Wednesday, December 17, 2014

Advocating for the Common Core

I support the Common Core. In 2010, when I was first introduced to the standards, the geek in me was excited about diving in, making sense of what they said, and creating learning opportunities for students. I embraced the change because the new standards are better than what we had.

Here's a comparison.

Previously, students were to use linear functions and now they are expected to create linear equations. The change in verbs is a critical transition from the old standards to the new standards. The expectation of what students are to know and be able to do increased. When I noticed this difference in the expectations I began to seek a better understanding of the standards and what I really needed to get my students to do.

In 2012, I became a math coach and a large part of my job is supporting teachers to implement the new standards. One standard in particular is
G-GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

What? I didn't know how to do this much less teach students how to do this. Thus, I began my journey into learning about partitioning. Did you know that students in elementary grade partition? Yep - it's true.
  • 1st grade: Partition circles and rectangles into equal shares.
  • 2nd grade: Partition a rectangle into rows and columns of same size squares.
  • 2nd grade: Partition circles and rectangles into two, three, or four equal shares and describe the shares.
  • 3rd grade: Interpret whole-number quotients of whole numbers (56/8 is 56 objects partitioned into 8 equal shares)
  • 3rd grade: Understand a fraction 1/b as a quantity formed by 1 part when a whole is partitioned into b equal parts
  • 3rd grade: Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts.
  • 3rd grade: Partition shapes into parts with equal areas.
  • 5th grade: Interpret the product (a/b) x q as a parts of partition of q into b equal parts.
Now, in high school Math 2, students must partition a directed line segment.

I looked for resources and found examples of how (procedural understanding). I found a few examples of why (conceptual understanding) but they came from the approach of vectors (not a prior understanding for Math 2 students). I didn't find anything that built upon the previous standards (coherence). So, what did I do? I wrote an investigation which can be found here

This is the stuff I love - learning, creating, making sense of the things. The new standards have challenged me to think and that is a good thing. The new standards have prompted me to learn about how students are thinking about and doing mathematics in grades K-8. The new standards have introduced me to new concepts.

I am an advocate for the CCSS because of what it offers teachers and students - a focused, coherent, and rigorous mathematics education.

Wednesday, October 29, 2014

44th Annual NCCTM Conference

I am excited about this year's NCCTM State Math Conference. It is a great time to talk with others who are as interested (and yes, passionate) about teaching and learning mathematics. This year's theme is Big Ideas for Teaching and Learning Mathematics.

Each year I try to share one workshop that examines a specific content area and one session that looks at a teaching practice.

This year's content workshop is "Transforming the Way We Teach Transformations." I was inspired by an article with a similar title in the August 2010 Mathematics Teacher written by Eileen Fulkenberry and Thomas Fulkenberry. (You can find the article here.)

"What Does a Grade Say?" is my session addressing a teaching practice. I will discuss Outcomes Based Grading. This is a practice that I started in my classroom in 2011 and now, as I coach, I support and help teachers implement this practice in their classrooms. It's been an interesting endeavor to put into a presentation all of the complexities regarding something that seems simple.

For those at the conference, I hope you have an opportunity to join me. Resources from the presentations can be found on the Presentations page.

#1325  Transforming the Way We Teach Transformations  10:30 - 12:00  Colony A
#1538  What Does A Grade Say  12:30 - 2:00  Meadowbrook

Sunday, October 12, 2014

Creating Curriculum Resources

I don't remember when I started developing my own resources for teaching and learning. (To be clear, I am referring to engaging learning tasks and not worksheets for practice.) It certainly wasn't when I was a beginning teacher. In my second year of teaching I was responsible for the textbook adoption at my school. What influenced my decision the most? The amount of "extras" that was included. Yes, I was impressed by the boxes of ancillary materials and the promise of consumable workbooks for each year of the adoption.

The year after the adoption, when I was using the new textbooks with all the "extras", I was introduced to a new curriculum resource Core-Plus Mathematics Project. It didn't have all of the extras. As a matter of fact, the textbook wasn't even in color unless you consider pink accents as color. The use of these materials has shaped my philosophy on teaching and learning. After years of using Core-Plus, whenever I needed a resource that was not included in the textbook, I began creating my own. It was out of necessity because those boxes of "extras" didn't provide learning tasks that assisted me in facilitating students thinking about and constructing their own understanding of the mathematics.

