The importance of questioning

Over the past few weeks the topic of questioning has come up many times from various viewpoints.  Since I'm not currently teaching, these are more reflections and thoughts than observations from my classroom.

Listening to Dan Meyer's talk really challenged my thinking and reinforced the importance of asking the right questions.  With the changes in curriculum, we have moved toward this way of thinking and questioning but it is easy to fall back on the textbook and old ways of doing things.  Time is a big factor, but I would like to start incorporating more open middle problems in my classes.  Meyer made the point that rarely in life are we given exactly what we need to solve a problem.  So why are we doing that for our students?

The answer lies in part in our lack of preparation in leading discussions.  We are number people, not word people.  We are used to letting the numbers, formulas, and processes do the talking.  It's hard to draw the line between asking guiding questions and asking questions that lead to the desired solution.  What would it look like to have student questions guide the lesson?  What if we let our students discover new topics instead of teaching them?  This would be a challenge for me but I'd like to incorporate more of this idea into my classroom.

My project for this class is focused on creating these types of problems or tasks for seventh grade students.  So far I've found a lot of great questions and resources.  Now my goal is to take them, strip them down to the basics, and re-structure them in a way that forces students to slow down and think through what they know, what they need to know, and how they can accomplish the task.  This is my goal...hoping it will work!

Diversity comes in many shapes and sizes

When I hear the word diversity, my mind automatically thinks of ethnicity or socioeconomic status.  While these factors are present among my students, the biggest form of diversity I see is parent involvement and support.  Both areas take on a variety of forms.

Parent involvement.
This ranges from the "has no idea what's going on in their child's life" to "hover parent".  In my opinion, both extremes are detrimental to the student's growth and learning.  The first tells the student that school is not important.  The second places a suffocating amount of pressure on the student to the point of rebellion or resentment.  Sadly, many of my students fall in one of these two extremes.  It is rare to find a student somewhere in the middle.  A student who is held responsible for their work but also given encouragement and guidance along the way.

Parent support.
This ranges from full to none.  Thankfully I don't see many students who are completely void of parental support.  But what does "full" parent support look like?  I feel old saying this but, when I was in school, parents supported the teacher and their child.  Now I often feel that parents support their child over the teacher.  It's not that this is entirely bad, but I do often see parents who will defend their child no matter what (even if it is ridiculous).  The parents I love to see are the ones who hold their student to high expectations while providing them with the love and support to figure out who they are and how to be successful.  This type of parent is not the norm.

My questions.
How can I support all my students without showing favoritism?  Is it possible to do without totally draining myself emotionally, mentally, and physically?  What are ways that I can more clearly convey to my students that I'm here, wanting to encourage and support them not only in math but in becoming successful young adults?

The next step.
I by no means have figured this out.  Outside of school, one thing I do to keep parents in the loop is send out frequent email updates.  I also keep my website and homework calendar up to date.  Parents are able to check their student's grade but I will also contact parents if I am concerned about their student's performance.  This has worked pretty well so far but there are still students who slip through the cracks.
In school, I try to make my classroom a safe place but also a place that expects students to do their best.  I am a warm and encouraging person by nature.  However, my students know they can't get away with slacking off.  I've tried to create a balance between high expectations for their work and actions and supporting the students as people.  I can't totally fill in the gaps left by the parents, but I'm going to try my hardest!

It's All a Balancing Act

Balance.  This is something I try to find in my teaching.  Balance between being nice and being strict.  Balance between building foundations and challenging the limits of student thinking.  Balance between predictable routine and thinking outside the box.  Balance between direct instruction and activity-based learning.

With all the changes that are coming with Common Core and Smarter Balanced Assessments, I feel the tension of this balance even more.  What can I do to prepare my students for a new (and yet to be determined) standardized assessment?  How can I help shape them into more critical thinkers?  How does that affect the way I teach, the homework I give, and the expectations I have for my students?  I want my classroom to be one that exposes them to technology and is a place where high cognitive demand is expected and achieved.

As a math department this year, we have been revising the 7th grade curriculum to include such things.  Some ideas have been successful, and others have not.  It is my goal this semester to try to assess and clean up our work in attempts at improving the curriculum and increase academic rigor for next year.

