What was your
school inquiry team focus question?
What pedagogical strategies can be
engaged in to move children from Stage Four (Counting) to Stage Five (Part
whole thinking)?
Having working in Year 3/4
for many years I always found that there were a few children who found this
shift in mathematical thinking particularly difficult. My question is why?
How did this
impact on the acceleration of student achievement? What is your evidence that
acceleration occurred?
Comment on the
effectiveness of your design.
Observations
Children were identified
within the middle syndicate as needing intervention based on the schools
strategic plan. The children who were chosen had not had intervention and at
the mid-point in the year there was a distinct group of Year 4’s who were still
counting and that were without part whole thinking. On observation of these
children within a classroom situation there appeared to be a number of common behaviours:
Ø Task avoidance – pencil
sharping, getting tissues, wandering, not following teacher instruction and therefore
needing to double check, disengaging from the task
Ø Non Participation (one watching
and listening but no participation) in a hands on activity
Ø Copying and agreeing with
others answers
Ø Fiddling, wriggling, silly
noises and off task talking.
When observing in class
work it was evident that many of the withdrawal group were unable to verbalise
their thinking in mathematics and I wondered how regularly they had been called
upon or challenged to explain their thinking. (This point will be discussed
further when discussing my work with the withdrawal group)
Two girls were focused and
listened carefully however on explanation of the work with their teacher their answers
made no sense and they were only able to describe their thinking as far as “my
head thinks it”.
Establishing
Relationships.
We began our classes at the
beginning of the Term 3 from Monday to Thursday immediately after lunch. We had
a dedicated room which was attached to my class so this certainly made it easy
for transportation of equipment and for me to move from area to area.
I ensured in the last week
of the term 2 that I meet briefly with these children as a group to establish
what we would be doing over the following term and to get to know me. These
children are from the middle school and I teach in the senior area. I explained
to them where they were at with math’s and they mostly agreed that they needed
extra help. I told them that we had a special name; we were to be called the
“Marvellous Mathematician’s”. I answered any questions they had and explained
that we might try doing math’s in a different way they would be used to.
Feedback received from one
teacher was interesting. He asked what I had told the children they would be
doing because they were so excited when returning to class about the prospects
of working on math’s. This really made me think about the relationships that
teachers build with students and how imperative it is for children to feel safe
in the knowledge that, even if they are below where they should be, teachers
are here to support them and want the best for them, all children want to feel special
and be part of a group.
Working
together as a group and building relationships
Our first week together was
about getting to know one another, establishing routines and behaviour, much
the same as it would be establishing a classroom at the beginning of the year.
From my observations I had observed many bahaviours which were not conducive to
learning. We co-constructed “rules for learning” and these were written into
the modelling book. These rules were referred to many times in the early weeks
however as time progressed it was seldom that they needed to be bought to the
attention of anyone.
We began with a fun task of
estimating jellybeans in a cup. A fun yet interesting mathematical task of
working together and learning skills of estimation. The majority of the
children, apart from two, had estimations which were highly inaccurate. It was
an informative task in that children were unable to interact within a group to
explain why they thought about something or even to discuss how they might go about
a task. Several children just worked independently even though they had only
one cup of jellybeans amongst three.
I also began with
challenging children thinking when were one child declared that they had more
than the other group I queried this. How did he know that? This is when it
became very evident that this group of children was rarely asked to explain an
answer when it was correct. The child immediately starting using a learned
strategy of guessing other answers in the hope he would be right. When I
explain he was actually correct and that I just wanted him to tell me how he
knew that he looked completely puzzled. Why would I ask him to justify a
correct answer?
This was a starting point
to encourage children to verbalise their ideas correct or incorrect. As a
teacher this made me reflect that to help learners we need to know
misconceptions to help us teach but also that a concept is understood by a child
being able to demonstrate and explain it.
We practice asking each
other questions and I modelled the types of questions we might ask. These
questions were displayed so the children could easily refer to them. The group
got better at having their thinking questioned and being able to discuss their
mathematical thinking.
Home/School Relationship (Whanau involvement)
At the beginning of the
project the parents were informed by letter about the project and its
purpose. I also provided a games pack
which included dice, laminated games, pens, spare paper and a pack of cards.
The children remarked on what fun they were having at home being supported by
their parents. Of note was one of my Pacific Island boys who comes from an
unsettled background. His sister would seek me out during interval or lunchtime
to tell me she had been practising the games and homework with her brother. It
was very encouraging to see that type of support from another child when
parents were unable to help. Homework was returned by most children each week
with varying support from families. One boy lost his notebook twice I kept
replacing this in the hope that he may take some responsibility to do some
homework. There was little support from this child’s family.
Two thirds of the way
through our ALiM sessions we had a family day. We invited our parents and
siblings (at our school) to come and see what we had been learning. The session
was run as usual for about 10 minutes. The children then had sharing time to
show their work books and then taught the family members how to play a math’s
game. At the end we had a shared afternoon tea. It was heartening again to see
such wonderful support from older siblings and in particular the tuakana teina
relationship happening. I wonder if this is something as a school we should
explore more with children who are underachieving.
