## Students at the Center of Learning

“Teaching and Learning” … a phrase often used in professional development for us teachers, as well as in titles of articles and books. Perhaps a better phrase would be “Learning and Teacher Behaviors”, or “Learning … Teaching without getting in the way!”

I am thinking about how well our Math Literacy course is doing in the Math Lab format. The Math Lab format creates a learning environment by establishing assignments and a structure for students to work through those assignments. The instructor ‘stays out of the way’ as long as learning is successful. This format has been used with very traditional content, and is now being used with a modern developmental course — Math Literacy.

Although some students struggle longer, and do not initially ‘get’ new ideas, the vast majority of students in the Math Lab Math Literacy course have been successful with:

- identifying linear and exponential patterns in sequence
- using dimensional analysis for unit conversions
- identifying the type of calculation for geometry (perimeter, area, volume)
- writing expressions for verbal statements

What’s been tougher? Anything dealing with percents — applications, simple & compound interest, etc. Of course, these are weak spots for students in any math class; over the years, I have not seen anything that ‘fixes’ these in the short term; the fix involves unlearning bad or incomplete ideas, and this takes time and long-term ‘exposure’ to errors (along with support from an expert). Direct instruction or group activities have limited effectiveness against the force of pre-existing bad knowledge.

The instructional materials form the basis for the learning in this Math Lab format. If the ‘textbook’ is focused on problems to do, contexts to explore, with the expectation that the instructor will provide ‘the mathematics’, then the learner centered approach requires that we use specialized processes in the classroom. The classroom becomes the focus, and we spend resources & energy on tactical decisions such as ‘homogeneous groupings’ or ‘group responsibilities’ or ‘flipping the classroom’. The materials we use in this course are well crafted to support learning; the authors ‘expected’ the classroom to be the focus, though our Math Lab ‘classroom’ is working quite well with the materials.

What if we could offer a true “student at the center of learning” design? Seems to me that this goal would lead us to use methods like our Math Lab, where students interact with the learning materials without an instructor mediating (as much as possible). Students in our Math Literacy course have been successful in learning new mathematics with decent reasoning skills in this format. Although initially confusing to students, the classroom is lower stress than a ‘regular’ classroom; there are no artificial social processes used to ‘facilitate’ the learning. Think of it as being more like a student as an apprentice, where direct engagement with the objects of the occupation is the key for learning.

Of course, we are not normally able to offer all math courses in this format of active learning. For me, the approach is to design my ‘lecture’ classes to be more like workshops. In a 2-hour class, I might deliver 45 minutes of very focused presentations (direct instruction) distributed in a deliberate manner through the class time. The length of ‘lecturing’ is varied according to the course and somewhat according to the needs of the students in a given class.

The point of this post is …

Stay out of the way of learning.

Students can learn by interacting directly with the learning environment.

We want students who are independent, and able to learn without a special structure. Prepare your students for the real world by creating learning environments where they develop those skills while they are learning mathematics.

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