Our education system was built to address a world that won't (or currently doesn't) exist for our students because it is changing so rapidly. When our students graduate, they will be faced with very different demands than many of us were faced with. The education system that most current teachers grew up in is not necessarily the system that will deliver the strongest skills to our students today. We need to teach our students skills that will allow them to be successful in this ever changing world. Students will be working in careers that don't exist yet and the technology that they will likely use in their everyday life we haven't seen or heard of yet. The onus placed on the education system is huge. The expectation is to have these students ready to change and adapt as quickly as the world around them and be creative, but still have strong communication, written and oral language skills, problem solving skills and the necessary math skills among others. Here is a quick, creative youtube video that reminds us of the 21st Century Skills.
The following article discusses how some of the schools in the US are changing their way of thinking and teaching to address this ever changing concern. It speaks of the many discovery and innovation classes that are becoming more popular. They are creatively responding to discovery learning at Harvard in many disciplines such as science, engineering, and business to provide a richer learning environment that will foster deeper learning. Several other US university campuses are also using an innovative discovery approach which is now filtering into high schools, middle schools and after school programs. It suggests how powerful innovative discovery can be and how meaningful and lasting the learning is.
I am interested in hearing your thoughts about innovation, discovery, the iterative process and the role it plays in education. What activities are you trying in your classrooms to move down this exciting road of learning?
I think it’s important as Math
Educators to watch the video of Mr. Conrad Wolfram who’s the Mathematician
himself and the CEO and the Co-founder of the Wolfram group. Mr. Wolfram
believes that the math education around the world has a problem, the Governments think their math is failing in their county,
students think its difficult, teacher’s find it a hug struggle to move the
mathematics of their students forward and people who want mathematics in the
outside world like employers find that they don’t have enough Mathematics.
He believes we are living in a
world that’s ever more quantitative and more mathematical than before however
we have got falling interest in education in Math. He asks, “Why do we have
this chasm between the two math” (math in education and math outside)? He
believes there is one simple answer to this problem: Computers.
Wolfram
points out how the math in the real world is problem solving, modelling, stimulating, thinking out what the questions are and analyzing the results but in education
its doing calculating mostly by hand and if your lucky by calculator, the
problems small and distance from real world. He believes that we should be trying
to bring the two together to engage students.
Mr. Wolfram explains the four steps in doing
math, posing the right question about your situation, turn that from real world in to math formulation and put it in to the specific
math setup to do step 3, calculating. The step 3 is taking it from your setup
to answer from mathematical form. Step 4 is from that mathematical form to real
world and crucially verifying it. He explains how, “Perhaps 80% of doing math
education at school is step 3 by hand and largely not doing steps 1, 2 and 4.”
He believes step 3 is something computers can do better than any human and as he points out we don't want our students to be third rate computers but to
be first world problem solvers.
In conclusion, he recommends an open-ended use of computers and encourage those who argue that computers "dumbs math down" to look in to the real world and see how science and engineerings and other things that depends on math have got much more conceptual. Please watch this video and share your comments as I think he has some great points and suggestions!
This article, http://www.macleans.ca/society/life/have-you-finished-your-homework-mom/
from MacLean’s magazine, two and a half years ago, is targeting parents whose
kids are not achieving in math. That is,
they don’t have the basic skills to undertake high school math and parents are
now asking why?
For me as a high school math teacher, it speaks to why
kids come into grade 9 math without basic computations skills. Why are we having such low math scores?It is not just Ontario, but across Canada.
The article explains how these gaps have developed
over the last ten years or so. I particularly liked the reference to the Tower
of Babel – building that tower to heaven (heaven being Math in our case) and
then finding one day that no one was speaking the same language while everyone
was working toward the same outcome – get these kids to Math Utopia. The endless ways of learning numeracy skills
is confusing everyone – especially K – 8 math students. Asking them which way works best for them when
they are presented with a myriad of basic computation lessons is puzzling for
the developing learner. There certainly
is a case for “over kill” in the computation department.
The downside of this article is that parents can, yet
again, place blame on schools. It is
best that all stakeholders work together to solve the gap conundrum in
computation skills.
