CMP-Inquiry Middle School Interview

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

For many years now, Salem-Keizer has modified the order and level of the CMP books from what the authors originally wrote.  With that being said, it seems like it was not aligned very well to the state standards.

With the upcoming national standards the district and the authors are working hard to find some alignment.  Last summer the authors of CMP held a workshop to introduce supplementary units which will patch up the curriculum to fit the new national standards.  However, I find the units a little disjointed.  The authors have begun a third addition of CMP to match the national standards.

2.   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? 

• The best way is to have a support class which helps the kids fill in during another period.  However, that is not always possible.  So the teachers spend a lot of time looking at the material the kids should have learned before and building those skills into warm-ups or 5 minute drills.
• In my class, I am lucky to have 15 computers which can be used to differentiate the classroom.  I have used them to do Math workshop which is basically different stations.  The lower kids are with me in a group and the higher kids are on the computer doing Math whizz or manga high as fun extensions.  In a perfect world I would like to do this once a week but I tend to get behind in my implementation plan if I do that.
• After school tutoring also helps.  Our special education department holds a mandatory special education help session twice a week.  Students get individual support on class work.
• About CMP and the inquiry approach and kids with low ability.  It is hard.  If you follow the grouping strategy of CMP then being very strategic in building the groups is important.  Most of the time, I try to put mixed groups together so kids can learn from each other.

1.   What is the role of homework (and accountability) in the CMP? ____

CMP has three levels of homework for each investigation.  The first are application, the second, connection and the last, extensions.  I believe that homework is practice of what the student has a beginning understand of.   However, the constructivist approach that CMP uses often follows through on the homework assignments making them a huge challenge for the kids.  I know we are trying to increase rigor with the work but we don’t want to deflate the kids.

Because homework is practice, I count it very little in my grade book.  I ask the students to try at home so that they connect to the problem and can find their mistake easier.  Since I stopped grading homework, I have less accountability from the students so this is still a place I struggle.  I have thought of doing all work in the room but there are not enough hours to do the teaching and practice of all of the standards.

2.   CMP Investigations compose of small-groups (pair-share, teamwork, cooperative learning).

§  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? 

I like using partners and then I ask who wants to share and pick the partner instead of the volunteer.

In groups of 4 I have assigned roles for the 4 students (recorder, time keeper, supply person, drill Sargent) and they have to do their roles.  One student is responsible for asking group questions so I will not talk to the whole group.

When groups are stuck or off task, I ask one member to huddle with me to get some questions answered and take the answers back to the group.

To establish roles, I have used cards that they pick or have them number off and all 1’s are recorders, all 2’s are time keepers…). 

Accountability is hard.  I ask each student to turn in work rather than group work.  I have done partner tests but I will also do individual tests.  I want to know what each student understands.

I often do formative exit quizzes on skill based questions.  Very simple 5 minute questions and I record these at 2 points or “not yet” in my grade book.  We circle back to make sure the students have a chance to show me that they understand.

Inquiry and CMP Research

Guiding principles:

•     Both the big idea of the curriculum or unit are identified for the student as well as the underlying skills and concepts, so the student will know what they are learning and how it connects to what they have learned. 
•      It is made clear how the concepts the student is currently learning are connected to what the student has learned in the particular lesson, unit, grade, and how the concepts are connected to what the students have learned in previous grades.
•       The most effective way of learning math includes a process of investigation for the student, where they are actively exploring and solving an idea or problem
•       The explorations are purposefully in depth to support deeper understanding and memory by the students.
•       Part of making problems in depth is having students read and write problems in multiple representations—graphic, numeric, symbolic, and verbal, and to fluently move between these representations.
•       Calculators and computers have changed the way people think about and solve mathematical problems, and the curriculum reflects this transition.

   Comparison of CMP and direct instruction:

In direct instruction, the initial phase is a set, or hook, where the teacher’s goal is to introduce and interest the student in the material. In contrast, the initial phase of CMP is Launch, where the teacher helps the students understand the problem setting, the mathematical challenge, and the concept. In both methods, the teacher is introducing the lesson.