Research into barriers to part whole thinking and
addressing these needs
To research my inquiry I
used a number of readings from the ALiM link on NZ Math’s and also did some
reading about subitising and how this skill aids the composing and decomposing
of numbers. Some of the barriers which may stop learners from becoming part
whole thinkers are:
Ø Limited understanding of
place value
Ø Limited knowledge and
recall of basic facts
Ø Poor estimating skills
Ø Limited knowledge of
grouping with ten and with decades
Ø Limited visualising of
part-whole
When beginning to work with
this group it was evident that many of these barriers where holding these
children back from being part whole thinkers. I went about researching a
variety of tasks and games that would address many of these needs. I
specifically highlighted several of these barriers to work on each week with my
planning. Place Value was represented in many different forms using materials.
Children made numbers and solved problems with money, place value houses,
unifix cubes, place value blocks, ice block sticks and jelly beans so that they
could be exposed to many different forms of the same thing. Subitising was
addressed through flash cards with tens frames and more random patterned
subitising cards. Recall of basic facts started with facts to ten and moved
through doubles to 10, to 20 and facts to 20. We did a one minute challenge of
ten facts each day. The children loved the challenge of limited time and enjoyed
seeing their improvement. Decades and knowledge of tens was address through
several different warm up games also.
What were the strategies/learning
conditions that supported acceleration?
Identify 3 key factors that made the
difference.
Rotation
of activities ( and short sharp, repetitive learning)
It
was obviously from the outset that these children had poor number knowledge.
Recall of basic facts knowledge was poor also for simple things such as doubles
and halves. I wanted to have learning games for the children to start with each
session so I went about teaching several different games which children would
then know well enough to play independently. The first game I introduced was a
simple “find the pairs” matching game of doubles. 5+5= 6+6= etc. We play this game over two weeks
in pairs for 2-3 minutes of our learning time. This game was then rotated into
“maintenance” or warm up activities when the children arrived each day. Other
knowledge activities were added progressively over the time such as ordering
numbers, groups to 100 and subtraction memory. The children spent about 5
minutes each day rotating through several games that they had previously
learnt. These games all addressed knowledge needs and the need for repetition.
As a teacher I reflected on the need for students who are struggling to improve
their memory. Repetition is a known help to improving memory.
Classroom Release
In
thinking through the way my regular day would be structured and so that my
classroom children got good quality focused teaching time I devoted my morning time
to them teaching mathematics, writing and topic work. I integrated much of the
writing and topic work so that the children would have sufficient time
allocated to these subjects to get good quality teaching, produce quality work and
it enabled work to be completed. In the afternoons my release teacher allocated
the afternoon to reading and a spelling programme. She used my term overview to
focus on the specific learning needs of each group. I was confident that the
needs of my children in the classroom were being met. This worked particularly
well as it released me from additional planning for the classroom to allow time
for me to plan for my AliM group. My classroom children had the continuity and
routines set early on and they knew what to expect each afternoon.
Method of
teaching and planning
I
used the MOVE model of teaching for both my withdrawal and in class ALiM
groups. This was the first time I had been introduced to this model. After
doing some research and reading of examples of this model in use I decided to
use it. I found this model useful in that it focused your teaching in
mathematics on the key areas that need to be taught on a regular basis. I feel
that possibly I and other teachers do not spend enough time on knowledge,
ordering, values and patterns whereas basic facts is often used as a warm up it
is sometimes assumed that these other things “will come with the teaching”. For
children who are struggling in mathematics I believe that all teaching needs to
be explicit and does not “just come” with the teaching. These children need regular
“short sharp and intensive” teaching.
As with
any Inquiry more questions presented themselves
New questions
to explore….
How might a tuakana/teina relationship
help support an underachieving child’s learning? (At home and at school)
How might our school intervene for
learners who are beginning to struggle in Mathematics? (Currently Successmaker,
ALiM what about teacher intervention?)
Are children being exposed to enough
repetition to learn basic facts? (Groups to 10, 100 etc)
As teachers are we exposing students
to challenging problems that enable to us to determine misconceptions and
understandings to inform our teaching?
Do we ask children to explain their
thinking correct or incorrect so that they are able to practice mathematical
talk?
Are we aware of children who are
“faking it” by participating enthusiastically, copying answers, guessing or
using opting out strategies such as “I forgot”? These are all strategies used
by struggling learners.
Changes in
Pedagogy
Within my classroom I have noticed
that I am much more aware of assessing misconceptions before teaching a new
concept. I ensure I understand all the thinking within the group I am working
with and am able to adjust my teaching and discuss misconceptions with children
immediately.
Having a greater awareness of
learners’ strategies. Not so much to avoid learning but show “or fake”
independence. I call it “learned independence”. Children guessing, copying
verbal and written answers, using “I forgot”, non-participation, waiting for
the teacher to supply the “answer” are all strategies that can be used. It is
important as a teacher to know every learner really well, but I think it would
be fair to say occasionally children “fly under the radar”.
I have gained new thinking about “at
risk” children and what model of teaching might work better for them. Next year
I will explore the MOVE model further with intense teaching for those children
are “at risk”, I also intend on exploring this (form) of model in other
curriculum areas.
