Share a plan for identifying and correcting misconceptions related to a key performance standard in one of your courses. Please share your lesson plan and then elaborate on your:

o Method of analyzing student work to identify student performance with respect to state standard (identify patterns of student errors and analyze these patterns to understand student thinking).

o Plan for next-steps support and instruction for the whole class, subgroups, and individuals. This plan must include a cycle of instruction matched with assessment for modification as the students move closer to achieving the learning target.

o Plan for student feedback so that the students can takes ownership of their achievement.

The attached document has helpful information about how to identify and interpret error patterns.Assessment and Remediation Plan

For this assignment I have chosen to create a lesson focused on the remediation needs when teaching students to write and graph equations of lines in an Algebra 1 class. This fall I will be teaching my first Algebra 1 class and I am anticipating this being a struggle for many of my students. I can safely say this, because even at the Algebra 2 level, many of my students in the past have been weak in this concept.

What I plan to do at the end of the initial day teaching this content is to have the students fill out a few question exit task that will demonstrate what each student understands as it relates to writing and graphing equations of lines. The reason I will have the students do this is, I want to begin class the next day (the day I will focus on remediation) with a class discussion looking over a few good examples of student work that display a high level of understanding, and some other examples with varying levels of understanding. What I hope to accomplish from this is to have those students that understand the concepts, gain an even deeper understanding as they try and explain why something was done correctly or incorrectly. I also would like to use these samples of student work to point out to the students any common mistakes and hopefully use them as a learning tool. Students then will receive their exit tasks back with feedback from me on their progress towards understanding the content.

I also plan to hand out a graphic organizer to each of my students which allows the students to break down the four common types of problems they are asked to do when writing an equation of a line. After doing this, I will break my class into two groups, those that understood the concepts after the first day (as demonstrated in their exit task) and those that need some extra instruction and guidance. With the first group, I have a couple fun worksheets/activities for them to work on tied to writing equations of lines/linear relationships. With the second group, I will have them practice a problem, and I will walk around the room assessing how they are doing after further instruction. As this group of students begins to better understand how to write and graph equations of lines, they too will be given another worksheet to be used to assess their level of understanding.

For the actual lesson and all handouts, please visit my blog: http://radmathteacher.edublogs.org/category/math-524/

Aaron Brien

The following lesson focuses on the 7th grade performance expectation of mentally adding, subtracting, multiplying, and dividing simple fractions, decimals, and percents. This performance standard can be divided into 3 subsections: simple fractions, decimals, and percents. Furthermore, each subsection can be divided by each mathematical procedure: adding, subtracting, multiplying, and dividing.

Students will be exposed to small sessions that introduce the concept of mental arithmetic and allow practice. Sessions will begin with direct instruction and followed by individual practice. Students will use color-coded response cards to indicate when help is needed (green=no help, yellow=quick help/check, and red=urgent help). This period of individual practice will be followed by paired practice. During this time students will complete a timed session of solving problems provided by the teacher. Partners will be provided the solutions to the problems in order to correct erring students. Student and partner will switch after a set period of time. Following partner practice, students will take a brief timed quiz. Student performance will be assessed through their response cards and their quiz results.

Students scoring 80% or above on the quiz will be considered Proficient. 50% to 80% will be considered Emerging for which an interview will be done to see if they simply need more time. Below 50% will be considered Basic or Below. These students will need to come in outside of class time for one-on-one help from me.

Lesson Title: Mastering mental math with simple fractions, decimals, and percents.

Outcomes:

Students will demonstrate proficiency in mental arithmetic of simple fractions, decimals, and percents.

Standards Addressed:

7.2 A: Mentally add, subtract, multiply, and divide simple fractions, decimals, and percents.

Materials:

Response cards: Red, Yellow, Green

Practice and Drill worksheets

Timer (optional)

Procedures:

Use direct instruction to cover 2-3 essential strategies/examples of the topic under consideration (i.e. mentally adding percents). Allow students to provide feedback of their initial learning using the response cards.

If enough students indicate “green”, then allow class to begin working on practice problems from a worksheet or other source. Provide direct intervention to students who indicated “red” or “yellow” after the direct instruction.

Distribute drill worksheets and allow students to do timed practice in pairs on the practice section of the worksheet. One student will have solutions with which to address errors of his or her partner. When time is up, students will change roles.

Conclude the session with a timed quiz. Quizzes will be submitted for evaluation according to the Advanced/Proficient/Emerging/Basic format.

For this lesson, I chose to re-use a lesson created for a previous class, where students are translating word problems into equations. Since this lesson includes two mini-lessons, it naturally allows for the teacher to identify and correct misconceptions.