The main difference between the two methods is evident in the next sections. Typically in the direct instruction method, the teacher moves on to the instruction step of the lesson while the CMP method moves to the Explore step. In instruction, the teacher is instructing the class how to accomplish the goals of the lesson, and providing examples of the concept that is being covered while the students are listening to the instruction, answering questions that the teacher asks, and taking notes or following along either in groups or individually. In the Explore step of CMP, the students are presented with a problem and they gather data, share ideas, and look for patterns, while the teacher roams the class and helps individuals and groups.

The final stage of the CMP method more closely resembles the instruction phase of its counterpart. This is where the teacher helps guide the students to the goals of the lesson, clearing up areas of frustration along the way. In case some groups did not make it to the final product of the lesson, the teacher must also find a way to get everybody caught up. In direct instruction, the final activity also wraps up the lesson, and makes sure everybody is on the same page about what should have been learned.  

Anticipatory Set and Closure

Anticipatory Set

http://www.edulink.org/lessonplans/anticipa.htm

http://nataliemckinney.com/downloads/Madelyn_Hunter_Lesson_Cycle_-_Anticipatory_Set.pdf

The anticipatory set is in the opening of the lesson and provides the hook to motivate students to be interested in the lesson. It can also focus students attention on a specific topic, provide a connection to a past topic, and provide a preview for what the lesson is going to be about.  

The anticipatory set can also provide priming for the lesson. Priming is important because it “accelerates the understanding of concepts and gives the brain information to build into a more complex semantic structure or hierarchy later on.” (Jensen, 2005). Examples of an anticipatory set include provocative questions, review of the previous lesson, a story, or an intriguing statement or fact.

Jensen, Eric (2005) Teaching with the Brain and Mind ASCD: Danvers, MA

Closure

http://www.edulink.org/lessonplans/closure.htm

http://template.aea267.iowapages.org/lessonplan/

Closure is the last activity done in the class. As such, it helps organize student learning by letting them know that they have arrived at the end of the lesson. One of the main ideas behind closure is that it will bring the lesson into a coherent picture for students in order to eliminate confusion or frustration with the lesson. A good closure activity will often summarize the main ideas of the lesson to let students know what they have learned or should have learned from the lesson. Another goal of a closure activity is to help tie the current lesson with the next lesson if possible. In order to do this, let students know what key information from the current lesson they will be able to use in the next lesson.

Not only is closure helpful for students but it is also vital for the teacher. A good closure activity will tell the teacher if additional practice is needed, if parts of the lesson need to be re-taught, or if the teacher is able to move on to the next topic. The ability to use closure as a means for adjusting the lesson is critical in education, and has become increasingly more important as the transition is being made to standards based grading and graduation because ideally every students needs to understand every topic. Examples of closure activities include a survey or exit card, asking the students what they learned, or having the students write a reflection or application.

Practicum- Sharing a lesson

This is a lesson that I taught in an algebra 1 class today at McNary High School. The objective for the lesson was for the students to be able to write an equation, a chart, and a graph from a word problem. The students had already been doing this for the past two days, so I was pretty confident that they could complete the task quickly. After the warm-up, I broke up the lesson into 3 sections. In the first section I went over a group/class problem and checked for understanding by a combination of randomly calling on students to contribute and doing a thumb check. As usual, it was hard to get a good picture of understanding with the thumb count because there was limited student participation. However, I think I was able to keep most of the students tracking by calling random names.  

The second section was individual work on a problem like the one that I did with the class. During this section I tried to go around and answer questions for student who were struggling. During this section of the class I was bombarded by quite a few students who wanted to go to the restroom/get a drink of water/ etc. Also, the students who finished with the problem quickly were left wondering what to do next. On the positive side, I think the students who got the one-on-one attention understood the concept much better than they had the previous days. I was also checking to see how students were doing by glancing down at their papers. I think enough students are having difficulty with it that I may do another review problem with the same concepts for a warm-up tomorrow.

The third section was supposed to be a short amount of time for the students to do homework in class, but I didn’t set that expectation strong enough in the beginning of the class so once students were done with the in-class problem they decided it was time to talk and goof-off. In reflecting back this was the section that needed the most work. If I were to reteach this lesson, I would add more structure to the lesson and pulled the students’ attention back to me more. I think if I would have had a little bit more for the students to do in –class, and if I would done a better job of setting up the layout of the class in the beginning, this last section would have gone much smoother. Yesterday’s lesson went much smoother, but the students had quite a bit more to do, giving it more structure. 

