This arrive in my inbox today and I felt it too was worth sharing.
What Counts as Meaningful Contexts for Learning Mathematics? At the beginning of each level of achievement objectives our (NZ) curriculum states:
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. As educators we are constantly challenged to find ways of making mathematics interesting and meaningful to our students.
Discussion Question: What is your perception of a meaningful context? •Out of school contexts - sport, national or international events, places (e.g.supermarket), the home •In school contexts - other curriculum areas, school events •Use of mathematics in different occupations
Points to consider: •What is everyday or real life for some may not be everyday or real life for all •some adults are efficient mathematical problem solvers in their jobs but still view themselves as “no good” at maths. Egan, K (1992) Imagination in Teaching and Learning challenges the assumption that to engage students in learning mathematics (or any subject matter) requires that they make connections with their everyday experiences.
Instead he suggests “the more distant and different something is from students everyday experiences and environments, the more imaginatively engaging it is likely to be” Personal experiences, like developing the Maths Trails using story books, Flat Stanley and The Tiger who came to Tea certainly engaged students in mathematical learning - to the point where the students were requesting to be taught “stuff” they didn’t know.
Both of these books are available from the online store under the Sales section for just $20 for both books. (Limited number in stock) The Wilkie Way
The quality of a task need not be judged by its relation to real life but in relation to how it engages students’ to think about and do the mathematics featured in the task.
It has long been understood that students will often become engaged, sometimes to the point of obsession in topics outside their experience:
Dinosaurs, Spaceships & aliens, Fairies, Superheros to name a few.
In these days of personalised learning individuals often have areas of intense interest - real experience, real in terms of an interest, eg Aztecs and imaginary that will motivate them to engage in thinking. (I taught an 11 year old to read using motorbike magazines - intense motivation to learn)
Imaginative contexts, stemming from real or more imagined situations, can be important resources for mathematical engagement.
We should not disregard making connections to students real-life contexts but perhaps we should broaden our conception of what counts as real:
Brown S (2001) Reconstructing school mathematics: Problems with problems and the real world. If we can speak of what is “real” in a more vibrant sense than what “exists” or what we can “touch” and “see” then we not only legitimize more interesting connections between mathematics and the real word but we also suppress the need to seek real world connections as a slave against an otherwise “unreal” world of mathematics. Escape from reality and engage students‘ mathematical imaginations.
There is a lot of discussion about appropriate activities for student learning. Many activities are completely out of the sphere of the child's experience or imagination. If we are to ensure great learning experiences for our students we have to make sure the activities are appropriate. How appropriate to our students are the majority of activities we present them with?
I was recently sent this "Linkedin Post"I hope it is of interest.
Let’s be honest. Worksheets, cookie cutter craft activities,
printables, and plastic manipulatives are widely reviled by early
childhood education experts, yet they are widely available and often
used in preschool and child care programs. At a recent luncheon with
early childhood professional development providers and authors, we tried
to sort out why this problem persists and consider why it is so hard to
bring the clear messages from research into play in classrooms.
Day in and day out we see posts defending “play based learning” yet,
in classrooms, we are seeing limited conversations, low quality play and
content-poor activities. Why do these differences exist? Who are the
people (teachers, caregivers and administrators) who really do implement
developmentally appropriate practice? How are they different from the
people who don’t use D.A.P.? Is there a gap in knowledge about what
D.A.P means and how it influences lasting learning outcomes? Is there an
informed rejection of the D.A.P approach to early education? Are old
ways too hard to give up? Are sales pitches from websites and catalogs
so irresistible? Do standards, QRIS systems and the Common Core play a
role in this discrepancy? Are we wrong to ask these questions? Here are
some of the developmentally inappropriate examples we use in our
A winter project that showed a teacher-cut shape of a giant mitten on
which children had glued cotton balls. Doesn’t look like a real mitten,
doesn’t function like a real mitten, isn’t made of anything a mitten
would be made of. And, even worse, no connection for students that live
in warm climates or students who live in the northeastern U.S. where no
one needed mittens till after the first of the year. This allows no
creativity, no meaning, no learning value and even no potential for
play. Doesn’t help children understand winter, doesn’t help them
understand mittens. What choices would have been better?
