Phase 3: Action Plan
Identify Desired Results
The main goal or “big idea” for the upcoming school year is to help my students to become mathematicians. I have identified three key areas they will need to master to see, act, think and communicate as a mathematician. These three components are perseverance in solving problems, number sense and productive collaboration. Each of these goals is hard to quantify and identify understanding with standardized assessments but they are essential to the mathematical discipline. All math stems from mastery of these components.
To determine success in perseverance in problem solving, I want students to be able to look at a real world situation or data and not only solve a specific problem based on that scenario, but actually determine, identify, analyze and solve what kind of problems this situation may provoke. To show desired results, students will be given a real world scenario and will need to first identify the information that they have and what it represents and why it is important. Then, they must determine what information they may need and what types of problems they can construct with the given information. Finally, the will analyze the data and solve the problem or problems they have developed. Perseverance will be assessed based on the student's willingness to continue uncovering problems and not giving up.
I think number sense is even harder to quantify, but if my students are able to identify reasonableness of solutions to problems, I would probably see that as being successful. I also want them to see and use friendly or landmark numbers as the view and work problems mentally. A lot of number sense also involves good estimation skills. Estimation skills are probably easier to determine student understanding through repeated practice and assessment.
I believe most people’s perception of mathematicians is that they work alone in small dark rooms and just constantly play with numbers. We know this is not true, that learning and understanding involves a collaborative effort and being able to communicate your mathematical thinking. Evidence of student success in productive collaboration will be the student’s ability to contribute equally in any size or type of group. The student must also be able to converse and explain their thinking using the correct mathematical language critical to the discipline.
Determine Acceptable Evidence (Performance of Understanding)
For perseverance in problem solving one form of assessment will be teacher observation when an assignment involving problem solving is being worked on by the students. This activity will also include questions related to the problem where student responses will indicate an understanding of the problem. Students will also be required to write about their strategies when identifying and analyzing a problem. They must also be able to explain and in writing how they solved the problem using the correct academic language. Students should be fully engaged in the activity. Other formative assessments will include daily warm-up problems, individual white board responses, exit tickets, class discussions and homework. The individual student responses will be assessed for understanding and interventions will be dynamic based on the data. Summative assessment will be based on content where students can demonstrate their understanding.
Students should be able to look at any situation in the real world and determine a problem solving scenario for that scenario. A simple example may be to ask students, “Why is the address of our school 4127 W. Hirsch St.?” A deeper problem solving understanding would inspire the students to analyze the numbers and what they represent. I would expect students with greater problem solving capabilities to ask questions about these numbers. Some related problems I would expect them to generate would include how does Chicago’s address system work, what does their home address mean, and what would the address be of a new building if we built it on the corner by the school.
Number sense evidence would be evaluated for understanding based on responses during number/math talks. Keen insight can be gathered based on how they described their thinking in solving the problem. I would expect them to use different number sense strategies including using friendly or landmark numbers, making tens or hundreds, picturing a number line, etc. Other good indications of number sense are predicting or estimating what would be the range or value of a problems solution. Students with good number sense would be able to determine the reasonableness of their problem solutions and make appropriate corrections. Students should also be able to compare the value of numbers in all forms including whole numbers, integers, decimals and fractions. They should know how numbers change when using the four basic operations.
To determine productive collaboration involves a lot of teacher evaluation especially in utilizing “Turn and Talks” and “Think-Pair-Share”. In larger group work, a rubric for productive collaboration will be developed that helps identify student contributions to the group. I find it to be a very effective tool when students evaluate their selves and their peers, along with a teacher evaluation. For whole class discussions, I would track a student’s participation in both responding to teacher questions and asking questions about what another student said.
Plan Learning Experience and Instruction
Context:
I teach 5th grade mathematics and 7th grade algebra at Alfred Nobel Elementary School. Nobel is a Chicago Public School located in the West Humboldt Park area. West Humboldt Park is an area of the city with a lot of gang activity and a high rate of poverty. The community‘s population is predominately Hispanic and African-American. All students qualify for and receive a free breakfast and lunch.
This will be my eighth year teaching at Nobel, but only my second year teaching 5th grade math. I have taught 3rd, 4th and 8th grades in all subjects, 6th grade language arts and science, and 7th grade math. I will be teaching three math classes for 80 minutes per class. I will also have a 40 minute intervention block where students are grouped by mathematical ability and the focus is will be on content for standardized testing. I expect each class to have between 30 and 35 students. Class demographics are about 70% Hispanic and 30% African-American. In one class about 15% of the class will be diverse learners, designated as those students that have IEPs.
