What Exactly is Student-Centered Learning?

I came across this entry saved to my computer… I guess I forgot to post it! I meant to upload it prior to blogging about my trials and tribulations of this inquiry. My bad. Pretend the date reads January 30th :)

As I become more comfortable with the teacher-inquirer that I am growing into, I have learned that before diving into a field study I need to make sure I have clearly defined for myself the definitions of the terms/topics/situations of which I am inquiring.

What does student-centered learning look like in a 21st century mathematics classroom?

I’ve spent significant time in my graduate coursework examining what a “21st century classroom” looks like and qualities that they may possess. The most important thing for me to wrap my head around now is what it means to have learning be student-centered. Starting out, that was simple: learning was either teacher-centered (knowledge is imparted by the teacher and instruction is direct) or student-centered (knowledge is actively constructed by the learner and the instruction is indirect). Right? Hmm. That was a bit of an assumption. Seems that like most things in education, nothing is really black and white, and it’s investigating those grey areas where my “aha moments” tend to occur.

So when looking for a definition, where does one go? Wikipedia of course ;)

“Student-centred learning (or student-centered learning; also called child-centred learning) is an approach to education focusing on the needs of the students, rather than those of others involved in the educational process, such as teachers and administrators.
Student-centred learning, that is, putting students first, is in stark contrast to existing establishment/teacher-centred lecturing and careerism. Student-centred learning is focused on the student's needs, abilities, interests, and learning styles with the teacher as a facilitator of learning. This classroom teaching method acknowledges student voice as central to the learning experience for every learner. Teacher-centred learning has the teacher at its centre in an active role and students in a passive, receptive role. Student-centred learning requires students to be active, responsible participants in their own learning.”

Okay, so the definition I originally had has been somewhat expanded. Looking at that, it made me think back to Educational Psychology 101, in my teacher-education days, and names like John Dewey, Jean Piaget, and Lev Vygotsky started swirling around my head. Oh yeah, I remember learning about that now – these guys practically came up with the idea of student-centered learning!

My next step was something I would not likely (correction = never) have done: refer to academic research to inform my understanding of student-centeredness. I came across one article in particular that caused such a shift in my thinking that I couldn’t stop talking about it to my friends and family. They were not nearly as excited by it as I was. Whenever I become energized about something in math or education (or worse, math education), I am usually met with family members pulling out their imaginary calculators, punching numbers furiously, and pushing their also imaginary glassed up their noses whilst snorting. I think they’re trying to tell me something. I once got a T-shirt for Christmas that read “talk nerdy to me”. Yup.

Back to the article. The citation for it is:

Elen, J., Clarebout, G., Lowyck, R., & Lowyck, J. (2007). Student-centred and teacher-centred learning environments: what students think. Teaching in Higher Education: 12(1).

This study focused on the relationship between teacher-centered and student-centered learning environments from the perspective of a student. It identified 3 views of this relationship: (1) the balance view: the more teacher-centered a learning environment the less student-centered it is and vice versa; (2) the transactional view: continuous renegotiation of teacher- and student-roles; and (3) the independent view: teacher- and student-centeredness are independent features of learning environments. Literature research done by the authors seemed to favor the balance view. From a curricular perspective, the results from the study suggest that the development of “powerful learning environments” are more important than the transition from teacher-centered towards student-centered learning environments. “Student-centredness and teacher-centredness are not the opposite poles of one spectrum… According to students, student-centredness and teacher-centredness are not conflicting but mutually reinforcing features of a learning environment. When properly combined they jointly contribute to its quality” (Elen et al, 2007)

Knowing this has opened my eyes to what my student-centered mathematics classroom could be modeled after. It definitely gave me food for thought.

Journaling in Math - Success??

In my quest to promote student-centered learning in math, I started to use journaling as a tool for my students to demonstrate their understanding of mathematical concepts and pinpoint areas where increased scaffolding is needed on an individual basis. From the students’ perspective, doing so was a challenge – far more difficult than working through questions from a worksheet or text. It required that they comprehend their own thinking and be able to identify what they understand and what they do not. I was fascinated by their journals, and marking (while more time-consuming), I was provided with meaningful feedback to support my own teaching.

In many cases, students were able to demonstrate capability to compute an answer and in most cases how they reached it, but not why they chose that particular method for solving. A common response when asked orally was “I dunno… I just did it.” Had they been required to simply provide an answer with or without showing work (like on a traditional homework assignment or quiz), they may very well have gotten the answer correct and I may very well have assumed that they understood the concept. Journaling forced them to think about the process of coming to an answer versus just arriving at an answer. Ahh, that must be where that old cliché “it’s about the journey, not the destination” came from… a math teacher ;)

This idea of metacognition in math has definitely sparked something in me – something I think I want to explore in greater depth in my next inquiry.