Warm-ups in Math Education

Warm-ups are an important aspect in a math classroom. Warm-ups serve many functions, including getting students in a “math” frame of mind, reviewing material from previous lessons, reviewing basic skills such as fractions, percents, etc, review skills that may not be a normal part of everyday lessons such as OAKS testing preparation or use of calculators, or even pre-viewing or priming what you will be doing that day.  Warm-ups can also provide the teacher an opportunity to check for students pre-existing knowledge and/or misconceptions on the lesson that is being taught that day, so the teacher can gauge how fast or slow he/she needs to go and which topics and students need special attention.

I believe that warm ups should take under 10 minutes, especially in a 40 minute or 50 minute period system. I also believe that warm-ups should not be graded, but instead should be checked by a group discussion or calling on individual students.    

Appropriate Use of Technology

Since I could not find an activity that matched my standards area of measurement, I chose to review the Area Tool at www.illuminations.nctm.org. The area tool is an exploratory tool that can be used to track how the area changes given different side lengths in triangles, parallelograms, and trapezoids. It could also be used in a lesson on proportions and similar triangles and shapes. Unfortunately, because the angles and lengths are on a slider scale and there is no way of getting exact measurements, it would be very difficult to use this tool in a lesson on the Pythagorean Theorem or trigonometry.

While it does have limitations, the area tool does accomplish its main objective of determining how the base length and height of a figure affects its area very efficiently. Using this tool is much more efficient than drawing the figures out on graph paper. Students can instantly make connections between the areas instead of painstakingly graphing the figures out and running the risk of losing the information through the tediousness of the activity.

This same lesson could be taught using graph paper, plastic shapes, or other manipulatives. While these other methods would work, they do not provide the same efficiency that the area tool can. If I were designing this tool, I would include the option to input exact measurements and angles, and output angle measurements.

Standards, standards, everywhere

I chose to evaluate how the NCTM standard of “understanding relationships among units and convert from one unit to another within the same system” compares with a similar standard in the Common Core and CMP standards. For the most part all three standards cover essentially the same thing. However, there are several differences between the three standards.  One is that the Connected Math Project standards include conversion between customary and metric systems whereas the Common Core and NCTM standards keep the conversions within the same system. Another difference is the NCTM and CMP consider converting measurements a sixth through eighth grade skill where the Common Core standards place it in the fifth grade classroom. Lastly, the common core standards are the only ones that explicitly state that the skill must be implemented in multi-step, real world problems, which is surprising to me since that seems to be one of the main objectives of the Connected Math Projects standards. While the standards do not match up identically one to one, creating multi-step, real world measurement problems that include converting between customary and metric systems would easily cover all three sets of standards.  

OTEN Yodio

New Tech Standards & Requirements

Oregon Educational Technology Standards

There are currently six educational technology standards in Oregon that are aligned with the national NETS*S standards:

1. Creativity and Innovation
2. Communication and Collaboration
3. Research and Information Fluency
4. Critical Thinking, Problem Solving and Decision Making
5. Digital Citizenship
6. Technology Operations and Concepts

Below, I will discuss a few of these standards and how they can be implemented in a mathematics classroom.

Creativity and Innovation- Before I discuss ways in which students can use technology to show creativity in mathematics, it is important to discuss how mathematics can be a creative process.While it isn’t a standard that is normally thought of in mathematics, there are many ways of encouraging student creativity in math class. These include but are not limited to: students finding their own way to solve a problem, students coming up with their own examples of math problems, and students creating presentations of how they solved a math problem.  Therefore we are looking for ways in which technology can aid students in doing these creative activities. For example, students could use the smart board to show how they solved a problem, students could use Prezi or other presentation software to show their knowledge of a concept, or students could use a photo program with a draw or paint program to show geometric shapes are found in everyday life.