My 7th grade algebra class will be held after school, three days per week for 75 minutes. This class will have about 28 of the top math students that were selected based on their grades and test scores in math.
Each classroom is equipped with a SMARTboard, an Apple MAC laptop and a document projection system. For student use, my classroom has four DELL desktop computers. We have access once every six days to a computer cart with 30 Apple MAC laptops. My students have a Computer Technology class with MAC desktop computers for one hour every six days. In library, again once every six days, there are Apple tablets available for student use. Approximately 35% of the students have computers with internet access at home and//or smart phones.
Content:
The 5th Grade curriculum includes performing all four operations with fraction, multi-digit whole numbers and decimals to hundredths, place value, powers of 10, volume, graphing points on a coordinate plan to solve real-world problems, analysis of patterns, and writing and interpreting numerical expressions.
Students at this grade level really struggle with perseverance in problem solving, number sense and working collaboratively. These particular challenges lead to my main goal or “big idea” for this school year to have my students become better mathematicians. I believe in mastering these challenges, students will begin to see, think, act and communicate like mathematicians. Having these abilities are the cornerstone for success in mathematics.
Pedagogy:
The overall pedagogy we use at Nobel is the General Release of Responsibility model (GRR). In GRR, we model and guides students as we introduce content and then students collaborate and work independently. The GRR model is embedded in both a math and a reading block schedule. Based on my big idea, I plan to emphasize Problem-Based Learning in my math block schedule. Let’s explore the math block schedule.
Each day we start out with Warm-Up Problems based on past learnings. These are very straight-forward content problems for review. Next, a student will present his “Math is FUN”. Each day a student is assigned to find a Fantastic, Unbelievable Number to share with the class. The student begins this discussion with the question, “Did you know that……..?”, and then proceeds to give more information. An example, “Did you know that the average elephant weights ____ pounds?” These Math is FUN assignments will be written on special colored cards and posted outside the classroom. Eventually, I want the student to bring in a problem/situation from the real world to start our discussion for the day.
Next up is our Math/Number Talk. The entire class moves and sits down on a carpet at the front of the room. This is a great opportunity for the student to hone his or her mental math skills and build their number sense. During the Math/Number Talk is also when students explain their thinking and how they solve problems using the correct academic terms and language. I also find this talk to be very beneficial forum to discuss student misconceptions and/or mistakes. I purposefully display errors in student work throughout the math block. This usually leads to a rich discussion and deepens a student’s understanding of the math concept we’re discussing.
Students will then be given a problem based on the day’s content without the questions. We will analyze the information and discuss the potential problems we can synthesize from the data and how we will solve it.
The time has finally arrived when the lesson starts and the content of the lesson is introduced. We will discuss what we are going to learn today and why it is important to learn this information. I will introduce new vocabulary and students will fill in a definition on vocabulary cards. I will then introduce the content and model a problem while explaining my thinking as I solve the problem. The class will then watch an animated video that visually provides the information I just covered. There are multiple stopping points in the video for questions and discussion.
Students will then collaborate to gain a deeper understanding of the concept for the day. Collaboration activities will vary from day to day. Some will come from our improvisation session and various other sources. Students will then work independently and I will assess their understanding based on a few select problems called a “Quick Check”. I will provide intervention based on these “Quick Checks” and homework in small groups the following day.
Each unit (four to twelve lessons) will have a separate day for review, summative assessment and re-engagement lesson for those students that did not reach a specific goal on the assessment. Throughout each unit, we will also work on five problems based on the same situation, information and data. On the six day, the students will design their own problem based on this same scenario.
Technology:
I will continue to use the SMARTboard and document projection system to present each lesson, but will move beyond using it as a “glorified” white board. The SMARTexchange is a great source of visual materials. I also intend to show a video for visual learning each day. The publisher also has digital tools available that include interactive assessments, tools, help, interactive homework video and “practice buddy, a teacher video for each lesson, and math games. For those students with access to technology at home these digital resources will be available.
On days when we have the computer cart, we will work on projects that will be based on crossfires and some of the other technology projects we were introduced to in class. Student will also have technology-oriented group work and will be assigned days on the in-classroom desktop computers. I will also work very closely with the computer and library teacher on various technology-driven projects.