When I read Jessica Lahey'sarticleabout Steve Strogatz, a Professor of Applied Mathematics at Cornell Universityteaching an introductory math course for non-math majors who hate math, I am saddened. Strogatz has his students submit a math biography outlining their math encounters throughout their life. He shares thathis Liberal Arts students have had unpleasant math experiences and they blame themselves for not understanding math, they feel they are not intelligent enough or talented enough to do math. Strogatz (and others) teach an inquiry based math program at Cornell University to Liberal Arts students to help them see math in a different light and feel good about themselves and math. He states with the right approach he has been able to turn students views about math around. He feels this turn around is related to how the math is delivered to these students. The program he delivers is calledDiscovering the Art of Mathematics: Mathematical Inquiry in the Liberal Arts. If you follow the previous link there are student testimonials, quotes and videos describing the experiences they have had in their Cornell math class in comparison to their prior math experiences in high school. I believe these messages are important messages for us as secondary teachers to hear. Sometimes I think teachers don't always stop and realized just how much they can affect their students. Rethinking how we teach math and ensuring we do our best to reach every student using multiple means is important. Taking the extra time can put students on one future path or another, all because of the experience they have had in a classroom. Here is a video of Strogatz at Cornell with students who enjoy math and are studying Applied Math to use in pursuit of future careers.
In the
following video, Erik Stern and Karl Schaffer decided to take their love
of dance and apply it to their classrooms to teach math through dance
movements.
They
discovered a few key things about how to learn, the importance of how embodying
a problem is memorable, social and creative, the student’s physical energy is
no longer a concern and choreography and mathematical thinking are composed of
similar building blocks, remembering sequence, asking the things are bigger or
smaller and check your work to see if its consistent. They also explained
symmetry and mirror image with dance movements and by copying each other
movement and how we tend to think more effectively with special imagery on
larger scales. They want to create a mathematics classroom environment where
teachers would just say, “ put the books away, and push the desks aside, lets
warm up, its time to learn Mathematics”.
In
a video below, students use music and sound movement to help them describe
different graphs such as linear, quadratic, absolute, cubic. What I found
interesting about this approach is students learning these through sounds and movement,
which makes the learning more engaging and encourage learners to make their
Mathematical thinking more visible. What the words mean, sound and movement
help them identify different functions. In my classroom, my
students use dance movements to describes different types of graphs as well as
transformation concepts in grade 11 and 12. The students should create their
own dance movements to describe graphs and their transformations, which is
similar to the video here.
In another video,http://www.malkerosenfeld.com/math-in-your-feet-for-students.htmlthe students learn in a reach learning
environment which increase their understanding of mathematical topics such as
congruence, symmetry, transformation, angles and degrees, mapping on a
coordinate grid as well as deep experience with mathematical practices and
problem solving.
I do believe by the end of the
lessons students have a better understanding of the concepts learned in the
classroom and they learn that mathematics can be fun. I do believe bringing
dance movements in to Mathematics classroom could benefit students with
different learning abilities. Please share if you tried dance movement in
any of your lessons.
This morning on early morning news I saw a demonstration of this app. I have been thinking about it all day and
really only coming up with a question or two as to the implication in senior
math classes – or for that matter, any math course.
This article by Michael Thomas shows that the technology is similar to
taking a picture of a check to put in your bank account. As the camera takes a picture of the question
or problem, the answer is provided.
The article goes on to state obvious concerns that teachers may have to
be aware about students who may use it to cheat on tests and reducing time
spent thinking through questions and problems assigned for homework.
It did say that not all problems were able to be solved, but that the arsenal
of problem solving capabilities will improve and expand continually.
The purpose of this new app is not trying to be sold as a way to learn –
but as visionary technology. I am not
sure about the term or concept here of “visionary technology”. It seems to be a term to fleece consumers and
give math teachers more to blog about.
I do not think that math teachers have to beware
about this app.Yes, this app could be a
bit more than the answers in the back of the book, but could be used the same
way.Most of our senior students would
quickly learn to use the app in a helpful way.They would know that they will not learn by just copying the answers
from the app.Senior math teachers just
be aware and relax.
As an occasional teacher, I see different students every day with very different abilities and understandings when it comes to a variety of subjects. Gaps in education, math in particular, are inevitable and as an occasional teacher who is only working with students with gaps for a short time, I have had to develop a bag of tricks to give students tips and strategies for solving problems. I find that a lot of students struggle with mental math skills and multiplication seems to stump students. When I am working with a class for only a day, it is hard for me to teach the students complex math skills; thus I try to think of strategies I can leave with them that they can take with them and apply to every area of math. So many students turn to their calculator and no longer rely on mental math skills to complete simple multiplication. When it comes to such a crucial skills, I have a few strategies I like to introduce to classes - you never know what strategy may click with a student. In my experience, visual learners really seem to enjoy the Japanese technique of multiplying with lines explained in the following video.
