# Field Experience and Interpreting Linear Models

Field Experience and Interpreting Linear Models Order Instructions: My essay is already half way through so please follow the line of reasoning to complete a full essay on the subject. the essay is about a math lesson. I will upload the directions.

Field Experience Part 2

Part A: Context

I have been teaching mathematics at the New Britain High School in Hartford county Connecticut for six years, previously I taught at the middle school level in the same district for four years. New Britain High School has a very diverse population of  approximately 2700 students, the ethnic make-up include Hispanics, polish, Asians, middle-eastern, and others to a lesser extent.  The school’s diversity makes it mandatory for schools initiate programs to support students’ variability in the classroom (Marzano, 2009) and for teachers to make adjustment through differentiated instructions to create an equal opportunity for everyone to learn.

This field experience project will be done with a group of 10 standard algebra 1 ninth graders that I taught during the 2014-2015 school year at  New Britain High School. I handpicked these students specifically for this task because they fit perfectly into the situation that will produce the desired outcome for this assignment.  Four of these students are English language learners (ELL) that are still enrolled in the program at varying level, two of these students are level one and two ELL respectively and are receiving mandated language transition support and participate in a transitional bilingual education program. The other two participate in English as a second language (ESL) pull-out model program. Another student had a cerepalsry condition affect his speech and walking, it is recommended that he uses a wheel chair to move around and he also gets an elevator key. He however refused to use the wheel chair and seem to do fine without it, he just get out of his classes and the lunch room 5 minutes before everyone else.  He is very reserved and only rarely raises his hand to indicate that he needs something. One other student has a 504 plan to accommodate his ADHD diagnosis. The remaining students have problems ranging from math anxiety, poor retention and low skills.

The lesson content will be scatter plots, analyzing scatterplot, draw and find equation of line of best fit/regression line (linear model). Use linear model to make predictions about the data represented  by a scatter plot. This lesson covers Connecticut common core state standard  for high school algebra 1 and includes the following standards and skills

1. 9-12.HSS-ID.B.6c Fit a linear function for a scatter plot that suggests a linear association.

Skills- Scatter plot:  line of best fit

Skills- Linear regression

9-12.HSS-ID.C Interpret linear models

9-12.HSS-ID.C.7  Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. (The Common Core in Connecticut,  n.d.)

In addition to the content standards to be covered by this lesson several international standard for technology in education (ISTE) standards will also be accommodated. These include  communication and collaboration, critical thinking and problem-solving, communication and  collaboration and research and information literacy.

In addition to applying and learning new math skills and processes,  students will also be required to complete a performance task which involves gathering data and creating a report after analyzing the data. This performance task involves team work and research. The lesson itself is approximately 3 days however, students will be given extended time to complete the performance task. Skills to be learned includes, observing and drawing best fit line on scatterplots, finding the equations of the line of best fit using two methods and then using the line of best fit (linear model) to analyze the data. The performance task will be completed over several days, the students will be given the assignment during the second day of this lesson. Students will be required to research and collect data about a real life scenario, this assignment will require student to research, collect, and organize  a scatter plot of data showing the rise in sea level over the past century.  Fit a trend line, find the equation of the trend line and use it to predict the sea level in the year 2020 or any year thereafter.  Students will create a report of their finding and given options to present this report to the class.

# Part B: Pre-assessing and lesson planning for Field Experience and Interpreting Linear Models

In order to fully comprehend the mathematical process involved in this lesson, students need to know and be able to apply some perquisite skills. Since this lesson is continuation of a series of units in logical sequential order. These skills were taught in previous lessons. After these previous skills were taught, students were assessed to determine mastery of the content or skills. The results of these assessments were used to determine what area needs review and whether students were ready for the next lesson/unit. Some of these skills included finding slope and y-intercept from a linear graph, finding the slope from two points on the line, identify slope and y-intercept from an equation in slope-intercept form, finally finding the equation of a linear model from two points on the line. I specifically designed a pre-test for the ten students in my study group; this test was to determine the readiness of these students for the lesson ahead. The pre-assessment determined that eighty percent of these students were ready to move on, and twenty percent needed remediation, I  continued to reinforce necessary prerequisite skills through daily do nows to help the struggling students solidify  needed concept.

