This post was published as part of an assignment in EDSE 338 in the Faculty of Education at the University of Alberta.
The recent introduction of a new mathematics curriculum in Alberta has sparked a debate about how we are teaching mathematics in schools (CBC, 2014). In this debate the new mathematics curriculum, focusing on having students developing their own personal strategies for solving mathematical problems using 21st Century teaching methods, is pitted against some parents advocating a simplified curriculum focusing on basic mathematics skills such as rote memorization and repeated practice taught using traditional teaching methods. The parents’ main argument is that the new curriculum deemphasizes the learning of basic mathematical skills and puts too much emphasis on open-ended problem solving ending up confusing and demoralizing children (CBC, 2014). While it is easy to point out the differences in the two views it is also easy to overlook that they have more in common that what meets the eye. The cornerstone of both arguments is based on the insight that mathematical literacy, in particular quantitative skills, are important in a changing and increasingly quantitative society (Steen, 1999).
An increasing number of studies are showing that Canadian students have been falling behind in their basic mathematics literacy skills over the last decade (Brochu et al., 2013). The revision of the mathematics curriculum and the current discussion about how mathematics should be taught is a direct response to this trend. For example, by looking at the description Alberta Education has on their website it is clear that the new mathematics curriculum has been shaped by the demands of the 21st century information driven society:
"Everybody uses math whether they realize it or not. Like reading and writing, a solid understanding of mathematics is essential for everyday living and in the workplace. Mathematical skills help us to shop wisely, buy the right insurance, remodel a home, interpret statistics, understand population growth, calculate travel distances and so much more. Through mathematics we develop numeracy, reasoning, thinking and problem solving skills. These skills are valued not only in science, business, trades and technology, but in other areas like fine arts, music and sports. More than ever, Alberta students need a strong grounding in mathematics to meet the challenges of the 21st century and to be successful in their futures.” (Alberta Education, 2014)
While juxtaposing the Alberta Education approach with the “back to basics” approach advocated by some parents it is clear that while the objectives may be the same, i.e. ensuring numeracy skills for the 21st century, the belief in how to best achieve this is fundamentally different.
To understand the background to this debate one has to first understand why mathematics education is changing in the first place. Historically in North America mathematical education, including numeracy, has been taught by using rote memorization (e.g. the multiplication table) and algorithms (e.g. the quadratic formula or common denominators in fractions) and repeated practice. This approach is often referred to as a “traditional” or “back to basics” approach (CBC, 2014; Cogito, 2014). While this approach continues to be used in certain alternative school programs in Alberta, e.g. the Cogito program (Cogito, 2014), the revised mathematics curriculum signals a move away from this approach among the majority of schools in Alberta. One important factor that is contributing to the reshaping of the mathematics education landscape is the increasingly quantitative world we are living in. The 21st century is information driven with massive amounts of data being collected by companies, governments and on Internet. As a result we are exposed to data, graphs and statistics in school, work and in our personal lives from an early age. For example, being mathematically literate with strong quantitative skills is increasingly becoming a requirement in a much broader range of professions than what it has been historically, including in professions that have traditionally not required strong mathematical skills, e.g. trades. This trend will undoubtedly become even more engrained and pervasive in the future.
Strong quantitative skills have many advantages; it creates informed citizens, it promotes critical thinking and, ultimately, a more democratic and equal society. Information that is made accessible to the broader public in the form of summary graphs and statistics has the potential to create a more informed and engaged public. For example, one of the most accessed public dataset in Canada is the Fraser Institute School Ranking (www.compareschoolrankings.org). This annual report ranks the academic performance of schools and allows anyone to view and analyze the data through an online interface. This data set illustrates how public data and quantitative skills among the general public are able inform citizens, promote debate and create social change.
Although it is clear that mathematics education is evolving in response to the demands of a changing society, other aspects of mathematics education remain relatively unchanged. Independent of how mathematics is taught the teacher still has to make the learning experience authentic and relevant with tangible connections to the students’ own lives. Achieving this will enable students to think of mathematics as something that arises naturally in their daily lives and not just as exercises on school worksheets or computers (Steen, 1999).