My lesson plan and reflection can be found using the link below:

http://pierckat.edublogs.org/2011/07/26/planning-for-remediation/

-Katelyn

I chose to do this lesson on inductive and deductive reasoning. I previously created this lesson knowing that inductive and deductive reasoning seem to be a missing piece in high school courses, but many professionals believe it has significant importance.

This lesson is broken up into two different mini lessons, so it will allow me to assess my students more easily before I move on to the next little piece of the lesson. I will start by giving students a simple logical statement and having them determine if it is correct or not. After they have determined this we will discuss our findings as a class. While discussing our findings I will lead the students to actual definitions of deductive and inductive reasoning by giving simple hints. Once we have come up with this definition I will turn the students loose to let them come up with their own statements as a group. During group work I will be able to move around more efficiently to assess individual abilities. After a few minutes students will write answers on the board and the class will assess them as a whole.

These small discovery steps will occur throughout the lesson will be assessed during class on a group discovery basis. After the class is over students will be required to go home and do the same types of questions on their own so I am able to assess if they comprehended the concepts of the lesson on their own.

An even more descriptive lay out and assessment strategies of this lesson can be seen in my blog by using the link below.

http://jacobsod.edublogs.org/2011/07/27/assessment-lesson-plan-inductive-and-deductive-reasoning/

This lesson is to review or teach a different way so they students can grasp the characteristics of the graphs.

http://elenalala.edublogs.org/transforming-graphs/

Here is a lesson on solving one-step equations by adding or subtracting.

http://oursland.edublogs.org/files/2011/07/a1_ch02_01-1rouncx.ppt

One concept that was most difficult for my students was solving equations. Students had a difficult time wrapping their heads around what was going on. It didn’t help that many had poor skill when adding and subtracting integers. This aside, students will be taught using the text book curriculum (linked above), but an alternative method for remediation using a hands-on activity will be used the following day.

Students will be given a check-in activity like a quiz in the entry task the following day. I f many students are struggling or miss more than two questions on the five question quiz-like entry task, I will flow into remediation activity, otherwise I will move into the next lesson and save the beans for another day.

Remediation : I will be using bags filled with one of two different colored beans, maybe Lima beans and red kidney beans. I will engage the students by having them tell me how many beans are in a covered bag. From there I will show them how to use the beans for their equations, red beans will be negative, Lima beans will be positive, and when they group a lima bean with a red bean it will represent zero. You get the idea. This will work for remediation for students whom didn’t get it, or still weren’t solid on their understanding. To promote collaborative learning, poor scoring students will be grouped with higher performing students.

An official quiz will be given the following day. Students still in need of remediation will work with the ParaPro in a small group tutoring session. Students will then be given an opportunity on the test to raise their quiz grade if they exceed their score. It’s not as much about when they learn it, just that they learn it.

Since the following lesson incorporate addition steps including adding and subtracting to solve equations, students will have addition time to work on the learning goal.

As an exit task, after the second day, I will ask my students for some feedback. I will have them fill out a quick questionnaire that asks them:

On a scale of 1 – 5 (5 being best)

How on task were you today? 1 2 3 4 5

Are you confident in solving equations by adding or subtracting? 1 2 3 4 5

What is something about solving equations you are still having trouble with?

What is something you have learned about solving equations?

Remediation Lesson Reflection

The remediation lesson I chose is for an Algebra 1 class. The concept is: given a slope and a point, or given two points, two write an equation in slope-intercept form, point-slope form, or standard form, and be able to translate between the forms. This is a chapter that in the past my Algebra 1 classes have really struggled with. They have a hard time keeping the forms straight, as well as determining which form to use and when. In the past, I have used this lesson in what we call an Algebra Skills class. Students enrolled in this class are students who have been noted by a previous instructor to be struggling in math. Therefore, they are in an Algebra Skills class and a regular Algebra 1 class at the same time. The benefit to this is students are seeing the same material twice a day, and are given the opportunity to reinforce those skills that they learned in Algebra 1 in Algebra Skills. The class also works on remediating some lower level math skills that may also be preventing students from being successful in their regular Algebra 1 class. Although I have used this lesson in a remediation class, I think it could be helpful for remediation in a regular Algebra 1 class, and I also think that it could be used as the original lesson or way of taking notes in an Algebra 1 class.

What is so great about the lesson I chose is that it uses foldables as a way of organizing the concepts. Foldables are a great way to encourage note-taking and because they are more like an art project, and not just a piece of generic paper that students are used to taking notes on, it seems that students seem to stay more engaged during the process.