Being the first time through, I think we often are operating in "survival mode"...sometimes only a day ahead of the students.  It is difficult to find time to stop and assess the successes and areas of improvement in what we just completed because the pressures of tomorrow are creeping in.  And there it is again...balance!

Proportional Reasoning and the Olympics

In light of the Olympics, I found this activity on proportional reasoning: http://mathalicious.com/lessons/on-your-mark

I'm rather bummed that we just finished our unit on proportions because this would have been a really fun thing to incorporate!  The activity poses the question: Do taller Olympic sprinters have an unfair advantage?

First students calculate how far each sprinter would run if he ran a distance proportional to his height (using the tallest runner to set the ratio).  Using this information, they are asked to calculate how long it would take for each sprinter to run his new distance.  Based on these calculations the students are asked to find the new winning order.  Will the medals still be awarded in the same order?  The answer is no!  The original gold medalist will now earn bronze.

Next students use the second tallest runner to set the ratio.  Does this effect the original winning order?  The revised winning order?  Students will find that both revised winning orders are the same.  This is a great point to talk about what it means to be proportional.

The final task is to look compare a scatterplot showing actual time vs. height results to one showing the proportional results.  Students use these to discuss whether races should be reorganized by height.  In looking at the data, students may conclude that reorganizing would not be fair to taller runners.  In other words, there seems to be no good solution.  Someone will always be at a disadvantage.

I like this activity because it could be used to introduce proportionality or can be used as an extension to the lesson.  Student interest in the topic will help with engagement.  I also like that you can extend this discussion to other sports (ie. swimming, wrestling).

Gradual Release of Responsibility

Direct Instruction vs. Discovery...two opposite approaches to teaching.  Both can be effective and appropriate in different situations.  In my experience (though it is limited), students tend to zone out during the first and get frustrated during the second.  I really like the idea of Gradual Release of Responsibility because it seems to bridge the gap and allow students to build confidence in their abilities while still asking them to be active participants in learning.  I was first introduced to this concept in a literacy course but feel it works really well in a math classroom.  Here is the general idea:

1st:  I do, you watch.
2nd:  I do, you help.
3rd:  You do, I help.
4th:  You do, I watch.

As I progress through a lesson I try to incorporate this idea in my teaching.  Since I teach 7th grade and we are building the basis of algebra, many times my notes have a number of similar problems.  That means "drill-and-kill" is often my method for presenting notes.  It's easy to just talk at the students and then ask, "Any questions?"...to which I hear mostly crickets :)  Using this method during my lectures, I find my students are more likely to ask questions and take ownership over their learning.  I like that my students are beginning to pick up on patterns of thinking and solving.  I've found that there are fewer students who say, "I got it in class but when I got home I couldn't do any of them."  During the third phase I walk around the class to catch student errors and answer questions.  Students aren't able to tune out.  During the fourth phase I have students present their solutions.  Depending on the lesson, I may have them compare with a partner first.  My goal in this is to keep them engaged, build their confidence, and have the content stick with them.

Teaching: International vs. West Michigan

My teaching career started overseas in Casablanca, Morocco. Teaching at a small international school was a challenge because resources were few and the latest technology was an overhead projector! As one of two math teachers at the school, I had 5 different preps and was responsible for creating major pieces of the curriculum. Then there were the kids: trying to learn in a language not their own, hungry for relationship, appreciative of my efforts to be a good teacher. Kids will be kids no matter where you are in the world. These kids weren't perfect, but they stole my heart.

Two years later I moved back to West Michigan and got a job in a district much like the one I grew up in: supportive administrators, lots of resources, a collaborative staff. I am so blessed. Teaching here my biggest resources are my colleagues. I love working in such a supportive community. For me, one of the biggest challenges is connecting with kids who expect you to be amazing and engaging and include all the latest technology. In our world of instant gratification, I struggle at times to figure out how to reach kids and help them develop deeper critical thinking skills.

This year, teaching at the junior high level, I feel like I have the best of both worlds. My kids are young enough that they aren't "too cool for school" and haven't been too jaded by math. I'm able to teach math to the best of my ability and have relationships with students.