Since this lesson will involve the use of technology, we did a brief overview of the different technology that were available to us. Students were questioned about their familiarity with the different technology tools and which ones they are most comfortable using to. Although the internet has surpassed other traditional media forms for information gathering in many schools, homes, and the workplace, many people are unable to use this resource effectively. (Eagleton & Dobler, 2007).

In order to make the students aware of the expectation or outcome of this lesson and get a  better understanding of any real life experience they may have. I have engaged them in a conversation about some real life scenarios that could  involve the use of scatter plots example, I started a discussion about a company yearly net profit and the amount spent on advertising life expectancy and year of birth, number of horsepower and fuel efficiency

Students are expected to learn and apply three  main skills/concepts in this lesson

Find the equation for the line of best fit/regression line by problem-solving  and or using a graphing calculator. Once students find the equation there are expected to be able to use it to make predictions about the data (answer questions). The pre-requisite skills had a direct bearing on this lesson, like I said these skills were reinforced in previous classes, I started the lesson off by having students finding the equation  of a line given two points on the line, this warm-up/review activity is important because students will use the same skill to find the equation of best fit lines in the lesson. I will then introduced/show several pictures of scatterplots with best fit lines . I will then guide students by modeling how to draw their own best fit line on a scatterplot hand-out. Students would now reflect on the starting activity and suggest ways how they could find the equation of the of best fit line displayed on the whiteboard, this scatter plot will be interactive so the dots representing the scatterplot can be hidden leaving the best fit line only. This will help students to more readily make connection to previous lesson or the lead off activity.

This lesson is designed to be more student-centered therefore to shift the responsibility to the students they will get in their pre-assigned cooperative group (citation) to discuss and apply a previously learned strategy to come up with the equation for the line of best fit. The teacher will walk around and check the accuracy of student’s work. Once students are done they will write their equation on the board. I will now use modeling/scaffolding the step-by-step  problem-solving strategy that will be used to find the equation of the line of best fit, then we will compare answers and students who used the correct mathematical process will know, those who did not would have learned the process while modeled the steps on the whiteboard. This whole process will involves motivation, collaboration, problem-solving, and critical thinking and build self confidence. The process also allow students to see relationships and make connections to earlier learning experience. I will continue to use the strategy of scaffolding and questioning to demonstrate how to use the equation of best fit to answer question (extrapolate/interpolate)) about the data represented by the scatterplot. Questioning will activate previous knowledge and simultaneously assess student’s comprehension of the concept while the lesson is in progress (citation).

Day two, students will be taught to use the graphing calculator to derive the line of best fit for a scatter plot, each student received a graphing calculator and a hand-out with step by step direction of how to use the t-83 graphing calculator to derive the equation of the regression line. I will also walk students through this process on the whiteboard (modeling/scaffolding) . Students who are more advance will be allowed to follow the direction on the hand-out to complete this activity on their own or if they so wish they may follow  while I model the process first. The whole idea here is to differentiate the lesson, doing the same thing in different ways. This will ensure that I am giving each individual a fair chance of learning the concept. Add more here and (cite).

Once I am done modeling this strategy students will get another handout with data for a scatterplot, they will now get in their pre-assigned group and working together as a team they will use the calculator to find the equation of the regression line and make predictions about the data using the regression line. During this time I will play the role of a facilator, walking around the room and giving advice and help where needed (CITATION).

Finally students will be required to used both strategies, problem-solving and calculator to find the best fit line for the same problem, students will know that both methods will give slightly different answers and should be fine. Students will identify the slope and the y-intercept after deriving the equation and discuss in their groups what these values represent in the context of the problem.  they have previous knowledge of this and should not have much trouble here, otherwise I will use questioning to elicit the correct answer from them.(cite)

Various strategies were utilized throughout this lesson including, modeled talk: Show while you talk, visual scaffolding, questioning sessions, cooperative learning, and multimedia presentation. Modeling and talking allows me to provide examples  in a step-by-step fashion using gestures and visuals to help students easily make vocabulary connection. Students also had the choice of writing down the steps of the problem-solving process so that can make reference to it when the need arise, this strategy was very effective for all students especially English Language learners (Herrell & Jordon, 2008).

