Dave McKae teaching

The purpose of this video is teaching the mean as a balance point. Most people understand the algorithm, but they have never considered it as a balance point. I use a ruler, a paper towell roll, and 3 quarters to demonstrate how to do this. I then explain it using a line plot.

It took me a while to navigate my way around between emails and blogger because Willamette.edu accounts through gmail are not compatible with blogger and my blogger account is through gmail. Each time I tried to switch between documents, I had to log out and log in to the other account. Other than that, I found that it was easy to record video of my lesson using a tripod, though you never see my face. I had trouble embedding the video and chose to post the link instead. The website said I had to wait in line while the video was being converted (plus members don't have to wait).

Dave McKae teaching mean as a balance 11-5-11 from Dave McKae on Vimeo.

If video does not embed, link to video is below, click to view.

Dave McKae teaching

CMP - Inquiry based teaching interview

Interview with LK, 10/24/11

Interview Questions to address the following:

How does the CMP curriculum align with the national Common Core and NCTM standards?

It was picked because it does align. You can move the concepts around. For instance, Data Distribution is 7^th grade booklet but it is an 8^th grade concept for Oregon, so it fits our needs really well.

Numerous students are a year or more behind in the basics. How does one address the needs of these students on a daily basis so they can get up to grade level and also experience success in the inquiry to investigation philosophy of the CMP?

We do starter activities and review concepts, but for the most part we just give these students a calculator. If they do not know how to add or subtract by the time they are in 8^th grade, we do not have enough time in the day to help these students master these skills. They will get too far behind the rest of the curriculum. We want them to focus on problem solving skills, not calculating skills.

What is the role of homework (and accountability) in the CMP? ___CMP Investigations compose of small-groups (pair-share, teamwork, cooperative learning).

Practice skills learned in class. Accountability is up to the teacher, but it is not part of the CMP. We are not required to assign homework.

Describe several classroom management techniques that ensure all students are actively engaged. Eg, how are individual roles established? Accountability (Group, individual)? Ongoing assessment(s) and checking for understanding?

We use our protocols of turn and talk, go around, private think time, a and b partners, etc.

When students are working on problems I walk around and do selecting and sequencing. I also ask students to revoice either what I said or what another student said.

Warm-Ups in Math Education

In my research and experience, warm-ups are a very valuable component to a lesson as they provide an informal assessment of information that you would expect students to already know. Furthermore, it is actually like warming up the student's brains as their brains begin firing and re-kindling stored information so it can be used. In essence, it acts like a "grabber" to engage the students. The warm-up is generally most effective when the problems target skills that are required in order to complete the task on that day. Sometimes, these warm-ups can be geared toward skills required for passing OAKS and by reviewing them daily in these warm-up activities, they are getting extra repetition.

Traditionally, math warm-ups consisted of the teacher placing 5 problems on the board or overhead projector and the students privately work on each problem when the tardy bell rings. The teacher then goes over the answers and asks if there are any questions. With the new and improved teaching methods such as CMP and inquiry based teaching, it is possible that the warm-up activities consist of the teacher posing a question, the students thinking about it, then turning and talking to their partner or table group in a discussion. The class then discusses some of the answers the groups came up with. The students warm up their brains through active discussion and listening to their peers instead of the traditional "chalk and talk" method, which can be boring for students. When the students come up with the answers themselves, it gives them a greater sense of ownership and can increase motivation.

CMP vs. Inquiry Based Model research

The Connected Math Project (CMP) emphasizes inquiry and investigation which forces students to be more engaged in the curriculum. This models shows that there is more to mathematics than calculating answers and memorizing definitions or processes. The goal is to be able to solve a variety of problems, and therefore students needs to spend time solving problems that require "thinking, planning, reasoning, computing, and evaluating". Students will be able to make sense of what they are learning and will be able to retrieve the information better at a later time than if they were simply memorizing a definition or process. Information is also connected to prior knowledge so that students can better retrieve information.

"Tell me and I forget, show me and I remember, involve me and I understand." The last part is what inquiry based learning is about. Students become involved in questioning to gather information as they seek understanding. It involves developing experimental and analytical skills more than accumulating and memorizing facts and knowledge.

The CMP model is far from the traditional "chalk and talk" methods of teaching. In the traditional methods, the teacher answers most of the questions and tells students what they should know as they stand in front of the class and preach. The CMP model is more closely tied to the inquiry based model in that the teacher asks more thought-provoking questions and the students come up with answers. In essence, the teacher becomes more of a facilitator of discussions rather than the one doing the discussing. The class as a whole may agree or disagree as part of the learning process, which engages the students. Teachers have to learn to be comfortable with long wait times as students are thinking about what to say. This is important because if the teachers intervene too early, then the learning opportunity for the students is lost. Students are much more engaged and involved in the learning process in this environment than in traditional teaching methods.