Communication and Collaboration- This standard caught my eye because it mentions communicating with experts in the field. Most students know so little about what mathematicians do or even how math is applied in other fields. Through the use of technology (Skype for example) students can connect with experts in the mathematics field or other fields that use mathematics without the headache of scheduling visits to the class. This also expands the base of experts the teacher has to use because the expert no longer needs to be a parent of a student or even a local. Another way students can use technology to communicate and collaborate is through conferences or data sharing activities that are not limited to the class size. Students could collaborate with other classes in their school, or even throughout the world using conferencing software or cloud computing documents and spreadsheets.

Technology Operations and Concepts-  While not specific to mathematics, being able to select, use, and troubleshoot tools effectively is a key component of technological literacy. Often, the ability to troubleshoot computers separates the technologically literate from those who are not. Just like learning a language, the best way to become comfortable with technology is through practice. As a teacher this means having technology available, implementing technology appropriately into the curriculum, and allowing students time to experiment with computers and technology.

Possible Challenges

The first, and perhaps most obvious challenge that I see teachers facing when implementing technology in the classroom is a lack of funds and resources to support the latest and greatest that technology has to offer. Just because there may not be sufficient funds to have computers or a smartboard in every classroom for every student, does not mean that we should give up in trying to integrate technology into the curriculum. Many schools have computer labs that teachers can hold classes in or portable smartboards that can be borrowed from the school. Also, as new technology comes out at an exponentially increasing pace, there is no shortage of secondhand computers or companies willing to donate. Most of the applications that are run in an educational setting do not require the latest technology has to offer.

A second. more difficult challenge is finding time to include computers when faced with the pressures of standardized testing and shortened class times. There is no easy answer to this roadblock. Teachers need to think creatively about how they can integrate technology into activities that enhance the curriculum, rather than viewing technology as a separate activity.  Teachers examine there lesson plans  “Can I use technology to enhance student knowledge in this lesson?” “Can my students use technology to further their understanding of the concept?”.     

educ 533- Best Practices Research

Best Practices in Education

SERC- http://www.ctserc.org/s/index.php?option=com_content&view=section&id=8&Itemid=28

Parent/Community Involvement  - Parent and community involvement is vital in education because the same work ethic, subject-area skills, and social skills that are learned and reinforced in the schools need to be also learned and reinforced at home in order for them to be remembered  and internalized by students .

High Standards and Expectations – All students need to be held to high standards and expectations because often as soon as they suspect that they are being held at a lesser standard they will underperform. Providing students with challenging material will often increase motivation as well.

NEA- http://www.nea.org/tools/17073.htm

Block Scheduling- Nearly all the research that I have read about brain theory has stressed the importance of pre-exposure, previewing, engagement, framing, acquisition, elaboration, review, and revision information as part of the learning process. With class periods that sometimes do not even reach forty minutes I have trouble seeing how teachers can implement this research into the classroom.  Block scheduling provides the additional time that students need in order to learn and remember subject matter.

Best Practices in Instruction

http://blogs.scholastic.com/top_teaching/2010/12/implementing-best-practices-for-math-instruction.html

Provide differentiated classroom instruction using a variety of  instructional methods and interventions- Too many times teachers fall in a rut of teaching material the same way, regardless of the content they are covering or the different learning styles in their classroom. This an ineffective method because it ignores  the fact that each class will have a different student population with different classroom dynamics and learning styles. Not differentiating instruction is also dangerous because the lessons could become routine and boring to the students.

Assess to inform instruction and summarize learning- I think this may be the most important practice of them all. The teacher must be constantly assessing and evaluating their own instructional methods to see if they are the best fit for the students in their class. Angela Bunyi goes on to talk about how she uses her peers to better assess and inform instruction. I think it is important for teachers to collaborate consistently and to realize that their own practices should be tweeked and changed based on the input of others. Unfortunately, at my student-teaching site there doesn’t seem to be a collaborative effort at all and the math teachers seem to be unaware of what the others are doing.

Marzano’s essential 9 

http://www.middleweb.com/MWLresources/marzchat1.html

Setting objectives and providing feedback- Although objectives were not a part of my student experience, I can see the value of giving students an idea of where the lesson is going and what they are trying to achieve. When students understand the overall concept that they are trying to learn from a particular lesson, they can pick out the individual parts of the instruction that make the most sense to them in understanding the overall concept. 