Identify Desired Results
The main goal or “big idea” for the upcoming school year is to help my students to become mathematicians. I have identified three key areas they will need to master to see, act, think and communicate as a mathematician. These three components are perseverance in solving problems, number sense and productive collaboration. Each of these goals is hard to quantify and identify understanding with standardized assessments but they are essential to the mathematical discipline. All math stems from mastery of these components.
To determine success in perseverance in problem solving, I want students to be able to look at a real world situation or data and not only solve a specific problem based on that scenario, but actually determine, identify, analyze and solve what kind of problems this situation may provoke. To show desired results, students will be given a real world scenario and will need to first identify the information that they have and what it represents and why it is important. Then, they must determine what information they may need and what types of problems they can construct with the given information. Finally, the will analyze the data and solve the problem or problems they have developed. Perseverance will be assessed based on the student's willingness to continue uncovering problems and not giving up.
I think number sense is even harder to quantify, but if my students are able to identify reasonableness of solutions to problems, I would probably see that as being successful. I also want them to see and use friendly or landmark numbers as the view and work problems mentally. A lot of number sense also involves good estimation skills. Estimation skills are probably easier to determine student understanding through repeated practice and assessment.
I believe most people’s perception of mathematicians is that they work alone in small dark rooms and just constantly play with numbers. We know this is not true, that learning and understanding involves a collaborative effort and being able to communicate your mathematical thinking. Evidence of student success in productive collaboration will be the student’s ability to contribute equally in any size or type of group. The student must also be able to converse and explain their thinking using the correct mathematical language critical to the discipline.
Determine Acceptable Evidence (Performance of Understanding)
For perseverance in problem solving one form of assessment will be teacher observation when an assignment involving problem solving is being worked on by the students. This activity will also include questions related to the problem where student responses will indicate an understanding of the problem. Students will also be required to write about their strategies when identifying and analyzing a problem. They must also be able to explain and in writing how they solved the problem using the correct academic language. Students should be fully engaged in the activity. Other formative assessments will include daily warm-up problems, individual white board responses, exit tickets, class discussions and homework. The individual student responses will be assessed for understanding and interventions will be dynamic based on the data. Summative assessment will be based on content where students can demonstrate their understanding.
Students should be able to look at any situation in the real world and determine a problem solving scenario for that scenario. A simple example may be to ask students, “Why is the address of our school 4127 W. Hirsch St.?” A deeper problem solving understanding would inspire the students to analyze the numbers and what they represent. I would expect students with greater problem solving capabilities to ask questions about these numbers. Some related problems I would expect them to generate would include how does Chicago’s address system work, what does their home address mean, and what would the address be of a new building if we built it on the corner by the school.
Number sense evidence would be evaluated for understanding based on responses during number/math talks. Keen insight can be gathered based on how they described their thinking in solving the problem. I would expect them to use different number sense strategies including using friendly or landmark numbers, making tens or hundreds, picturing a number line, etc. Other good indications of number sense are predicting or estimating what would be the range or value of a problems solution. Students with good number sense would be able to determine the reasonableness of their problem solutions and make appropriate corrections. Students should also be able to compare the value of numbers in all forms including whole numbers, integers, decimals and fractions. They should know how numbers change when using the four basic operations.
To determine productive collaboration involves a lot of teacher evaluation especially in utilizing “Turn and Talks” and “Think-Pair-Share”. In larger group work, a rubric for productive collaboration will be developed that helps identify student contributions to the group. I find it to be a very effective tool when students evaluate their selves and their peers, along with a teacher evaluation. For whole class discussions, I would track a student’s participation in both responding to teacher questions and asking questions about what another student said.
Plan Learning Experience and Instruction
Context:
I teach 5th grade mathematics and 7th grade algebra at Alfred Nobel Elementary School. Nobel is a Chicago Public School located in the West Humboldt Park area. West Humboldt Park is an area of the city with a lot of gang activity and a high rate of poverty. The community‘s population is predominately Hispanic and African-American. All students qualify for and receive a free breakfast and lunch.
This will be my eighth year teaching at Nobel, but only my second year teaching 5th grade math. I have taught 3rd, 4th and 8th grades in all subjects, 6th grade language arts and science, and 7th grade math. I will be teaching three math classes for 80 minutes per class. I will also have a 40 minute intervention block where students are grouped by mathematical ability and the focus is will be on content for standardized testing. I expect each class to have between 30 and 35 students. Class demographics are about 70% Hispanic and 30% African-American. In one class about 15% of the class will be diverse learners, designated as those students that have IEPs.
