EDMA262 | Assessment 2: Enacting the ‘Explore, Respond, Reflect’ Teaching
Model- Mary-Anne Sammut (S00103680)
EDMA262 Mathematics: Learning & Teaching 1
Nutshell statement template
Pre-service teacher’s name: Mary-Anne Sammut
Student ID:
S00103680
Student A: Haley
Year Level: Prep
Nutshell statement:
When using concrete materials to assist her in keeping track of where she is when counting,
Haley demonstrates that she has the ability to count to 20. However when attempting to count
abstractly without the said materials to assist her, she struggles. Haley has demonstrated the
ability to count to 20, however only through memorization of the sequence, and when
counting beyond 20 repeats the sequence of 20 beginning at 1 again. Instead of counting
from one again, Haley needs to recognise the pattern involved with counting on, by simply
changing the unit numbers between 0-9.
Since Haley has shown a thorough ability to recognise coloured patterns, and when asked to
continue patterns of such, has shown a great aptitude to do so, it exhibits that with some
further assistance, Haley will be able to recognise the pattern sequence with number
counting, and will develop the ability to count on from or back from any given number.
[Word Count: 157]
EDMA262 | Assessment 2: Enacting the ‘Explore, Respond, Reflect’ Teaching
Model- Mary-Anne Sammut (S00103680)
Student B: Micheal
Year Level: 4
Growth points reached:
Domain
Growth
point
(number)
Counting
Growth point (in words)
Counting from x (where x >0) by
5
2s, 5s, and 10s. Given a non-zero starting point,
can count by 2s, 5s, and 10s to a given target.
Place Value
3
Reading, writing, interpreting, and ordering
three-digit numbers. Can read, write, interpret
and order three-digit numbers.
Addition & subtraction strategies
3
Count back/count-down to/count up from. Given
a subtraction situation, chooses appropriately
from strategies including count back, countdown to and count up from.
Multiplication & division strategies
2
Modelling multiplication and division (all objects
perceived) models all objects to solve
multiplicative and sharing situations.
Nutshell statement:
Michael has shown an adept ability in counting number sequences using known facts to help
him when needed. Michael demonstrates the ability to count from a non- zero or unfamiliar
starting point in factual increments until guided to stop, however at times because of the
unfamiliarity of the sequence pattern, Michael counted by ones for the first few increments
until he could notice a distinguishable pattern to help him continue the sequence. When
reading and writing 1, 2 and 3 digit numbers, Micheal demonstrates a clear understanding of
the place value system of units, tens and hundreds, and although Michael clearly
demonstrates that he can read and write 4 digit numbers, he demonstrates difficulty
subtracting or adding and amount to a four digit number when the thousandths column needs
to increase or decrease. However demonstrating this using concrete materials, may assist
Michael to have a greater understanding of the place value system of 4 digit numbers.
Michael has a clear understanding of how to add and subtract, and although he can add and
subtract two numbers correctly, Michael needs some assistance as the strategies he uses are
not always the most efficient. Therefore to help Michael develop this skill, different strategies
for adding and subtracting should be discussed and explored, and their effectiveness
assessed.
Michael’s understanding of division and multiplication is ample, in that, he has the ability to
memorize facts, however when asked to represent an equation using models, Michael is
hesitant in doing so, which shows that he needs further assistance in his understanding of
what and how multiplication and division can be represented and modelled. Michael was able
to recognise on occasions, when prompted, how we can group numbers together to help us
count in a more efficient way, instead of counting group separately.
[Word Count: 251]
EDMA262 | Assessment 2: Enacting the ‘Explore, Respond, Reflect’ Teaching
Model- Mary-Anne Sammut (S00103680)
Critique
During the ENRP Interview with Michael, I noticed that although he had the ability to answer
multiplication equations efficiently, when modelling multiplication equations, or looking at
multiplication being modelled, Micheal used addition to work out the answer, as opposed to
multiplication strategies of grouping. As a result of this, I decided to base my lesson plan on
the modelling of multiplication, in order to help develop Michael’s relational understanding of
multiplication in terms of the ways we can use multiplication in our everyday lives to help us
solve problems, as well as show Michael that using multiplication is a more efficient strategy
to use (Mulligan and Watson, 1998).