Turning a Teacher-Centered Math Class into a Student-Centered One

If you read my earlier posts, you’ll recall that I approached the instruction of my Math 8 algebra unit in a very different way this term. The students had not had experience in solving algebraic expressions prior to this and it was not “instructed” as I traditionally do. In many cases they were given questions and corresponding answers, and were asked to figure out how to get from one to the other on their own. They had to come up with algorithms and illustrations to demonstrate understanding of the foreign concepts, in addition to creating new examples and solutions for their peers to solve. In most cases, they were paired up and worked through problems together, re-enforcing their comprehension and fine tuning problem-solving strategies. The process was frustrating for students who were used to being told how to do the math, and often learned by example. You could take a poll in my math class (and I’m sure that of most Math teachers) of how many students hate problem-solving questions, and I would almost guarantee the percentage to be in the high 90’s. There’s always a collective groan when word problems are thrown into assignments and tests. The concern for me as a mathematics educator is that life is not a series of computations and numbered questions – the types of problems that arise in the “real world” will require students to make inferences, draw on past knowledge, and make connections. So, my inquiry was to approach algebra in a way that fostered the problem-solving process in a way that was meaningful for each student individually, and have the learning be centered around them.

This was achieved through various learning activities I tried throughout the 2 month field study, note-worthy ones being:

• Learning how to collect like terms: Each pair of students was given a mini whiteboard and markers, and were given a question and corresponding answer, based on their ability level. The ability to differentiate the instruction based on mathematical strength attributed to the success of this activity. An example would be: Given 4x – 3y + 2x + y, show how we get the simplified form 6x – 2y. Be able to describe your method in words and come up with a new example with the correct solution. Students were then required to “teach” their peers how they came to their conclusions. As the teacher, I made myself available to scaffold and support the students as questions arose or to challenge their thinking.

• Learning how to solve linear algebraic expressions: Each pair of students was given an iPod Touch and worked through an app called “Algebra Touch”. This app started with a question (an example would be: 2x + 4 = 10) and the goal was to isolate x. Students could “drag” terms around and noted what happened to them when they crossed the equals sign. “Tapping” a term would factor it, and “striking out” a term would cancel like terms in a fraction. The app would complete the calculations, but the goal was for the students to predict what would happen before they dragged/tapped/struck out each term, and most importantly, be able to explain WHY that was happening.

• Learning how to solving more difficult linear algebraic expressions: Each pair of students was given a Macbook and used a program from the National Library of Virtual Manipulatives that illustrated balancing equations where the variable was on both sides of the equals sign, and then solving it. This program was easy to differentiate as there were varying levels for the varying abilities that exist in each class. Like the iPod, the computer program performed the calculations and students were left to answer how and why, rather than what.

21st Century Literacy

My ideas of literacy and learning have been shifting so much over the course of the grad program I’m in. With all the information, opinions and ideas out there, I don’t know if I am now more informed or more confused than I was to start with.

“Literacy” to me always had to do with reading, or proficiency with comprehending what you read. I wasn’t ignorant to the fact that digital media was becoming increasingly prominent in teaching and learning, I just didn’t always make the association between it and literacy. For example, one of our school goals last year involved increasing literacy (like every other school in the district/area/province…). The assumption was that to increase literacy, we had to work on reading and writing. This was left mostly up to Language Arts/English teachers, with other subjects integrating literacy improvement strategies where possible. In my domain of mathematics, it was suggested to me that I use “word problems” in my math class to assist with the literacy goal. Then we would test the students on their reading and writing and hope to see improvements. But who said “literacy” is just reading and writing?

We live in a world where:

• if you can’t spell, the computer will fix it;
• any information we need is at our fingertips and can be retrieved in mere seconds;
• shorthand writing is not only acceptable, but more common than not in written communication and networking using social media;
• people don’t write letters anymore: they text, IM, tweet, blog.

This list could go on and on and on.

The technological advances that have taken place in the 21st century have been colossal. I’m not saying that reading and writing are obsolete, but the medium in which they currently exist is drastically different than before. Technology is not just a compilation of bells and whistles that are trendy for the moment and will disappear after its 15 minutes of fame. The Digital Age is an era that while difficult to stay ahead of, we as educators at least have to keep up with. We need to increase and adapt our current notions of what it means to teach, what it means to learn, what it means to know something.

So with that, our definition of literacy needs to continue to shift. It does not have to have a definition that is static, but rather one that is living and continually changing.

21st century learners need to be equipped with 21st century literacy skills. What does that look like?

The International School Bangkok (ISB) is an impressive institution that delivers 21st century literacy curriculum.
“The mission of 21st century literacy education at ISB is to prepare students to meet the demands brought on by our rapidly changing global community. In order to meet this goal it is essential that we continually seek out and embed innovative strategies, emerging technologies and a variety of information sources into our learning environments. With technological change happening at exponential rates, students need to be able to independently learn, unlearn, and relearn in order to be successful in the future (and the "now"). Becoming an independent learner is at the core of ISB's vision for learning.”