Gone are the days when teaching should be uniform, as education has evolved, we have come to see that each student learns in their own unique way. What better way to reach out to students and instill a love for mathematics than offering them a variety of strategies they can use to solve a problem in a way that makes sense to them. Do you have a trick that will help students with mental math? I'd love to hear from you and add it to my bag of tricks so that I can share it with my students.
One of my favourite strategies to use when writing poems is to try to incorporate mathematics terms, formulas, and theories into the story, image, or moment I'm presenting in my poem. This comes from a deep love for mathematics and calculations, and I am not the only poet who expresses her or his love or fascination for math in this way. Take this poem "Burial" by Robert McAlmon for example where he uses mathematical principles to explore his understanding of life and death:
Burial
by Robert McAlmon, 1895 - 1956
Geometry is a perfect religion,
Axiom after axiom:
One proves a way into infinity
And logic makes obeisance at command.
Outside of the triangle, cubes, and polystructures
There is restless pummeling, pounding and taunting.
The end is diffused into channels
Every step into eternity—and steps are endless.
There's even an entire movement of poetry devoted to applying mathematical principles to poetry in order to explore the potential of poetry within specific restraints and formulas: OULIPO. For example, you might create a new poem by applying n+7 (i.e. replacing every noun in the poem with the noun that comes seven entries after it in the dictionary).
In my own attempts to connect math and poetry, I incorporated poetry into my grade 7 teaching practicum by asking students to create concrete poetry (where the image/placement of the words is as essential to the meaning of the poem as the words themselves) that demonstrates knowledge of translations, reflections, and rotations. Here's an example of one student's work (that I thought showed nice understanding of the concept):
Lastly, I think Slate has a very good idea right here. I am completely embracing this next April.
I am so inspired when I read Rafranz Davis' article about providing her math students with a shelf of manipulatives and tools that afford them the opportunity to express creative freedom and ask wonder questions. She calls this shelf a Wonder Shelf and it has been many years in the making. She includes simple household items from the kitchen, toys, blocks and lego pieces, arts and craft items as well as a variety of forms of technology. Read about at,
Her students are able to access this shelf during class and before/after school not only to extend their learning in areas they are studying, but also to reach out and explore other topics. I can only imagine her surprise when she turned on an ipad to find stop motion clay figures demonstrating changes in volume of a cylinder, when this was not even assigned. A student took it upon themself to create the clay figures and produce the stop motion clip possibly as a way to help them understand the concept being taught in class. How exciting for a teacher to make this discovery! Students can surprise us in so many ways when they are given the freedom and space to be creative. I'm certain this particular student will remember changes in volume of a cylinder for many years to come because the memory of creating the stop motion clip in Ms Davis' class will stick with them forever!
As an English major and teacher, I hear a lot of negativity
about mathematics: “We’re English teachers—we can’t/don’t do math.” “Math can
stay over there.” “Ugh. Math.” “You like math?” “I’m good at English, but not
math.” To which I say, “Really?” I don’t believe that math and English are as
disparate as some people make them out to be. So, with only a slight
confirmation bias, I went to the internet to prove my claim that math and
English are not opposing ends of a subject-spectrum.
One observation I have made in my teaching career is that
students that do very well in English usually also do very well in math.
Actually, the grades that students get in English are usually very similar to
their math grades, even when they tell me that they are very good in English,
but not very good at math (which in itself is an interesting perception). For
this blog post, I wanted some objective evidence to validate my observations,
and I found one
interesting infographic based on SAT statistics that suggests that math and
verbal scores on the SAT are comparable. According to the stats presented here,
very few students had completely divergent scores in math and language.
The idea that math skills and English skills are divergent
seems to relate to the Left Brain/Right Brain myth. People fall back on the
right brain/left brain theory as if we simply work with one side of our brain
when tackling certain subject areas. And then, to add insult to injury, some
decide that math is associated with left brain thinking and language arts with
right brain thinking. It’s absurd to think that math does not incorporate
creativity or English class does not endorse logical, analytical thinking. Luckily, the right brain/left brain theory is
simply
a myth that we simply like to believe because it lets us easily categorize
our skills (and sometimes, I think, excuse our perceived weaknesses).
