Interview Q & A's

Question 1:

Perfectly, that's how it was designed. It was designed at Michigan State University with NSF funding to perfectly align with the NCTM standards and then matched to the Common Core standards in their second edition.

Question 2:

Students that are behind need math intervention, including math lab with instruction aide support. The CMP was designed for student to be able to gain conceptual understanding through problem solving which should also help them build those skills from a conceptual level - because the CMP is so hands-on, it was designed to be accessible to students.

Question 3:

The application sets are designed to give students opportunities to practice their skills and also verify that they have an individual understanding of the skills because they often learn skills in a group setting but need to know how to complete problems by themselves.

Question 4:

Group roles are regularly assigned and rotated within their group. The teacher also has to be good about actively monitoring the students and helping to guide their exploration. Once the expectations are established, the majority of the students do not have issues. Troubled students are targeted, both by their seating arrangement and group placement for better supervision.

The ultimate accountability will be of course completion of the required task in the required amount of time. Individuals also have homework to complete.

The teacher's guide comes with excellent guidance for launching and closing the exploration periods, including checking for understanding and methods for ensuring that all group created algorithms produce correct results. Regular homework and quizzes also assist with assessing student understanding.

Inquiry & CMP Research

Google turned up a few different sites that were worthwhile in learning what is meant by "inquiry-based learning." Wikipedia was naturally helpful and described the difference between "inquiry-based learning," and "open learning." (The latter basically being students exploring without an educational goal or end in mind...risky...) The site that I felt put it into a good group of words was this one by MSU. It used "five E's" to discuss inquiry-based learning (Engagement, Exploration, Explanation, Elaboration, Evaluation). This connects well with the CMP model of Launch, Explore, Summarize...in a simpler and more to the point manner.

The CMP seems to be on the right track with mathematics education. The idea of a cohesive stream of learning is a positive that isn't taught well currently. Getting lessons to segue from one to the next is something that I often struggle with between units (likely because I'm teaching an integrated curriculum, but nonetheless aggravating at times...).

The goal of the CMP is simple...get students to investigate mathematical concepts and learn lessons for themselves in realistic contexts. The practical application is I think one of the missing links between where we want our mathematics students to be and where they are now.

Based on my teaching thus far, and the evaluation process of CMP lessons, I'm not doing badly at the "explore" section. I spend the majority of my time when not instructing floating around the room. One of my goals for the year was to spend less than 5% of class time sitting down...and let me tell you, it is already paying dividends! Although much to my surprise, we're not that far off from the end of the first quarter.

When compared with the traditional "direct instruction" model, there are correlations that can be seen between direct instruction's "instruction, guided practice, and independent work" and inquiry-based instruction. When the teacher is simply "instructing" students how to work a particular type of problem, the inquiry teacher is posing a question to students that will lead them to a problem. When the direct teaching is having students work through guided practice, the inquiry teacher is having students explore the problem and work through a problem. In this stage, many of the same things are happening: the teacher floats around the room and helps students when they need it, they ask leading and open-ended questions, etc... The real difference is in the last portion. When the direct teacher is having students do independent work to reinforce the learning, the inquiry teacher is having students explain what they learned. This promotes higher-order thinking skills as well as deeper learning of subject matter.

When I was fourteen years old, I won my first national title in trap shooting. It was only when I was twenty-one and acting as the shooting sports director at a Boy Scout camp and teaching rifle shooting every day that I had the deepest understanding of the subject matter (although I was no slouch seven years earlier...)

I think that I should add a goal for my teaching this year, something realistic that I know that I can attain if I work at it. For at least 50% of the lessons that I teach, have students explain to me either verbally or in writing, what it is that they learned and how they can apply it.

Closure and Anticipatory Set

Okay, for this one I'm not talking about what psychiatrists are always wanting you to find after you lose a relative or a finger to an unfortunate industrial accident.

My quick Google search for "closure in education" brought up a couple of things that were helpful, and some that were not.

First/last (it didn't really take long to find what I really wanted) on the "not" list was one dealing with the closure of I-405 in Los Angeles. They pontificated on whether or not homeschooling or other "alternatives" to traditional public schooling were viable alternatives to the "situation" in public education today.