While the focus on repetition and memorization in traditional mathematics education is often associated with tediousness, boredom and irrelevance to the real world, the move towards more quantitative skills and 21st century pedagogies in mathematics education does not come without risks. Conrad Wolfram, an executive at a large corporation specializing in developing mathematical software, holds the view that we should be “Teaching kids real math with computers” (Wolfram, 2010). He argues that our time would be better invested if we teach math through computer programming. While this idea may be a sign of times unfortunately some of his arguments lack merit as they do not reflect what is in the best interest of young students. Furthermore, the fact that he works for a large corporation that develops and markets mathematical simulation software to researchers and schools creates an obvious conflict of interest between Wolfram’s interest as an executive and the message he is advocating. While I agree that the best way to check if you understand math is to write a program to do it, I disagree with his view about using computers to teach basic mathematics. Wolfram argues that you want to use the best tool for the job when teaching mathematics. While that statement is correct in principle, the problem is that Wolfram assumes that the computer is the best tool for all mathematics, including basic mathematical concepts. I would argue that your own mind is the best tool for not only basic mathematics, but also for advanced mathematical concepts. Point in case, relative to its size, Hungary is probably the country that has historically produced the largest number of world-renowned mathematicians and for many decades Hungarian students have placed themselves consistently in the top positions in mathematics Olympiads. Is this just a coincidence or are Hungarian schools better equipped with advanced mathematical software and computers? On the contrary, the Hungarian approach to mathematics education is renowned for valuing mathematics and focusing on deep conceptual understanding, justification and proof (Price, et al. 2012). Neither the “back to basics” mindless memorization and repetition nor the 21st century view of mathematics education that Wolfram advocates give students this deep relational understanding of mathematics (Skemp, 2006). While the traditional approach to teaching mathematics often provides “rules without reason” (Skemp, 2006), Wolfram’s approach provides quick results without reason or understanding, e.g. using a computer it is straightforward to visualize a quadratic function and determine the number of roots it has but without necessarily providing any insights as to how to arrive at the answer algebraically.
I agree with Conrad Wolfram’s words that;
“…we have a more mathematical world, a more quantitative world than we ever have had”.
This means that the path into the 21st century of mathematics education and interpretation of numeracy in light of an increasingly quantitative society involves embracing the quantitative nature of the world around us. Recently I was asked what numeracy means to me by one of my instructors. I jotted down “mental math + logic + problem solving savviness = numeracy”. A few days later I got my note back with the comment “What about context?”. Just like one would not typically specify what values x can take, unless there are clear limitations (e.g. x/1 versus 1/x where x≠0), I had simply assumed that because math “it’s everywhere” (Wolfram 2010; Alberta Education, 2014) so is the context. In other words, there is no specific context for numeracy – it is all around. It is in the produce section at the grocery store, it is in putting together the latest LEGO model with your child, it is in counting the beats in violin class, it is in deciding if you should run to try to catch the bus or wait for the next one, it is in playing board games at the dinner table, it is in cooking your favorite meal, it is in swimming laps in the pool.
Science classrooms are unique learning environments unlike any other classrooms. As a matter of fact, some things only happen in science classrooms. Here is a collection of event that happened in my own science classroom over the last school year. It's a growing list, so check back for updates.
Report from yours truly live-tweeting and navigating the melee at GETCA 2015 (Annual Greater Edmonton Teachers' Conference).
Can a pencil be more than just your average run of the mill pencil? The legendary Palomino Blackwing Pearl can take a student or teacher's writing to new heights. We have taken a batch of the Pearls for a spin and are blown away by how much writing and sketching can be transformed by this unassuming pencil.
Dr. Pineda's Classroom is going YouTube with the release of its first screencast on the exciting topic of calculating percents. Only time will tell if this is the start of something big and shiny or just a passing fad.
After several weeks working on setting up habitats for new classroom animals the big day finally arrived. The newest addition to our classroom include aquatic denizens in our new aquarium and a teenage bearded dragon with lots of attitude and no table manners.