Closure and Anticipatory Set

http://k6educators.about.com/od/lessonplanheadquarters/g/closure.htm
http://www.edulink.org/lessonplans/closure.htm
http://www.proteacher.net/discussions/showthread.php?t=197015

Closure: wrapping up, or summarizing a lesson plan while providing the context and "big idea."

Activities:

1) 3-2-1 method: Have the students write down 3 things they learned, 2 questions they have, and 1 thing they liked.

2) Have a class discussion where the students compare and contrast newly learned concepts with old concpets. How do the new concepts build off of the old concepts?

3) Either write down or discuss 3 whats: 1) What did we learn? 2) So What? and 3) Now What?




Anticipatory Set: informing the students of the lesson objective while activating their prior knowledge to lead into the lesson. A unit opener.

Activities
1) Start with a question and have the students use their thumbs to indicate their level of understanding. The question should be based on previous knowledge and the next unit.

2) Ask students if any of them think they might want to use their creative skills to build something in the future. Could they see themselves doing it for a job? Provide examples of jobs that use mathematics such as engineers, builders, contractors, etc. Then introduce the next concept and how it directly relates to those jobs.

3) Review what an equation is and how to solve a one-step equation with one variable. Give them private think time: What do you think you would do to solve this two-step equation with 2 variables, x and y?

http://k6educators.about.com/od/lessonplanheadquarters/g/anticipatoryset.htm
http://www.hope.edu/academic/education/wessman/2block/unit4/hunter2.htm
http://creatinglifelonglearners.com/?tag=anticipatory-set
http://www.lessonopoly.org/node/2690

Practicum - Sharing a Lesson

The lesson objective was to have students discover that the length and width of rectangles are inversely related in regard to a constant area. Students were expected to come up with 5 dimensions of rectangles with a constant area of 350. (Examples, 1 X 350, 2 x 175) Students created a table and then plotted these points on a graph. The end result was a curve that is symmetric about the line y = x.

Prior to assigning this problem, students were asked for the general formula for area of a rectangle (L x W = A). They also tried solving dimensions of rectangles with area of 24. Overall, the class had a good idea how to do this and there were hardly any questions. They came up with all possible dimensions using whole numbers. The "AHA!" moment did not come until later.

I assigned the problem and required that students work with their elbow partners. The only students who struggled with the problem had their general equation mixed up ( Some of them solved for W or L and had the area on the bottom instead of the top). I stopped the class, asked for everyone's attention, and cleared up the problem since more than a couple groups had done the same thing. I had to stop later to talk to the class about their graphs because several groups did not have incremental changes on their axes. Each line must go up by the same amount in order to draw the graph properly. Some students also connected their lines to the axes, which could never be true for dimensions of a rectangle. Neither dimension can ever be zero. This was our final discussion right before the bell rang. The student's attempts and failures allowed them to learn more about the concept of inverse relationships.

If I were to re-do this assignment, I would not have changed a thing. It is OK for the students to struggle and somewhat necessary for them to learn. If I gave them ALL of the answers upfront, I do not think they would feel the same sense of pride and ownership over their work when they figured out the right answer.

The Appropriate Use of Technology

Under the NCTM algebra standards, I have selected a lesson called Barbie Bungee by Samuel Zordak. In this lesson, students will use rubber bands and a Barbie doll to simulate bungee jumping. The students will collect data, design a scatterplot on Excel with a line of best fit, and predict the number of rubber bands needed for jumps at any given distance. Since the height of the doll’s fall is directly proportional to the number of rubber bands used, the students will realize that this is a linear relationship.

Samuel first explains the main idea and purpose behind this lesson and then clearly states 3 objectives using bullet points. After listing the materials, the author goes into the instructional plan. The first thing he does is critical for the success of this lesson and is an excellent teaching strategy. Samuel asks the class a couple questions to capture their attention. He asks, "Do you think the length of the cord and the size of the person matters when bungee jumping? Would it be smart to lie about your height or weight?" To further increase the student’s interests, Samuel shows the class a video or two on bungee jumping so that students who may not be familiar with the activity understand what it is. I also noticed that in a way he challenges the students with this lesson by asking them to see how close they can get the doll to the ground without touching. This almost makes it like a competition and gets the students excited to build it and try it out.