On the attached lesson plan I mentioned several forms of assessment that could be used. Ideally, once I knew that remediation was needed, I would help students to make the foldables. Then as a means of practicing using the foldable I would go through a few example problems with students to encourage them to use the foldable and turn to specific pages when they get stuck. As a formative assessment I would play white board jeopardy in teams. However, each student would be accountable for completing the problem on their own white board, but they can use their foldable and their teammates as a resource. To ensure that the remediation was successful, I would give students the same assessment (or a very similar assessment) as the one that I used to determine remediation was needed in the first place. This will really help me determine whether the remediation has been helpful or not.

The following is a link to a website full of foldables and directions on how to make them.

http://www.fultonschools.org/k12/math/documents/FoldablesBook.pdf

The following is a link to my blog where you can find the lesson plan:

http://jcoulson.edublogs.org/remediation-lesson-plan/

For this plan, I choose to visualize the funtion ax ^ 2 + bx + c. To identify and correct misconceptions, I did quizz and test and I used a scale of Likert with five points: No enough, Regular, Well, Excelent. I would like to analize the nurture of the mistake, so I can make change in my lesson plan.

La activities, quiz, survey and test can be found in:

http://estradaa.edublogs.org

My idea for this lesson on mastery-learning and remediation would be to have a review lesson on linear functions the day before a test of mastery on this concept. The students would have been taught multiple representations of linear functions, so they would be familiar with describing a linear function as a graph, in a table, and as an equation. I would start the lesson with 21 graphs, tables, and equations on the SMART Board and have the students come up individually to the board and drag the multiple representations of the same linear equation on one line. Each of the 7 lines should have a table, graph, and equation of the same linear equation. The students would have to justify why they chose to group the representation together. Sharing their thinking would help those who struggle with the concept of multiple representations of linear functions. It would also help solidify the thinking behind these different representations and help everyone see why they can be represented differently but still describe the same function.

They would then use their SMART response systems to find the slopes of different linear equations. After each question was answered, I would immediately see who needs the information re-taught. The students would also get immediate feedback to know if they got the answer correct or not. I would ask several students how they got their answer. If they got the answer correct, it would help others find out what the necessary process is to finding the slopes. If they got the answer incorrect, I would ask a student who got it correct, to explain to the class how he derived his answer. This should help those unable to find the slope. By asking the questions one at a time, I can give the help necessary to help all students build the skills to correctly find the slopes of linear equations and then test those skills with a similar problem.

Finally, they would have a chance to write a journal entry towards the end of class where they would describe how to find slopes of linear equations and how to know how to describe a linear function using a table, graph, and equation. This would give them ownership of their learning. I would read their entries over their shoulders and address any misconceptions right then privately with each student.

This lesson plan would include: Title: Review of Linear Functions; Learning Outcomes: At the end of this lesson the student will be able to group multiple representations of the same linear function together and to find the slope of linear equations; Standards Addressed: A1.1.A “Students are expected to select and justify functions and equations to model and solve problems;” Materials: Class set of SMART Response systems; matching lesson on SMART Notebook; questions on SMART Notebook involving finding slopes; Procedures are in my reflection above; the assessment for the lesson is formative assessment in the form of matching questions and slope questions. The summative assessment would take place the next day as a test of mastery of linear functions. The remediation would take place as mentioned above. Hopefully nearly everyone would be able to attain mastery on the linear functions test, signifying that the remediation steps worked!

My plan for presenting this lesson as an artifact of Math Methods was to demonstrate how I will take an arbitrary lesson and build an assessment and remediation plan into it. I assess constantly where students are at motivationally and within their math ability. I check to see if students “got it” by asking them to work on problems as we go through the lesson. I hold students accountable to their thinking by having them present their solutions to a partner and then holding the pair accountable by having them share out their thoughts. And the conversation of the group-share is directed by the use of my select-and-sequence tool which I’ve used to log responses from each student or pair. I will use the highlights from the conversations (checking with “fist to 5” for understanding) and the results from the tasks, especially the exit task, to assess the levels to which students demonstrate understanding.

For those situations where students do not “get it,” I’ve set aside problems, time, and a structure for cycling back through the information about areas of regular polygons. By periodically bouncing back (1,3,5 days, etc.) I can keep the discussion fresh in their minds, and I know that some students will be better retainers of information and understanding if they can see it again and again. I will teach more about the concept in the immediate days following the lesson, but as the days add up between the lesson and when they should and must need to know the information, the discussion prompt gets shorter and shorter to reflect that students don’t need extended prompts in order to recall what it is that they must do.

http://gplb.edublogs.org/files/2011/07/Assessment_and_Remediation_Problem_Solving_Lesson-2goa7qw.pdf