About.com actually provided what it was that I really wanted to know about closure. Essentially, closure is what you do at the end of the lesson to reconnect students to the content. You want to review what it is that was learned and how they can relate themselves or the content as a whole to that lesson. H. Jurgen Combs provides a fairly comprehensive site on lesson plan design. In his page on closure he lists that closure helps teachers to decide upon three things: 1. if additional practice is needed; 2. whether you need to reteach; 3. whether you can move on to the next part of the lesson.

Synthesizing this into a statement for myself:

Closure, when relating to lesson planning, is the act of review with a class what was learned during the lesson to accomplish two main purposes: one, to determine understanding of students; two, to determine whether or not the students are ready to move on or if reteaching is required.

As for anticipatory set, About.com strikes again with another article in the lesson planning series. Having been familiar with terms like, "activate existing knowledge" or "scaffolding" or even "building upon prior knowledge," I finally have a group to which they will be assigned. Essentially the anticipatory set is where you introduce the students to what they will be learning and getting them to relate what they already know to what they will learn during that lesson.

Combs describes the anticipatory set as the "attention getter." I couldn't think of a better definition for part of it.

Some things that I may do as part of the anticipatory set are have quick discussions about past material that leads into the day's lesson. Adding and subtracting in solving one-step equations as a lead-in to multiplying and dividing to solve one-step equations would be one example. For my LEGO robotics class, I may ask students if they have tried to organize their robot's missions before they take off of if they just start out and go for gold. This would be an anticipatory set conversation for a lesson on mission planning. (Further discussion on getting stuck and frustrated for that one as well...)

Practicum - Sharing a Lesson

So this isn't from a practicum or even from one of my normal classrooms. For my first three years of teaching I did academic support and enrichment for the Mapleton L.E.A.F. (Learning Enrichment and Fun) after school program. Last spring, I was doing a unit on astronomy and I wanted to teach kids about why there was less or more daylight during different seasons.

Here's what I did...I took a 500W light bulb that I borrowed from maintenance and screwed it into my desk lamp (I took the shade off). Then I put that on a chair, on a desk in the middle of the room. Then I grabbed the stick that I had dutifully duct taped a globe to the end of, pulled the shades, turned out the overhead lights, turned on the desk lamp, and was off to the races.

I started by showing the group of children what the earth looked like during the summer in Oregon. (I only had seven kids, mostly 4th and 5th graders, that day.) I asked them to put a finger on where they lived in the world, I only had to correct two that thought we lived in France. Then I had them watch as I rotated the "earth" through a few days. I asked them if there was light on Oregon for "a lot" or "a little" of the day. Then I asked them when the days were longest, then I asked them what season our "classroom earth" was in at that particular moment. It was fun, I moved through the equinoxes and winter and showed them the same types of things, equal amounts of light and dark, more dark than light, etc...

Likely one of my favorite lessons of all time. What was great was that I was (I just used the word "was" three times) able to gauge understanding constantly by listening to the childrens' answers to my questions and seeing the "a ha" moments with others.

Were I to reteach the lesson, I'd likely do it as a "discovery activity." I'd give students styrofoam balls with sticks through to represent the axis and a worksheet.

Warm-ups in Math Education

"So, Mr. Longo, based on your research and personal philosophy, what is the purpose of warm-ups in your classroom?"

The question really has two answers. The first has to do with classroom management. If I am able to get students into the classroom and immediately on task, the first few minutes of class that are usually lost doing attendance are no longer lost, but gained as valulable instruction time that not only increases a student's contact with the content, but also gets them in the correct mindset for the rest of class thereby encouraging positive behavior during class.

The second, has to do with the student's learning more directly. Warm-ups can be used for a variety of reasons: I may want to activate prior knowledge so that I can get the day's lesson moving easily without having to review content as I go; I may want to address a common gap that came up while grading a quiz or a homework, I can put a similar problem on the warm-up and do it with the students as a group; I can use it in conjunction with current content and test taking strategies - I will sometimes use content that I know that the kids are doing well with and frame questions in the style of a standardized test...this way I'm able to accomplish my management goal but also reinforce or help teach students strategies that will help them on standardized tests later in the year. Also, let's say for the sake of argument that I wanted to teach students how to find the internal angle measures of irregular polygons. I would probably put a series of questions on the warm-up that contained finding the internal angle measures of regular polygons and finding missing angle measures in irregular triangles. I could then mash these two skills together during the lesson and have students on the same page as me as soon as I start the lesson.

"I hope that answers your question Mr..."