Making “goop” or similar substance with 2-year-olds. It doesn’t mix
like anything else you would mix. Has no purpose – can’t be eaten,
molded or used so mixing the ingredients doesn’t lead to any
understanding. When you’re done – you just throw it away. Teachers have
defended this by saying “but we just want the children to experience
different things.” Or “sensory”. But the truth is, there are so many
real things for them to experience that will help them understand the
world around them while also being fun and sensational – why choose this
instead of mixing sand and water to make a structure or mixing two
colors of paint to make your picture? What choices would have been
Dinosaurs. How often do we hear – “Kids love dinosaurs and D.A.P.
says we should follow children’s interests!” Very tricky… but kids love a
lot of things so you don’t have to pick dinosaurs. What do we have
against dinosaurs? They don’t exist. There are so many animals in the
child’s real world that could be studied and identified and cared for
that would have real world meaning. Why choose dinosaurs that are only
seen as plastic toys or cartoons? What choices would have been better?
Handing out black paper and orange paint in October. No choice
allowed for children, yet no meaning to the activity. Stripes of orange
paint do not help them understand what a pumpkin is or how it grows or
what it looks like on the inside. But this is also not art. There is no
creativity or independent thought or opportunity for rich, engaging
conversation. What choices would have been better?
A poster in 3-year-old class with the sign language alphabet. When
children do no yet know any alphabet, hand spelling doesn’t mean
anything to them. Pictures of hands in different positions are not going
to support “diversity” because they have no relevance for the children
nor will they signs be used in the classroom. USING sign language for
words like eat, drink, toilet, hurt, more and stop could be a more
useful strategy to help children of all languages and abilities
understand. What choices could have been better?
Precut red and black ladybug with counting spots. Gluing circles of
paper onto other precut paper has no meaning. It may look like a ladybug
to an adult, but to a child it is just something to copy for no
purpose. Counting the spots has no meaning if there’s no value to the
number of spots. What difference does it make if there are two or four?
It matters if you have two cookies and your friend gets four. It matters
if the puzzle has four spaces but you only have two pieces. It matters
if you have two feet but only one shoe. What choices could have been
Printable coloring page with leprechaun. Is this really what you want
children to learn about Ireland and Irish culture? Is coloring a
printable picture of a leprechaun providing anything to discuss or
create or imagine? What is the holiday of St. Patrick’s Day? What
meaning does it have for children? Is this just cute or is it quality?
What choices could have been better?
Skill-based activities with no real content. You can teach sorting
plastic things for no purpose and be pretty sure the children can’t
generalize to any real life items that need to be sorted. Or you can
teach sorting by asking the children to help you find the pieces for
each puzzle from a pile of puzzle pieces, or sort the markers that work
from the markers that are dried out, or sort the newly washed clothes
for the dramatic play area. True D.A.P. based on the research tells us
that skills and letters and phonemes should be learned in the context of
useful, authentic content. An activity that teaches nothing more than
sorting doesn’t really teach sorting either. An activity that involves
playing with realistic items that need to be sorted teaches content and
vocabulary as well as a lasting, generalizable understanding about
sorting. What choices could have been better?
Voices of professional development presenters:
Rosanne Hansel, PA pushes kindergarten teachers to look for deeper
meaning and purpose when choosing activities, not just counting for the
sake of counting.
Barbara Capra, NJ asks her teachers “Is it cute or is it a quality
early learning experience?” She advises teachers to evaluate activities
by looking at skills/standards/objectives, time, implementation and the
source to really be sure they are making the right choices for young
Liz Vaughan, PA, asks teachers to know the difference between art and
crafts, but she recognizes the value of predictable, developmentally
Pam Brillante, NJ, asks teachers to “step away from the Pinterest”
because young children, particularly children with disabilities, need
learning that connects with experiences they recognize from their daily
life rather than isolated activities.
And, these connections to real things and experiences are even more
important when teaching young children who are dual language learners!
This is one of the reasons these questions seem so pressing right now.
We find it so difficult to help teachers give up activities they’ve
been using. They put a lot of energy into defending the old ways instead
of using that energy to learn new ways. How can we help? How can we
make our writing and our workshops more effective? How can we reach out
to those old websites, app developers and Pinterest pages that keep
publishing inappropriate materials and activities?
The questions we want teachers to ask are: What for? And What more?
In other words, when choosing any activity, can the teacher explain what
the children will learn from it that they can really use? We don’t mean
to just imitate, or experience, but actually use in their life? And if
they find that the activity does provide some learning experience that
the child can really use, can the teacher identify related activities
that will extend the learning and allow the child to put his new
learning to use? Teaching kindergarteners to identify a picture of an
asteroid may seem like science, but if they never use that word again or
see anything to do with asteroids or have any asteroid activities again
for the rest of the school year – they won’t remember it. What for? and
What more? Can these questions help early childhood educators break
through the D.A.P Gap?