Fast forward 14 years. I am now a high school math coach and part of my responsibility is to assist my teachers in curriculum resources. This includes obtaining, evaluating, developing, and using the resources. One of my goals in coaching is to influence teachers to become "standards based" teachers and one strategy is using quality learning tasks. This is a challenge for a myriad of reasons of which I will not expand upon here. Suffice it to say, as a result, I find that I am writing curriculum resources.

One of my professional goals is to create curriculum resources that
  • are good, interesting, and beneficial for teaching and learning math
  • explicitly address the instructional shifts (especially for concepts that are lacking in our primary curriculum resources),
  • include instructional strategies for use with students
  • and inspire others to create learning opportunities specific to their students.
You will find these resources (and some created by my colleagues) on this site. I offer them to you to try, share, tweak, critique, and learn from. All I request in return is feedback. What worked? How can it be improved? What did students say and do? I value your input and appreciate you joining me in this important work.

Wednesday, September 17, 2014

Trouble with File Access - RESOLVED

The file links are working once again. If, in the future, they are not working, please let me know.

It has come to my attention that visitors are not able to access some of the files that I have shared. This is apparently a problem with Google Drive which is where I store all of my files. The Google Forum has posted that they are aware of the problem and are investigating.
I will be monitoring the progress. If not solved soon, I will look into other options for file sharing. If there is something you need, please comment below. I will email you the file as soon as possible.

Sunday, September 7, 2014

To Reason Quantitatively

The other day I was listening to a class discussion about independent and dependent variables. The teacher provided students with two related variables and asked students to determine which one was dependent on the other. For example, price of a ticket and number of customers.

What I observed is that few students responded. More importantly, after the discussion was over, I still had no idea which students could identify and justify which variable would be dependent and which would be independent.

The teacher and I met afterwards and planned an activity that we thought would generate more student engagement and provide information about what students really understood. The plan was to ask students to generate variables they thought were related. Next, each student would share the variables and the rest of the students would move to one side of the room or the other as to which variable they thought was the dependent variable. Students would provide their reasoning for their choice. Repeat...

So what happened? Here are some samples of what students wrote:

Hmmmm... Not what we anticipated. It appears that students identified "things" that are related but without thought about the measurement or quantities. How can we discuss independent and dependent variables when students don't recognize the quantities that are represented by the variables?

The second Standard for Mathematical Practice is to "Reason abstractly and quantitatively." What does this mean, especially to reason quantitatively? What does this mean students can do? How do we, as teachers, design experiences that increase students' ability to reason quantitatively?

 6 Principles for Quantitative Reasoning and Modeling
I recently read the article "6 Principles for Quantitative Reasoning and Modeling" by Eric Weber, Amy Ellis, Torrey Kulow, and Zekiye Ozgur (Mathematics Teacher August 2014 Vol. 108 pp. 24-30.)

The authors describe quantitative reasoning as a "specific way of thinking about mathematics" and focuses on its role in the modeling process. The first of six principles for integrating quantitative reasoning in instruction is "Rewrite a problem situation or prompt so that students must identify the quantities that they believe are relevant to solving the problem." The key idea that really stands out to me is the students identifying the quantities.

I am coaching the teacher to infuse this principle through every activity she can throughout the next module and then repeat the activity again. We agree that this must be an ongoing theme and not something a single lesson will address.

Through this experience I have become "hypersensitive" to whether students are reasoning quantitatively and if teachers are providing opportunities for students to develop this habit of thinking about mathematics. So, when a teacher asks me for advice on a lesson plan or an activity this is one of lenses I am using.

How do you address this mathematical practice? Share your experiences and strategies.

Saturday, August 16, 2014

The 1st Day of School

What should students do on the first day of math class? It seems that the standard introduction includes a syllabus, grading policy, rules, and procedures. What seems to be debatable is whether or not students should do math on the first day. Huh?

When I think about the first day, I want to clearly communicate expectations. One of the expectations is that everyone will engage in the teaching and learning of math on a daily basis. This means every day - including the first day.

The first day would include making sure the students are in the right class, briefly introducing myself, go over three rules (Be Ready, Be Responsible, Be Respectful), and then do a math task.