My 7th grade algebra class will be held after school, three days per week for 75 minutes. This class will have about 28 of the top math students that were selected based on their grades and test scores in math.
Each classroom is equipped with a SMARTboard, an Apple MAC laptop and a document projection system. For student use, my classroom has four DELL desktop computers. We have access once every six days to a computer cart with 30 Apple MAC laptops. My students have a Computer Technology class with MAC desktop computers for one hour every six days. In library, again once every six days, there are Apple tablets available for student use. Approximately 35% of the students have computers with internet access at home and//or smart phones.
Content:
The 5th Grade curriculum includes performing all four operations with fraction, multi-digit whole numbers and decimals to hundredths, place value, powers of 10, volume, graphing points on a coordinate plan to solve real-world problems, analysis of patterns, and writing and interpreting numerical expressions.
Students at this grade level really struggle with perseverance in problem solving, number sense and working collaboratively. These particular challenges lead to my main goal or “big idea” for this school year to have my students become better mathematicians. I believe in mastering these challenges, students will begin to see, think, act and communicate like mathematicians. Having these abilities are the cornerstone for success in mathematics.
Pedagogy:
The overall pedagogy we use at Nobel is the General Release of Responsibility model (GRR). In GRR, we model and guides students as we introduce content and then students collaborate and work independently. The GRR model is embedded in both a math and a reading block schedule. Based on my big idea, I plan to emphasize Problem-Based Learning in my math block schedule. Let’s explore the math block schedule.
Each day we start out with Warm-Up Problems based on past learnings. These are very straight-forward content problems for review. Next, a student will present his “Math is FUN”. Each day a student is assigned to find a Fantastic, Unbelievable Number to share with the class. The student begins this discussion with the question, “Did you know that……..?”, and then proceeds to give more information. An example, “Did you know that the average elephant weights ____ pounds?” These Math is FUN assignments will be written on special colored cards and posted outside the classroom. Eventually, I want the student to bring in a problem/situation from the real world to start our discussion for the day.
Next up is our Math/Number Talk. The entire class moves and sits down on a carpet at the front of the room. This is a great opportunity for the student to hone his or her mental math skills and build their number sense. During the Math/Number Talk is also when students explain their thinking and how they solve problems using the correct academic terms and language. I also find this talk to be very beneficial forum to discuss student misconceptions and/or mistakes. I purposefully display errors in student work throughout the math block. This usually leads to a rich discussion and deepens a student’s understanding of the math concept we’re discussing.
Students will then be given a problem based on the day’s content without the questions. We will analyze the information and discuss the potential problems we can synthesize from the data and how we will solve it.
The time has finally arrived when the lesson starts and the content of the lesson is introduced. We will discuss what we are going to learn today and why it is important to learn this information. I will introduce new vocabulary and students will fill in a definition on vocabulary cards. I will then introduce the content and model a problem while explaining my thinking as I solve the problem. The class will then watch an animated video that visually provides the information I just covered. There are multiple stopping points in the video for questions and discussion.
Students will then collaborate to gain a deeper understanding of the concept for the day. Collaboration activities will vary from day to day. Some will come from our improvisation session and various other sources. Students will then work independently and I will assess their understanding based on a few select problems called a “Quick Check”. I will provide intervention based on these “Quick Checks” and homework in small groups the following day.
Each unit (four to twelve lessons) will have a separate day for review, summative assessment and re-engagement lesson for those students that did not reach a specific goal on the assessment. Throughout each unit, we will also work on five problems based on the same situation, information and data. On the six day, the students will design their own problem based on this same scenario.
Technology:
I will continue to use the SMARTboard and document projection system to present each lesson, but will move beyond using it as a “glorified” white board. The SMARTexchange is a great source of visual materials. I also intend to show a video for visual learning each day. The publisher also has digital tools available that include interactive assessments, tools, help, interactive homework video and “practice buddy, a teacher video for each lesson, and math games. For those students with access to technology at home these digital resources will be available.
On days when we have the computer cart, we will work on projects that will be based on crossfires and some of the other technology projects we were introduced to in class. Student will also have technology-oriented group work and will be assigned days on the in-classroom desktop computers. I will also work very closely with the computer and library teacher on various technology-driven projects.