Hey good morning my name is Katie and together with my colleagues Sonia
and Zara we're going to be presenting our work on physical manipulatives that we've
done this year thinking about student engagement so building on the work that
we did here last year and using a fraction bar app we got some nice results but they
were slightly inconclusive so for example if you look at the bars at the bottom of the screen there
and students were unsure about whether the app had helped them to be independent and solve problems
but they did suggest that they agreed with the idea that the app would help them understand
fractions better and you can see that by the blue bar and the blue part of the bar being larger
than the red part so the blue part indicates that they agree that the app would help them
understand better so a bit of mixed results and slightly inconclusive but we did also feel like
we needed more time in lessons with students to get used to using the app both for them and for us
so this year what we've been doing as you can see here is we've been experimenting with a couple of
other resources and this time we've used physical manipulatives rather than virtual manipulatives
and we've planned all our own resources as well as borrowing some stuff from the TES website
we've all done a bit of planning and we've selected our own classes
this week so here are the six areas of results that we're going to present to you
and they range from our own experience as teachers but also the experience of students as well
and yeah so these are our research interests and aims we started with the idea that we wanted to
make learning of maths more accessible to learners and this led us to think about student engagement
which we've defined in the box at the bottom we were careful not just to focus on sort of like fun
activities we saw in the literature that thinking manipulatives just as a fun activity can subvert
their value as mathematical tools to engage people in mathematics and in cycle two we also started
thinking about teacher confidence and how that was affecting things and also about our task design
so over to Sonia
- I'm muted apologies I was talking away apologies so good morning here's a map of our research
cycles and the journey that we took this year initial teacher questionnaires indicated that none
of us had much experience using manipulatives although some of us had recent training
we conducted AR cycle one in order to get us into the classroom there were short lesson segments
with low stakes student interviews were conducted in pairs randomly selected out of those who had
over 90 attendance from that we realized we needed more time in lessons with the
resources and students we also did a training with Mike Ollerton who suggested there may be
benefits in students covering a range of topics with one manipulative to increase familiarity
this also allowed us to be more accommodating to different schemes of work we aim to each
teach three topics with one or two classes with geoboards AR cycle 3 had no intervention but
aimed to collect more detailed data from teachers and quantitative data from all students involved
data is analyzed informally from AR cycle 1 and 2 to inform subsequent research cycles all
qualitative data from the interviews reflections and class discussions were coded for themes and
were quantified to verify dominant themes quotes and case studies were pulled out quantitative data
from an example from the students was analyzed using simple statistical diagrams
one class of learners aged between 16 and 19. as you can see most of
our learners started the year on grade 2 in GCSE math followed by a grade 3.
we believe that small class sizes were a result of the disruption from covid 19
over the past two years different teachers taught different amounts
teachers talk different topics as per their preference and scheme of work
and looking at the table we question why was there a difference in the teacher uptake
now as you can see from the quote time constraints were a concern both in planning and lesson time
the quote exemplifies why planning may take longer we would have all liked more
experienced colleagues to work with and we really couldn't collaborate a lot as we were
working from different sites the researcher Moyer found that the teacher's prior beliefs
about how certain groups of students learn or concerns about their behavior affected their
uptake of manipulatives and that was also our case we were quite concerned about student behavior
so confidence generally improved over time through planning and practicing
teachers gained confidence from student feedback and their own reflection on how things had gone
some things didn't go so well some topics were harder than others sometimes ways of working were
different and new and after looking at the data gathered from myself members of the team and our
students it was very confidence boosting to see the positive feedback from the students I think
as teachers we need to be aware when introducing something new to our teaching skill sets there
tends to be our insecurities but we tend to get comfortable teaching in a particular way
Good morning and our finding about the students engagement
as shown on the pie chart on this slide a majority of students would like to use manipulatives again
students were more positive about geoboards this may have been for a variety of reasons
we addressed a few issues in the second research cycle for example taking longer in lessons
doing more lessons on different topics getting some training and increasing teacher skills
and confidence geoboards are less rigid in the way they can be used allowing us to plan
more open and varied activities quotes from students also showed they were engaging in
mathematical activities such as measuring and visualizing not just fun activities
here we asked students to comment on their concentration as a proxy for engagement which
we thought may be a more accessible term again we see that the students preferred their geoboards
from analyzing and quoting their qualitative data from all research cycles themes around a student
engagement emerged these are on the right of the screen the quotes from students exemplifying some
of these themes are on their slide the first one students not engaging because of alternate
existing methods this was most common in students who were more confident with formal methods in the
second one a student's engagement changing as they become familiar with the resource in the third one
there are some examples of why the students commenting on interactivity the last one
an example of a student becoming more confident
these are two quotes from
teachers the first exemplifying the power of the visual aesthetic to boost engagement
the second exemplifying students being able to access more mathematics
through the resource once they are familiar
we also had some interesting and positive case students for ALS and SEN
students indicating enjoyment engagement and increased access to mathematical activities
on this slide we can see mixed reviews from students class discussions and interviews although
again mainly positive in the survey we asked the students which statement they agreed with most
and the results are shown under pie charts over 50 percent of the students believe
the manipulatives were useful for learning maths this is the orange bit
around 25 percent believe that manipulatives helped prepare them for the exam
the green bit on the pie chart and with around 10 percent believing they were for fun only and
the rest agreeing with none of the above the pie chart on this slide shows that more students than
not felt the resources were age appropriate they were mixed reviews from teachers on whether they
felt they prepared the students for the exam but more positive than negative especially in
the interviews in AR cycle 3. Overall the data gives a positive picture of a student
and teacher perceptions of the appropriateness of these resources for this cohort
so we also thought about open and closed tasks and the top task and there the Pythagoras theorem
is an example of an open task where students are just invited to make any triangle on their board
and the bottom the enlargement activity is an example of a more closed task where
students are told exactly what to do and then to work something out
and and we were inspired by some of the tasks introduced by Mike Olatin to try and make
more open tasks but we didn't gather enough data on this to report on it properly but
at least two of us indicated that when the initial task was open for example allowing
students to make their own shape there was an increased engagement within the room
so I just want to talk a little bit about bridging activities and the point of using manipulators is
for us was to help students engage and access mathematics but also to be able to apply those
skills for, into an exam and this is where bridging activities come on to move you from
being able to work on the manipulative resource to being able to work on sort of a more formal
bit of work and you can see in the bottom left diagram you've got a reflection that's been
copied down from a geoboard on when it was on the geoboard it was correct and it moved
onto the paper and became slightly incorrect and there's a nice quote from the learning assistant
who is working with that student above it just highlighting the difficulty between moving between
different modes but also from the literature we know that Mason and Watson say that the learning
occurs specifically in the multi-directional movement between different stages so inactive
iconic symbolic or concrete pictorial and abstract and we also know that hart said that
formalization often fails with manipulatives due to a lack of bridging activities so we were keen
to think about this so conclusions and take-home messages we think that there's been a positive
effect on student engagement but there's lots more for us to learn and we think if you want to
try this give yourself time give your students time to become familiar with the resource and
keep building your confidence and skills and also consider the time of year that you start working
on this you need time for people to get used to doing to working with these resources and do think
about the bridging activities for us our next step so we're going to make more time to plan with the
manipulatives before next year and we're going to embed what we've learned into our schemes of work
we also want to think about differentiation comparisons between different student working
levels and also the different types of tasks that manipulatives afford us to use
and we're going to work hopefully more on bridging activities as well
so thank you so much for listening and we look forward to your questions and if you want any
of the references that we've cited today then they're there on the screen, thank you.