What kind of tasks are good for the first day? I look for a task that:
  • is engaging / interesting
  • has students collaborating
  • has multiple entry points for students
  • has multiple solution methods
  • includes math ideas that launches the first unit of study (if possible)
One of my favorite tasks for Math 1 is Crossing the River. The premise is that there are 8 adults and 2 children that need to cross a river. The boat can hold either one adult OR one child OR two children.

The Launch: (I like to tell stories to engage students in the situation. So I tell them...)
Calderwood Lake - The Men's Camping Trip
My husband and son go on a Men's Camping trip every fall. On one of these trips they were going to hike around the lake. Eight of the men, my son, and another young boy took off early in the morning. When they were about halfway around the lake, the sky began to get cloudy and it appeared that a storm was arriving. One of the men noticed a boat and suggested they take the boat across the lake to quickly get back to the campsite. Testing the capacity of the boat, they determined that only one adult OR one of the boys OR both of the boys could be in the boat at one time. Now what?

Students are provided the opportunity to ask questions. These include:
  • Are the boys capable of rowing the boat on their own? Is it safe?
  • Should they be taking a boat that doesn't belong to them?
  • Is there rope so they can pull it back across?
  • How much time would it take for them to walk back or continue on?
  • How much time does it take to get across the lake?
  • How many trips would it take to get everyone across the lake?
The types of questions students ask indicate if students are thinking quantitatively. The first few questions are about the situation but not ones we can explore. The last few questions are ones that involve some quantitative reasoning. After the questions are posed, we discuss which ones can be explored with the information we have at hand. The last question is the one we focus on.

The Exploration:
I inform students that there are materials available for their use located in the resource center. These include paper, colored paper, graph paper, rulers, chips of different colors, scissors, etc. (Doing this on the first day introduces students to the resource center and sets the procedure that they can access these tools whenever they need something.)

Students work in groups to determine an answer to the question. (I prefer groups of 3 and no more than 4.) Some draw pictures while others get the color chips and begin manipulating them back and forth across an imaginary or sometimes drawn lake. Eventually, they determine the number of trips. I ask extension questions to groups. What if there were 15 adults? 30 adults? What if there were 5 kids? 

The Share Out:
For this activity I tend to focus on the different ways groups approached the problem. I select and sequence how groups share with the intent of creating opportunities for students to compare their methods; understanding the differences and the similarities.

Now that the students have a shared common experience I use it to discuss expectations such as making sense of problems, collaboration and student discourse.

For the next two weeks students will learn the different procedures for the classroom when they need to know them. For example, where do they put papers that need to be turned in? We will go over this the first time they have something to turn in. Another example, what is the procedure for leaving the classroom? I go over this the first time a student asks. I have determined that students often don't really learn the procedures for the classroom until it becomes something they recognize they need to know.

The first day focuses on the expectation that math class will be about developing and exploring ideas using math.

Saturday, August 9, 2014

5 Reasons I Started McPherson Math

#1 To become a more reflective educator.
        The school year is very busy with each day bringing its own set of priorities. I am constantly asked for help on a variety of issues that teachers deal with on a daily basis. As a reflective teacher, I must be purposeful in thinking about what I have planned, observed, and experienced. How did my actions effect teaching and learning?

#2 To document my own professional growth.
         My job as a high school math coach involves focusing on the professional development of teachers. I am constantly researching and developing plans specific to my teachers' needs. Whether it is new content, new technology, or a new teaching strategy, I am always learning and growing as a professional.

#3 To engage in conversations that challenge me to think about educational issues.
         I like to debate the issues because it helps me develop and/or clarify my viewpoint. It also helps increase my capacity to communicate with others. I'm invested in teaching and learning and want to be knowledgeable of the issues so I am able to advocate effectively.
#4 To impact others by sharing ideas, struggles, and triumphs.
         For years I have referred to myself as a BASE teacher. (That stands for Borrow And Share Everything.) I enjoy collaborating with others, sharing whatever resources I have, seeking solutions, and celebrating our successes. I've tried other digital platforms to share resources and I hope this one is easier to maintain and for others to use.

#5 To have fun with math.
         I like math and I really like a good math problem. It's the geek in me and I own it.

So, there you have it. Five reasons why I started McPherson Math. I hope you join me for this journey.