I actually see math and English as having a fair bit in
common. Math is a language after all. In both math and writing, we abide by
rules, order, structures, and symbols. We must interpret and analyse the
information in front of us. We use numbers, rhythms, and patterns in writing
just as we look for in mathematics. The skills we use in both subject areas are
not divergent, but rather interconnected. For another perspective on this, I
direct you to an article by Melanie Carbine, “Math
and English: More in Common than Different”. She too notes the connection
between math and English language.
Probably the best piece of information I came across is that
having a strong English teacher actually makes students stronger in
mathematics. Stanford researchers determined that “students of good language
arts teachers had higher than expected math scores in subsequent years” (“Stanford
research shows long-run benefit of English instruction”). I would think,
then, that being strong in English also leads to stronger skills in
mathematics—which can also be seen in the SAT stats as well since so few
students who scored well in verbal did poorly in math. Therefore, with regards
to all my English major math-naysayers who claim they are math-impaired, I say
they are actually well-equipped to tackle mathematics (so stop dissing it!)
This post is to go on about a comment that was made by Mr.
Anderson in his blog “the ultimate question of life the universe and everything”.
Learning would definitely be a lot less adversarial if
students could think about math positively! I feel as educators we need to
change the way we talk about math and be mindful of the language we use
surrounding the teaching and learning of math.
For example, perhaps we could regard “math problems” as “math puzzles”. I understand this may seem unusual and very
minimal in targeting student reluctance and hesitation to math, however word
associations are deep rooted in one’s thoughts and beliefs. The word problem is synonymous with the
following: dilemma, predicament, crisis, setback, and more, all of which can be
related to feelings of fear, difficulty, uncertainty, and trouble. The word puzzle on the other hand is
synonymous with riddle, mystery, brainteaser, ect, which often relates to
feelings of excitement, curiosity, and interest. The word puzzle has a more positive connotation
than the word problem. In my opinion
students would be more inclined and more interested for that matter in solving
puzzles and than solving problems. I
realize this may seem a bit absurd; however as teachers I feel we must be conscientious
of the language we use in our classrooms and try and take our students’
perspective. I myself would be more engaged in solving puzzles because it
sounds fun and inviting.
There are many other terms or phrases we could also modify that
are not necessarily restricted to math.
For instance, I once worked with a teacher who hated the word “test”. She was adamant about not using the term,
especially with students. She would however
use terms like activities, or in class assignment, or challenge, instead of using
tests. Her view was that students often
respond to the word test with fear and anxiety, which countless studies and
personal experiences have proven to be true.
At first I thought this teacher was rather over the top and just maybe
was taking this a bit too fair, but I was surely proven wrong. Students were eager to complete their “math
challenge” and less worried about studying or how they should prepare for a
test. It was the simplest thing and yet
it made such a difference in student response. It’s funny how a word can change
everything!
By no means am I trying to say that math language is the ultimate
cause of why students are resistant to engaging in math! I think that if we
make an effort to change how we discuss math and the language surrounding it, students
may be more inclined to participate, or at the very least be less negative
towards the subject. I urge all of you
reading this to try and replace the term “math problem” with “math puzzle”. I
am curious to know if you find any differences in student participation and
overall sentiments!
Now if only there was a more positive way to say “I’m late
for work!”
I find Cross-Curricular Teaching very essential. In my
opinion, it provokes and creates deep learning and engages the whole student –his
heart, mind, body, and soul. This website takes you to “Cross-Curicular Math” resources
created for you to explore how Math can be connected with other subjects and how it
is needed in a real life.
This web site, I would like to share with you, will take you into some deeper cross-curricular ideas,
such as Exploring how Math is used in helping to restore medieval frescoes; How
can Math help us understand musical pitch and rhythm; or How mathematicians and
scientists use experiments to model what happens in avalanches by using collecting
data and displaying their findings with graphs. Just watching this I am ready to teach with more
of Cross-Curricular Maths Resources shared on MOTIVATE:
How about using Math when creating a movie with students.
How
do they create those incredibly life-like computer generated images in the
movies?
They say, that one of the basic movements an object can perform is a
rotation around a given axis and through a given angle.
Co-ordinate
geometry gives us the tools to calculate the position of each point on the object
after it has been rotated. They definitely use and need Math for that.