Wallace and Gurganus (2005) state that “Rote memorization of basic facts is not fluency” and
it is only the ground work for the development of further learning. Teachers need to teach for
understanding by providing students with contextual examples of multiplication which relate to
them and which they can make clear sense of. Therefore teachers need to help students
understand that multiplication is not just a sequence of facts, but has a variety of meanings
and uses in our daily lives (Wallace & Gurganus).
This lesson plan therefore aims to show Micheal and his peers how addition and multiplication
are linked through the modelling of problems, and thus demonstrate how multiplication can be
used as a more efficient means of working out the same problem (Van de Walle, Karp & BayWilliams, 2013). Based on the interview, when asked how many dots were in a 4 by 5 array,
Micheal counted each dot individually, which demonstrates that he may have little to no
understanding of how multiplication is used to group and help us count a set number more
efficiently.
Therefore this lesson is created to help Michael make relational sense of Multiplication, as
well as division, in terms of the ways we can model equations using an array, an equal set
model and thus make connections with the ways multiplication is used in our everyday lives,
by writing their own and making sense of worded multiplicative problems.
EDMA262 | Assessment 2: Enacting the ‘Explore, Respond, Reflect’ Teaching
Model- Mary-Anne Sammut (S00103680)
Introduction
A student’s mathematical reasoning can communicate a great deal about what a student
understands and thus needs further development and assistance with. Teachers can access
a student’s reasoning and understanding in a number of ways (Gervasoni, et al, 2012). This
paper will outline the effectiveness of the ENRP mathematics interview as way to access what
a student understands, analyse which growth point they have reached and then plan
appropriately to assist this child in the learning development to move towards reaching the
next mathematical growth point. In order to complete this paper, an interview was conducted
with one grade prep student and one grade 4 student. The results were then analysed,
accessed and the growth points of each student, pinpointed. This paper will therefore outline
the outcomes of the interviews in a nutshell statement, to outline the skills that the students
showed, as well as the mathematical concepts that the students struggled to understand, a
copy of the interview record sheet, a lesson plan which was informed through the assessment
of the grade 4 student, as well as a critique which explains the reasons for developing such a
lesson for this student.
EDMA262 | Assessment 2: Enacting the ‘Explore, Respond, Reflect’ Teaching
Model- Mary-Anne Sammut (S00103680)
Conclusion
This paper has highlight the effectiveness of the ENRP mathematics interview, in its ability to
assist teachers to access student knowledge and reasoning. Through such interviews
teachers can intern plan lessons to cater for children and their learning needs. This paper
therefore develops my understanding of how the interview can be used, and outlines for me
how a student’s growth point can be assessed so that teachers gain knowledge of where a
student is levelled in terms of their mathematical understanding in specific areas. In
conducting the interview with Micheal I was able to understand which areas of mathematics
he struggled with, so that I could then compare his knowledge with the growth points so that I
could intern create a lesson plan which would build upon his knowledge and help him reach
the next growth point.
EDMA262 | Assessment 2: Enacting the ‘Explore, Respond, Reflect’ Teaching
Model- Mary-Anne Sammut (S00103680)
References
Van de Walle, J. A., Karp, K.S., Bay-Williams, J. M (2013). Elementary and middle school
mathematics: Teaching developmental (8th ed.). Boston, MA; Pearson.
Wallace, A. H., & Gurganus S. P (2005). Teaching for mastery of multiplication.
The National Council of Teachers of Mathematics. Retrieved from
http://www.cusdmathcoach.com/multiplication.pdf
Mulligan, J., & Watson J (1998). A Developmental multimodal model for multiplication and
Division. Mathematics Education Research Journal, 10(2), 61-86.