Part B
Diagnostic Interview and Tutoring Sessions
Permission was granted (Appendix A) to interview and tutor Athena*, who is a 9 year old student in Year 4 who returned to Australia in the middle of Year 3, after living in the United States for 5 years. The Mathematics Assessment Interview (MAI) was conducted on a weekend afternoon at Athena’s home shortly after lunch (Australian Catholic University, 2011b). She did not seem to be nervous and was informed that the purpose of the questions was to help a pre-service teacher learn and develop some effective ways of teaching through the follow up tutoring sessions.
Athena began the MAI confidently and could read, write (on the calculator) and order two digit numbers with ease. With the bundling …show more content…
It became evident that while Athena was confident in reading, writing and ordering numbers up to and beyond the thousands, which aligns with the Year 4 ‘Number and Place Value’ content descriptor in the Australian Curriculum: Mathematics (ACMNA072), her lack of understanding about place value within a base-ten system meant that she could not interpret numbers comfortably in order to solve problems to align with (ACMNA073) (ACARA, 2016). While she knows the procedures for adding and subtracting numbers that bridge decades and hundreds and can show correct working out on paper, her mental strategies regarding place value needed practice. It was determined that activities in which manipulatives could support the mental strategies needed could help, as suggested by Burns (2004). The intention was to segue into this first by revising her understanding of two digit numbers and developing sense of number …show more content…
Partitioning relates to thinking flexibly about numbers and links to Key Understanding 6 in FSiM (DETWA, 2013a, p. 60). During the subsequent sessions, activities using place value mats, tens frames, MABs, abacus, bundling sticks, arrow cards, and number expanders allowed Athena to show the same numbers in various formats (multiembodiments) as advised by Reys et al. (2012). This helped her to recognise the visual and symbolic nature of the numbers and see how numbers can be partitioned in both standard and non-standard ways (Appendix D). In extending her writing of numbers on the place value mat, in addition to using the iPad abacus app with digital readout, and playing Place Value Knockout, Athena began to also recognise the multiplicative nature of the place values (ACU, 2011a, pp. 44-45; DETWA, 2009, p. 2; Ross, 2002, p. 419). This was followed up with trading play money pieces, and in the last session, Athena had an ‘Aha!’ moment where she commented that “If the number goes to the left, it goes up one place and it’s ten times bigger but you have to put the zero in the ones, but then if it goes down, it’s ten times smaller! Like two dollars goes to twenty dollars or five dollars goes to fifty cents...” While she still needs more practice to develop her understanding of place value, Athena has demonstrated great improvement throughout the
Diagnostic Interview and Tutoring Sessions
Permission was granted (Appendix A) to interview and tutor Athena*, who is a 9 year old student in Year 4 who returned to Australia in the middle of Year 3, after living in the United States for 5 years. The Mathematics Assessment Interview (MAI) was conducted on a weekend afternoon at Athena’s home shortly after lunch (Australian Catholic University, 2011b). She did not seem to be nervous and was informed that the purpose of the questions was to help a pre-service teacher learn and develop some effective ways of teaching through the follow up tutoring sessions.
Athena began the MAI confidently and could read, write (on the calculator) and order two digit numbers with ease. With the bundling …show more content…
It became evident that while Athena was confident in reading, writing and ordering numbers up to and beyond the thousands, which aligns with the Year 4 ‘Number and Place Value’ content descriptor in the Australian Curriculum: Mathematics (ACMNA072), her lack of understanding about place value within a base-ten system meant that she could not interpret numbers comfortably in order to solve problems to align with (ACMNA073) (ACARA, 2016). While she knows the procedures for adding and subtracting numbers that bridge decades and hundreds and can show correct working out on paper, her mental strategies regarding place value needed practice. It was determined that activities in which manipulatives could support the mental strategies needed could help, as suggested by Burns (2004). The intention was to segue into this first by revising her understanding of two digit numbers and developing sense of number …show more content…
Partitioning relates to thinking flexibly about numbers and links to Key Understanding 6 in FSiM (DETWA, 2013a, p. 60). During the subsequent sessions, activities using place value mats, tens frames, MABs, abacus, bundling sticks, arrow cards, and number expanders allowed Athena to show the same numbers in various formats (multiembodiments) as advised by Reys et al. (2012). This helped her to recognise the visual and symbolic nature of the numbers and see how numbers can be partitioned in both standard and non-standard ways (Appendix D). In extending her writing of numbers on the place value mat, in addition to using the iPad abacus app with digital readout, and playing Place Value Knockout, Athena began to also recognise the multiplicative nature of the place values (ACU, 2011a, pp. 44-45; DETWA, 2009, p. 2; Ross, 2002, p. 419). This was followed up with trading play money pieces, and in the last session, Athena had an ‘Aha!’ moment where she commented that “If the number goes to the left, it goes up one place and it’s ten times bigger but you have to put the zero in the ones, but then if it goes down, it’s ten times smaller! Like two dollars goes to twenty dollars or five dollars goes to fifty cents...” While she still needs more practice to develop her understanding of place value, Athena has demonstrated great improvement throughout the