Sources:

Bunyi, Angela (2010) Implementing Best Practices for Math Instruction retrieved September 18,2011 from http://blogs.scholastic.com/top_teaching/2010/12/implementing-best-practices-for-math-instruction.html

NEA Research Spotlight on Best Practices in Education retrieved September 18,2011 from http://www.nea.org/tools/17073.htm

SERC Best Practices in Education retrieved September 18,2011 from http://www.ctserc.org/s/index.php?option=com_content&view=section&id=8&Itemid=28

Varlas, Laura (2002) Nine Essential Instructional Strategies retrieved September 18,2011 from http://www.middleweb.com/MWLresources/marzchat1.html

Multimedia Project

To record this video of a Prezi, we used the online screen captioning tool Screenr. Screenr allowed us to capture video of what was happening on the screen while recording our voice over the top of the presentation. After registering a username, setting up the recording session was quick and easy and we were recording within seconds. Once we finished recording, the publishing process took about seven or 8 minutes for a video that was just over 4 minutes. After the publishing process, Screenr gave the video a web address so it could easily be posted in facebook, twitter, or a blog. Another advantage of Screenr is that it is completely online and doesn’t require any software download. This is important because many school computers do not allow users to install programs on their computers. My only complaint about Screenr is the quality of the final product. The video is extremely choppy compared to how it looked in Prezi. This may have been due to the speed of the computer or internet connection we were using since we were using both Prezi and Screenr simultaneously.  

As I mentioned in a previous post, Screenr can be used to add voice to online PowerPoint presentations, making them much more useful for students to retrieve at a later time. Another application of Screenr in the classroom is to challenge students to create videos that demonstrate their knowledge in the content area. For example, an assignment in math could task the students with creating their own Screenr to demonstrate practical uses of the Pythagorean Theorem. This is useful because most students will be extra motivated when they have to produce a product.  

Analyzing Student Data in a Spreadsheet

For the most part my experience with Goolge Sheets was smooth. I did the averages quickly and used the bottom right hand corner of the cell to efficiently copy the formula into the remainder of the cells. For the requirement about using only the students who were under average my original idea was to create a filter to filter out any students who’s average was under the 192 class average. This worked really well at first but unfortunately when I made a chart out of the selected cells, the chart included the data that had been sorted out by the filter. I then tried to sort the data from lowest to highest and delete the averages that fell below 192 and fortunately this method was successful. The chart was also fairly easy after I realized that I needed to switch the axis in order to make it more meaningful. The only hold-up that I had with the chart was when I attempted to change my vertical axis range, to make the graph more readable, the chart remained the same regardless of the numbers that I inserted.

Above is a chart that I made of how below average students progressed through the final five tests. Data for this chart can be found here. As an instructor, I would be pleased with the overall trend of the below average students. With the exception of Katherine’s dramatic loss in points from test 7 to test 8, and Queen’s slight loss from test 9 to test 10, all students progressed fairly linearly throughout the tests. If I had Queen, and especially Katherine in my class, I would ask them what they thought was difficult about their respective tests, or what outside factors (lack of sleep, didn’t study as hard, hungry, other things in their lives, etc.) may have influenced their scores.

My Favorite Web 2.0 Tools

Web 2.0 is moving away from the idea that browsing the web should be a process where users view material published on the internet by web page developers, and is moving towards an idea where users create content that is accessible on multiple platforms and devices. Web 2.0 applications include social networking sites such as Facebook (where the content is user-created profiles and groups),   Dropbox (where the content is users’ files and folders), Wikipedia (an online encyclopedia where users provide the content for articles), and Screenr (a web-based application where users create online videos and tutorials). In these cases, the websites merely serve as a tool for connecting with the world, sharing your information, and interacting with the web in ways that make sense to you, the user. This new way of designing websites and tools is in sharp contrast to the “web 1.0” format of web designers dictating the content of any given page.

