Inquiry & CMP Research

CMP is a student-centered, inquiry-based teaching model. First the teacher sets the stage, states the objective and provides real-world context and any necessary background information (Launch). Then the students work together to solve the problem or complete the project with the teacher acting as facilitator and offering open-ended questions as answers to students' inquiries (Explore). After students work independently in groups, the class is brought together to share what they've learned and share problem-solving strategies. The teacher summarizes what the students learned (Summarize).
Compared with the traditional model of instruction, guided practice and independent practice, there is less modeling by the teacher and instead students are more left to their own devices to discover how to complete tasks, and they share their strategies with the class. The CMP also emphasizes more group collaboration as a given.
As the Connected Math Project website states:

• Classroom instruction focuses on inquiry and investigation of mathematical ideas embedded in rich problem situations.
• Mathematical tasks for students in class and in homework are the primary vehicle for student engagement with the mathematical concepts to be learned. The key mathematical goals are elaborated, exemplified, and connected through the problems in an investigation.
• Ideas are explored through these tasks in the depth necessary to allow students to make sense of them. Superficial treatment of an idea produces shallow and short-lived understanding and does not support making connections among ideas.
• The curriculum helps students grow in their ability to reason effectively with information represented in graphic, numeric, symbolic, and verbal forms and to move flexibly among these representations.
• The curriculum reflects the information- processing capabilities of calculators and computers and the fundamental changes such tools are making in the way people learn mathematics and apply their knowledge of problem-solving tasks.

CMP-Inquiry Middle School Interview

Interview with Perrydale math teacher Bryan Toller, who teaches high-school-level algebra to middle-school students.

* How does the CMP curriculum align with the national Common Core and NCTM standards? 1. The CMP curriculum aligns well with the national standards. Each curriculum is unique and must be aligned to match the standards. It is the teachers responsibility to go through and ensure that the standards are met.

*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? 2. Inquiry based curriculums such as CMP present problems for struggling students because the problems are very contextual and if a student is missing pieces sometimes dealing with the context in addition to the mathematics can be overwhelming. On the other hand because of the context the problems tend to be less abstract and a struggling student can "put themselves into" the problem and then they are able to figure it out. The context also leads to a deeper contextual understanding that helps bridge the gaps between lessons and ideas.

* What is the role of homework (and accountability) in the CMP?
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?

3. It is the teacher's job to ensure individual and group accountability. On an individual basis the teacher must collect and assess classwork, homework and provide on demand assessments. On a group level classwork can be assessed on a participatory level, with some group projects, but ultimately grades are individual and should represent and individuals work and effort.

 Homework is critical in any math class, it is the daily practice that supports the lessons and learning that happens in the classroom. Homework needs to be assessed on an individual level but, homework in my opinion should be graded on completion rather than accuracy.

 When students are engaged and working on problem solving in small groups most classroom management issues dissolve. Most management issues stem from students being bored and finding alternative ways to entertain themselves by acting out or disrupting others.

Closure and Anticipatory Set

What is the purpose of the Closure component in a lesson plan?The closure is intended to reinforce the major points in the lesson that students are expected to have learned. It brings students' attention back to the original lesson objective, and what a teacher learns from the closure also can be used as an assessment tool. Here are two sites that discuss closure in a lesson. This could be a two-sentence summary about the main points of a lesson, a short whiteboard or interactive clicker quiz, an exit pass, a journal entry, etc.


What is the purpose of an Anticipatory Set in a typical lesson plan?
The anticipatory set is the "attention getter" of the lesson and introduces the topic about which you will teach. It usually takes the form of a question, an activity or similar set-up in which some prior knowledge/learning is elicited and/or some unknown factor is introduced to help the student mentally/physically get ready for the upcoming lesson. In addition to the site mentioned above in the closure segment, this site also offers information about anticipatory set. Examples of an anticipatory set include problems or open-ended questions on the board as students enter the classroom, a journal entry, and reading a book or literacy piece related to the subject at hand.


This site, at the bottom, discusses the The Madeline Hunter Lesson Design Model, which also includes brief descriptions of anticipatory sets and closure.

Practicum- Sharing a Lesson

I presented my first-ever lesson plan today, some fractions basics to a third-grade/fourth-grade combined class. My objective was to have students be able to define fraction and be able to accurately write a fraction. I started with a set asking them about pizza and thankgiving pie, which got their attention quickly. I drew a few common fraction pictures on the board, then asked if they knew that they personally also are fractions. I had them create their own index cards in which they are a fraction of their family (I limited it to who lived in the same house). We discussed vocabulary, and some drawing-and-answer on the white board, then I handed out a worksheet to write fractions and identify picture fractions.

I think the index card activity provided the students with a new way to consider fractions, and the white board segment went well. I spot-checked index cards at each step, then checked their index cards individually at the end for accuracy because the each were different, and reviewed worksheets at the end. Some students finished their worksheets quickly, and though somewhere in my head I knew I should have them doing a lesson extension, I was also working with the students who still were working, so that juggling was something I'll need to work on. I would do differently next time part of the whiteboard activity, because they way I was asking for information, at first students were using thumbs up/down in response but by the end they were blurting out answers. Again, classroom management on my part. I think next I will try the use of their individual white boards in similar activities as long as they aren't distracted drawing cutsie animals on them. The mini-whiteboards could be used as an additionsl formative assessment tool if I have them write answers on them. I also was surprised how long it took them to complete the index card activity, so there was a game I had to postpone until tomorrow.