Image from ISB's wiki

The enGauge 21st Century Skills define clearly what students need to thrive in today’s Digital Age:
As society changes, the skills needed to deal with the complexities of life also change. Major new studies now define literacy as the ability to use “digital technology, communications tools, and/or networks to access, manage, integrate, evaluate,and create information in order to function in a knowledge society” (ICT Literacy Panel, 2002).
Basic Literacy: Can students demonstrate language proficiency (in English) and numeracy at levels necessary for success on the job and in a digital-age society?
Scientific Literacy: Do students have the knowledge and understanding of scientific concepts and processes required for personal decision-making, participation in civic and cultural affairs, and economic productivity?
Economic Literacy: Can students identify economic issues; analyze incentives; examine the consequences of changes in economic conditions and public policies; collect and organize economic evidence; and weigh costs against benefits?
Technological Literacy: Do students know what technology is, how it works, what purposes it can serve, and how it can be used efficiently and effectively to achieve specific goals?
Visual Literacy: Can students interpret, use, appreciate, and create images and video using both conventional and 21st century media in ways that advance thinking, decision making, communication, and learning?
Information Literacy: Are students able to evaluate information across a range of media; recognize when information is needed; locate, synthesize, and use it effectively; and accomplish this using technology, communication networks, and electronic resources?
Multicultural Literacy: Can students understand and appreciate similarities and differences between the customs, values, and beliefs of their own culture and the cultures of others?
Global Awareness: Do students recognize and understand relationships among international organizations, nation-states, public and private economic entities, socio-cultural groups, and individuals across the globe?

Image and text from enGauge's "21st Century Skills for 21st Century Learners"

Using iPods in Math

So now that I think I’ve begun to wrap my head around the idea of student-centered learning in mathematics, I starting thinking about ways I could integrate technology into this learning. The idea of using iPod apps is not a brand-new concept, but it definitely was to me. I starting reading about different uses for iPods in the Math/Science classroom on Dr. David Wetzel’s blog and got hold of 10 iPod Touch devices .When searching for apps to use to support my students’ learning, a major problem I came across was that many of the apps were too primary or too advanced for Grade 8 Math. That being said, there are like a kazillion apps to choose from, and I exhausted from my search after about 2 hours. It was also important to me that the apps coincide with what we were actually learning about. We are just starting our Algebra unit, so while there are some pretty great apps on Fractions, it made no sense to use those. So finding just the right app was more of a challenge than I had anticipated.
I downloaded some different apps , some free and some not, and posted the list to my website so that any student of mine who owns an iPod Touch or iPhone could download them from home. It surprised me how many students purchased the apps that were not free!

In the end, only a few of them ended up being ones that I focused on using in class. They were:
Apps that are not free:
•Algebra Touch
•DiaMath (algebra learning tool - Diamond Math)
•Learn Elementary Algebra
•Pre-Algebra Guide
•Tic Tac Math Algebra
Free Apps:
•MATH ! Lite
•Khan Academy: PreAlgebra
•eTutor
•TwentyFour Lite - A fun math game!
•FREE Equation Genius - Math equation solver
•Pop Math Lite
•Math Drop- Free

Of them, the apps that are most valuable to my students at this point in our curriculum are:

•Twenty Four Lite – Game where 4 numbers are given and you have to make them equal 24 using basic arithmetic. Students could challenge other students by creating multi-player sessions over Bluetooth. This game supported problem solving skills and cooperative learning.

•DiaMath –The principle of DiaMath is to solve for the two empty spaces in the diamond, using the pattern rule of: the left and right spaces multiply to get the top number (product) and add together to get the bottom number (sum). The location of the empty spaces changes, and there are varying levels of difficulties – excellent for students of varying abilities.

•Algebra Touch – Covers: simplification, like terms, commutativity, order of operations, factorization, prime numbers, elimination, isolation, variables, solving equations. Drag to rearrange, tap to simplify, and draw lines to eliminate identical terms.


•Tic Tac Math Algebra – A basic strategy game like Tic Tac Toe coupled with the challenge of solving algebraic equations ranging from simple linear expressions to systems of equations. Can be played by one or two players.

Journaling in Math

In thinking about my inquiry on student centered learning in mathematics, it became clear to me that I needed to change my assessment practice a bit. In addition to Math 8, I teach a course called Health and Career Education. In this course, my main focus is to challenge my students’ thinking and have them analyze their own lives and make informed decisions. A major assessment tool I use requires them to formalize their ideas, opinions and learnings in journals. It isn’t so much “did they get it right/wrong?”, but more of “are they thinking and problem solving?”. At the end of the day, is that not what I want out of them in Math as well?I came across an articleby Deb Russell on using journal writing in Math (Math Journals For All Ages). She explains how journaling in Math can be a valuable technique to develop and enhance mathematical thinking. Students have to be able to think about what he/she did in order to communicate it in writing. “When a math journal entry is required as a follow up to the specific learning goal, one actually has to think about what was done and what was required to solve the specific math activity or problem.” (Russell).

So, I decided to give it a whirl. The idea was not warmly received by my students. Anytime they hear the word journal, they think that they have to get all mushy and talk about their feelings. After explaining it more, they started to realize that the journal process was not going to be emotional, it was going to be difficult!! That was even worse than being mushy!! Explaining how they got the answers they did and/or explaining their methodology was fairly foreign to them and was no doubt intimidating. I’m interested to see what they have to say.