX| 18 18 XXXXXXXXXXXXXXXXXXXXXXXXX| 16 1 16 19 XXXXXXXXX| XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 41 41 0 XXXXXXXXXX| 0 XXXXXXXXXXXXXXXXXXXXXXXXX| 3 8 3 8 18 XXXXXXXXXXXXXXXXXXXXXX| 17 17 XXXXXXXXX| 14 14 XXXXXXX| 16 16 1 17 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 5 27 5 27 39 39 52 54 61 61 XXXXXXXX| 2 2 XXXXXXXXXXXXXXXXXXXXXXXXXX| 6 11 6 11 60 60 - 1 XXXXX| 3 1 10 11 15 11 15 XXXXXXXXXXXX| 13 14 28 14 28 XXXX| - 1 XXXXXXXXXXXXXXX| 4 12 4 12 XXXXX| 1 12 13 XXXXXXXXXXXXXXXX| 23 4 23 40 XXXX| 5 5 XXXXXXXXXXXXXXXX| 59 59 - 2 XXX| 8 Stage II XXXXXXXXXXXX| 15 15 XX| 4 4 XXXXXXXXXXXXX| XX| - 2 XXXXXXXXXXX| X| XXXXXXXXX| 36 36 - 3 X| 7 7 9 9 XXX| 9 35 9 35 X| 6 6 XXXXXX| 34 34 X| XXX| 21 25 58 25 58 | - 3 XX| 1 7 1 7 - 4 | X| | | Stage I | Red = Kindergarten subtest - 4 | | 10 10 9 Theory Tests Current Research Empirical results – Rasch analysis Marko ‐ D Screening Stage V 5 X| | X| X| XX| X| XX| 5 X| 4 XXXX| XX| XXXXXX| XX| XXXXX| XX| XXXXXXXXXX| 4 XX| XXXXXXXXXX| Stage IV XXXX| 3 XXXXXXXXXXXXXXX| XXXX| XXXXXXXXXXXXXXXXXX| XXXXXX| 25 26 26 XXXXXXXXXXXXXXXXXXXXXX| 43 48 48 49 49 5 55 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 51 3 XXXXXXX| 20 XXXXXX| XXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 20 47 47 50 50 XXXXXXX| 19 2 XXXXXXXXXXXXXXXXXXXXXXXX| 22 26 26 2 XXXXXXX| XXXXXXXXXXXXXXXXXXXXXXXXXX| 24 29 29 XXXXXXXXX| 30 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 46 XXXXXXXXX| 32 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 38 XXXXXXXXX| 24 31 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 45 53 53 56 56 1 XXXXXXXX| 22 2 22 23 27 28 29 29 1 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 2 2 30 30 33 33 37 44 44 57 57 XXXXXXXX| 21 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 31 32 32 42 42 Stage III XXXXXXX| 18 XXXXXXXXXXXXXXXXXXXXXXXXX| 16 19 19 XXXXXXXXX| XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 41 0 XXXXXXXXXX| 0 XXXXXXXXXXXXXXXXXXXXXXXXX| 3 8 18 18 XXXXXXXXX| 14 XXXXXXXXXXXXXXXXXXXXXX| 17 XXXXXXX| 16 17 17 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX| 5 5 27 27 39 39 52 54 54 61 61 XXXXXXXX| 2 XXXXXXXXXXXXXXXXXXXXXXXXXX| 6 6 11 11 60 60 - 1 XXXXX| 3 10 11 15 XXXXXXXXXXXX| 13 14 14 28 28 - 1 XXXXXXXXXXXXXXX| 4 4 12 12 XXXX| XXXXX| 1 12 13 13 XXXXXXXXXXXXXXXX| 23 40 40 XXXX| 5 XXXXXXXXXXXXXXXX| 59 - 2 XXX| 8 Stage II XXXXXXXXXXXX| 15 XX| 4 XXXXXXXXXXXXX| XX| - 2 XXXXXXXXXXX| X| XXXXXXXXX| 36 - 3 X| 7 9 XXX| 9 35 9 35 X| 6 XXXXXX| 34 X| XXX| 21 25 25 58 58 | - 3 XX| 1 1 7 7 X| - 4 | | | Stage I | - 4 | Red = 1st grade subtest | 10 10 Theory Tests Current Research