Standards, standards, everywhere

Comparing Common Core, NCTM and CMP standards, in regards to LP assignment: Measurements
Common Core: (grade 5) M5.MD.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
NCTM: (grades 6-8) Understand both metric and customary systems of measurement; Understand relationships among units and convert from one unit to another within the same system; Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.
CMP: (grades 6-7) Relate units within and between the customary and metric systems.

There doesn't appear to be a specific Common Core for measurements in the middle grades (6-8). The closest one I found was the Measurement and Data listing under grade 5 of the Common Core standards. But it closely reflects the same standards expressed by NCTM and CMP. All three of these seek to relate units of measurement to each other, though the CMP also include converting measurement units between both metric and customary systems, whereas Common Core and NCTM specifically state within the same system of measurement. It also appears the Common Core and the CMP standards already expect a background knowledge and understanding of the differences between the two measurement systems. The NCTM standards also include a few other expectations (measure angles, perimeter, area, surface area and volume) that the other two standard categories have listed as expectations separately (i didn't include them here). The application to "real world problems," as expressed by the Common Core standards, seems to me to be understood in the general presentation of information in the classroom, but I like how it is explicitly spelled out. In short, the curriculum standards of all three are very closely aligned in regards to this specific topic, measurement.

Best Practices

Best Practices in Education:I came across several "best practices" that I found intruiging and some I recognized from my MAT classes. Among them are teaching for understanding (Bloom's and CAP); monitoring and assessment; parental involvement; individualized learning and (appropriate!) use of technology.

One link in particular, Connecticut's SERC (State Education Resource Center) listed several, but the one that caught my eye was Professional Development. I don't actively think about it too often, but the quote, "He who dares to teach must never cease to learn," came to mind when I saw that as a best practice. It also reminded me about an activity I did in my EdTech class in which we learned that we as teachers will be educating students to have the skills for jobs that don't even exist yet, and math/science/technology leads those types of jobs. So it is my responsibility to my students to continue learning myself about what's out there so that I am an effective teacher.

A second best practice is building a cooperative, collaborative classroom (a book, "Best Practice" offered a a good number of best practices, but I chose only one for the purpose of this post). When collaboration in maximized in the classroom, it opens multiple avenues for students to interact, can assist ELLs with understanding and improve classroom peer-to-peer relations. This is practice is adventageous for these and more reasons.

Best Practices in Instruction:
Searching this phrase along with "Marzano" revealed that this author has written several books about classroom methods, and he touts the following, as cited in this document about project-based learning:

1. Identifying Similarities and Differences

2. Summarizing and Note Taking

3. Reinforcing Effort and Providing Recognition

4. Homework and Practice

5. Nonlinguistic Representations

6. Cooperative Learning

7. Setting Objectives and Providing Feedback

8. Generating and Testing Hypotheses

9. Cues, Questions, and Advance Organizers
The three of these nine I find most relevant to me are the reinforcement/recognition; nonlinguistic repsresntations and cooperative learning. Already having discussed cooperative learning earlier, I will focus on the other two here. Nonlinguistic representations of lesson assists understanding among ELLs and other intelligences who may need other types of sensory data to process information, which is necessary when trying to reach every student. And providing the appropriate reinforcement and recognition of effort instills in students the inherent desire to learn and achieve without the external behavoral incentives that often lose their effect over time.

Another link I found discussed multi-sensory instruction, modeling and class collaboration. I also believe differentiated instruction is important. Teachers need to adjust their strategies to meet the needs of different groups, individual student learning styles and levels of readiness. Best practices in education and instruction are strategies that have shown to increase student participation, understanding and achievement, and because a solid educational foundation is so critical to so many arenas of success, as a teacher I must be willing to implement as many of these best practices that I can to reach the most number of students the most effective ways.

Warm-ups in Math Education

Based on your research and personal philosophy, what is the purpose of warm-ups in your classroom?

Warm-ups are valuable formative assessments, both reviewing topics that already have been taught in an earlier class or determining what students already know before a lesson is taught. Warm-ups also are a good routine to establish with students so they know what to expect and what is expected of them each time they enter the classroom. Establishing a routine reduces distractions at the beginning of class because students are expected to be seated and focused on the work by the time the tardy bell rings. This can be accomplished several ways, such as having daily worksheets, using warm-up notebooks or class games in which students go around in a circle answering the previous student's problem then formulating and presenting the next student with his/her problem.

As a teacher, I intend to include warmups as part of my classroom routine, and I likely will require students to keep a notebook for warmup exercises. Each class period I will post new question(s)/problem(s) and give the students about 5-7 minutes to complete them. Then I will ask students to share their answers, discuss the content and work it out on the board, then provide them with the correct answer, which they also will need to write in their notebooks. In doing this I will have reviewed/previewed lesson information, focused their attention to my class, checked their notebook for completion and assessed their understanding of the information, and provided them with the correct answer so they can use their journals as study guides.  At times, I will allow them to work the problems in groups depending on the topic, and though they come to the answer as a group, each student is responsible to recording what they learn in the notebook.