As I mentioned above, one of these Web 2.0 applications is Dropbox. Dropbox allows users to share files and folders to any computer or smartphone they have access to. Dropbox also has a separate folder that allows users to share files with anyone who has a specific link. One difference between Dropbox and the other web 2.0 applications is that it is not an application that is used through your web browser; you must download Dropbox onto your computer in order to use it. One of the biggest advantages of Dropbox for teachers is that it acts like a USB drive that you do not have to physically carry around with you, so you have one less thing to remember going from home to school and back. Another advantage is that unlike USB drives, it doesn’t matter if your home computer is Mac and your school computer is Windows based, Dropbox works across platforms. The “Share” folder in Dropbox, which gives a link to files in the folder, could be useful for teachers to post worksheets that they handed out in class for students who misplaced them or were absent that day. 

Screenr is another popular web 2.0 application. Screenr allows the user to record and share a video of what is happening on their screen (screencasts). The user can also use a microphone to overlay their own voice or other sound on top of the video. One use of Screenr for educators would be to include their own audio on presentations that they have available online. For example, not only would students be able to view PowerPoint presentations, but they could also hear their teacher talk about the presentation as they view it.

Google Spreadsheets Group Assignment

Just like the other programs in Google documents, Google Spreadsheets provides solid alternative to its Microsoft counterpart while adding the functionality of being able to share your spreadsheet with anyone else with a Gmail account. I can see myself utilizing Google Spreadsheets in several ways, including uploading and maintaining grades, creating unique classroom projects, and sharing the most up to date classroom data with students and parents.

·         Uploading and maintaining grades- Google Spreadsheets provides an advantage to other spreadsheet programs in that anything I enter into the spreadsheet will instantly be accessible from any computer, so student grades can be viewed and edited from home, school, or a smartphone. Google Spreadsheets also eliminates the necessity of back-up.

·         Unique classroom projects- I can imagine setting up a math project that spands several classrooms, and is updated simultaneously in real-time by all the classrooms involved.

·         Sharing up to date classroom data with students and parents- I would set up a unique spreadsheet for each student that would include grades and any comments that I have on their assignments.

While I do have some experience with excel, I did experience somewhat of a learning curve in Google Spreadsheets because the menus are quite a bit different than what I am used to in Excel 2007; they remind me more of the menus in previous versions of Excel. Besides the basic functions of AVG, MIN, and MAX, the more complicated functions weren’t as easy to access and I missed some of the cell formatting templates that are available in Excel 2007.

My main contribution to the group was my previous knowledge of excel. Our final spreadsheet is here,  and my group's reflections on the project are here.

Running List of Great Math Sites

http://teachhighschoolmath.blogspot.com/

Assignment #2

As a student, how many times did you get home from school only to realize that you forgot the homework assignment for the day? How many times did you leave from class, confidently knowing the material, only to open your book a few hours later and not have a single clue how to find the interior angles of a transversal, or even what a transversal is in the first place? For some students those worries are a thing of the past. Why? Because their teachers use blogs as part of their teaching, actively posting homework assignments, helpful reminders on the day’s lesson, and even responding to student questions before class the next day.

Not only do blogs help teachers access students in today’s ever increasingly technology centered world, they can also provide a place where students post their work, reflect on the day’s class, or connect with their peers or teachers. Imagine being able to get feedback on the day’s lesson from every student in the class, easily compiled and sorted using Google docs, or have an open chat session where students can post their (class related) comments and concerns.

Some other technology resources to consider:

·         www.goanimate.com   - Courtesy of Rebecca Garland, a guest poster on theEmergingEdTech website. Allows students (or teachers) to create animated sequences to convey information. Could be used for students to show comprehension or for a teacher who wants to use a new creative way to give the syllabus.

·         www.youtube.com - (blocked in some school districts) Hundreds of educationally valid videos showing everything from a proof of Pythagorean Theorem using tape, to 3d images of the most giant stars in the universe.

·         www.twitter.com -Students can use twitter in the classroom to see what experts in the subject are saying about the latest finding in real time.  

Assignment #1

Hi,

I'm Ben Kaufmann and I am a MAT student at Willamette University. I hope to be a middle school math teacher in the near future in the near future (next fall would be great). I will also be receiving an ESOL endorsement and am very open to the possibility of teaching in an ESOL classroom. If I am not able to find a job right away, I will be moving to Nicaragua and teaching in a small school in Bluefields.

Some of my hobbies include playing piano, working out at the gym, swimming, and exploratory eating. When I am not being a student, I like to explore the world, meet new people, and experience other cultures.