Before students begin, the teacher models how to tie slip knots and double-loops in the rubber bands. Once the data is collected, the teacher reminds the students to check for outliers as these may have come from errors in their data collecting. The outliers should be tested a second time for accuracy. Samuel goes on in his lesson plan and lists questions for students including reflection activities such as journaling. He provides a rubric with 5 categories to help with the grading. The NCTM standards are offered in the end along with a section for the teacher to reflect on and options for extensions of the assignment.

The main problem that the students are trying to solve is the relationship between the number of rubber bands and the maximum height at which the Barbie should be dropped. By doing the experiment and plotting the data on an Excel spreadsheet, they will see that they can predict the number of rubber bands needed for any height and the maximum height if given the number of rubber bands. There is a linear relationship between the two and that is the main lesson. Students become familiar with how to use Excel to go from a chart to a graph and draw the line of best fit.

This lesson had an excellent “grabber” at the beginning to interest students, adequate background information, materials, specific instructions, and the “wow” or “Aha!” moment came at the end when the students realized they could make predictions based on their findings. The journaling and student reflections are an important part of this assignment as the students are asked to think critically about the data and what it means. Perhaps the students could make a prediction at the start of the assignment as to what will happen.

Standards, Standards, Everywhere

I thought we would find more standards involving linear equations or at least more details on the CC standard. The CC standard was a bit more vague than the NCTM standard. When I read the NCTM standard, I immediately knew how we were going to structure our lesson to meet this standard. The CC standard is so broad that you could miss out on making an important connections between the equations and how changes to their properties transform their corresponding graphs or tables. The CPM was more similar to the NCTM in that it states the specific skills that students will learn in regard to linear equations. I feel like I will look more to the CPM for specific help than the other two. CPM has 7 bullet points regarding linear equations, NCTM has two main references, and CC only has one.

Task 1-3 - educ 533- Best Practices Research

Research on Best Practices in Education

Block Scheduling - I experienced block scheduling for the first time this past school year and I thought it was great. As the NEA website suggests, "Students have more time for reflection and less information to process over the course of a school day." This is a major pro in my mind for having a block schedule. With the current 7 period schedule, I find that students are overwhelmed with the information they learn in up to 7 classes in one day. In addition, the 7 period schedule seems to decrease what the teacher and students are able to accomplish in the classroom and therefore the teacher must schedule more homework to make up for the lost time. I also liked that the block schedule gave teachers more contact time with students for individualized instruction.

http://www.nea.org/tools/16816.htm

Cooperative Learning - The idea that students sit in teams and help each other learn seems like a great way to teach. For one, students often explain concepts in a language that is easy for their peers to understand. As I do my practicum in the middle school, I see students sitting in groups of 4 and there are specific rules posted on the wall for group work. The most important rule is that no one is finished until all group members completely understand the assignment. The other rule I liked is that no one is allowed to ask the teacher a question unless all group members are confused as well. Students will experience tremendous growth from this arrangement as they learn to struggle through problems and work in teams.

http://www.nea.org/tools/16870.htm

Research on Best Practices in Instruction

Math Power Hour - This one caught my attention because it was submitted by an elementary school near my hometown in Walnut Creek, CA. The school was able to raise state math scores from 85% passing to 100% passing and 35% Commended level performance to 43%. The school gave the students an assessment at the start of the year and a list of missed objectives was generated. The students were then placed into small groups based on the areas they missed for a weekly "power hour" where the teacher spent the entire hour working on mastery of those skills. I like this because the new principal saw that this was a problem and he did something about it. This method worked really well! I would consider this "deliberate practice" because they are working on specific areas with the intent to raise scores. It's shocking what happens when you actually teach to the student's needs.

http://ritter.tea.state.tx.us/bestprac/bpc_instruction.html

Reinforcing effort and providing recognition (Marzano) - Studies have shown that a little praise for legitimate effort goes a long way in building confidence in students and motivating them to learn. Teachers should show students the connection between the added effort and the quality result. This is something that may seem obvious, but not enough teachers praise their students when they do things well. Especially at the middle school level, students are so fragile at this point that they are deeply affected by feedback from the teacher.

http://www.slideshare.net/Lorrene/marzanos-best-practices-and-instructional-strategies

About Me

My name is Dave McKae and I am an educational assistant and the head varsity baseball coach for Mountain View High School in Bend, Oregon. I am 29 years old and married with no kids, just a golden retriever puppy named Murphy. I plan to teach high school math. I decided to become a teacher because I enjoy helping others achieve their goals, as I have done for the past six years with baseball instruction. Many people have the talent, they just don't have the skills or the knowledge of how to develop a strong work ethic to achieve their dreams. My job as a teacher will be to not only help them succeed and understand math, but to create life long habits that will give them the most opportunities and be prepared to succeed when these opportunities arise.