So I recently tweeted a nice article that I read that discussed “12 Questions to Help Students See Themselves as Thinkers” in the classroom (not specifically the math classroom

Nice article about helping Ss be metacognitive http://t.co/duD22w6RTu #PBLmath #mathed pic.twitter.com/JGA7dPv4wr

— Carmel Schettino (@SchettinoPBL) August 10, 2014

and appropriately, Anna Blinstein tweeted in response:

@SchettinoPBL These are fairly broad. How do you think they might be incorporated into a more “standard” high school curriculum?

— Anna Blinstein (@Borschtwithanna) August 10, 2014

So I thought I needed to respond in a post that spoke to this question. First of all, I should state the caveat that even when I am in a more “standard” classroom (i.e. not a PBL classroom) – which happened to me last year – I try as much as possible to keep my pedagogy consistent with my values of PBL which include

1) valuing student voice

2) connecting the curriculum

3) dissolving the authoritative hierarchy of the classroom

4) creating ownership of the material for students

I find that helping students to be metacognitive helps with all of this. An important aside her is also Muller’s definition of **21st century learning*** which is much more than that 20th century learning and education that often comes with direct instruction in the mathematics classroom (not always).I think it’s important to note that the more fluid concept of knowledge that is ubiquitous with technology today and is no longer static in textbooks or delivered by teachers. Students can go find out how to do anything (procedurally) nowadays, but it is the understanding of it that is more important and the true mathematical learning and sense making.

Anyway, I think I would write way too much if I responded to every one of the questions, but how would I use these questions in my direct instruction class that I taught last year? What I tried to do was introduce a topic with some problems (and then we would do some practice with problems from the textbook so I could keep up with where my colleague was in the material). Well, this course was Algebra II, which often referred to prior knowledge that always reminded students of something they had studied before. I let them use computers to look things up on the internet and use the technology at hand, GeoGebra, Graphing Calculators, each other to ask questions about the functions we were studying. They could look up topics like domain, range, asymptotes (why would there be an asymptote on a rational function)…but then the bigger questions like “what am I curious about?” had more to do with how did those asymptotes occur, what made vertical vs. horizontal asymptotes and then I would have them do journal entries about them (see my blogposts on metacognitive journaling – journaling and resilience, using journal writing, page on metacognitive journaling).

The more “big picture” questions like “Why learn?” and “What does one *do* with knowledge?” I find easier to deal with because the students ask those. I think that all teachers find their own ways to deal with them, but I enjoy doing is asking students about a tough question they are dealing with in their life – I use the example of whether or not I should continue working when I had my two kids. Was keeping my job worth it financially over the cost of daycare? and of course I had to weight my emotional state when I wasn’t working – this is why I enjoy learning and what I do with my knowledge. When kids see that there’s more to do with functions than just points on a grid, it becomes so much clearer for them – but you know that!

What I really like about Dr. Muller’s list is that he lays out some nice deliberate ways in which we as math teachers can get students to think more clearly and reflectively about mathematics as a purposeful process as opposed to a just procedures that they can learn by just watching a Kahn Academy video.

**”Learning – here defined as the overall effect of incrementally acquiring, synthesizing, and applying information – changes beliefs. Awareness leads to thoughts, thoughts lead to emotions, and emotions lead to behavior. Learning, therefore, results in both personal and social change through self-knowledge and healthy interdependence.”* Muller http://tutoringtoexcellence.blogspot.com/2014/08/helping-students-see-themselves-as.html