Part C: Implementing Lesson, Analyzing Student Work and Adjusting Instruction

• Implementing Lesson

Implementation of the lesson basically entails covering the content of the lesson. First, the 10 standard algebra 1 ninth graders would be taught scatter plot. During this lesson, these learners would analyze scatter plots, draw and find equation of line of fit or regression line; that is, linear model. They will use linear model in making predictions with regard to the data which is represented by a scatter plot. The lesson also covers Connecticut Common Core State standard for high school algebra 1 and are as follows:

9-12.HSS-ID.B.6c Fit

This is a linear function for a scatter plot which suggests a linear association. The skills that would be acquired by the learners are Linear Regression and, Scatter plots: Line of best fit (Algebra 1 – N.7). This lesson would also entail finding the equation of a regression (Precalculus –  Z.8) (Connecticut Core Standards, 2015).

9-12.HSS-ID.C Interpret Linear Models

This comprises 9-12.HSS-ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model within the context of the data. It consists of (i) Interpreting regression lines (Precalculus – Z.9); and (ii) analyzing a regression line with the use of statistics of a data (Precalculus – Z.11) (Connecticut Core Standards, 2015).

• Analyzing Student Work/Formative Data

Assessing the learning of the students has to be linked directly to improving student learning. To analyze the work of the students, formative assessment  would be conducted. This type of assessment basically entails using assessment in providing feedback to the educators and learners (Cornelius, 2014). The information which would be obtained from informal assessment will be helpful in making alterations to how I teach.  The objective of carrying out formative assessment is essentially to monitor the learning of students in order to provide continuing feedback which the instructor could utilize in improving his/her teaching and by the learners to improve their learning (Jacoby et al., 2014). In particular, the formative assessment which I will carry out will: (i) help me to know where my students are struggling and then I will immediately address any problems; and (ii) help the learners to identify their weaknesses as well as strengths and target the areas which require work. In general, these types of assessment are low stakes; that is, they lack or have low point value. Some of the formative assessments that I will carry out include asking the learners to do the following: submit  a few sentences in which the student identifies the key points of the lesson; draw a concept map that represents their comprehension of a given topic that I have covered in class; turn in a research proposal for early feedback.

Formative assessments offer comprehensive information regarding student learning clearly and directly not just to the educators but also to the learners. It is notable that formative assessments allow for re-doing and re-teaching of instructional tasks (Torrance, 2012). As the educator, using formative assessment will allow me to make necessary changes to learning and instruction activities in order to ensure that the students actually achieve learning goals. In addition, this assessment will provide me with opportunities of developing vital assessment skills as well as crucial knowledge of both standards and my students. The formative assessment will provide an effective way of building my ability to analyze the work of the students, plan and adjust teaching which is focused on the progression of learning and needs of the students, and comprehend the nature of educational goals (Cornelius, 2014).

The formative assessment with the right and proper feedback is a very effective moderator in enhancing achievement. The main elements of the formative assessment are as follows: (1) identifying the gap: the difference between what the learners know and what they really need to know would be defined. (2) Feedback: rich conversations between the learner and the educator would provide the educator with the information that is required to recognize the present status of a student’s learning and the exact steps which the educator could take in order to improve. As the educator, the feedback which I will give to the learners would be timely and constructive to allow the learners to advance their learning. Student feedback as well as reflection could alert me of the need to make modifications to instructional approaches.

(3) Learning progressions would be utilized by the educator in breaking a learning goal into subgoals that are smaller and more manageable. As the educator, I will identify the location of a student on the learning continuum and work with the learner in a collaborative manner to formulate a series of smaller goals (Jacoby et al., 2014). (4) Student involvement: involving the learners in decisions as regards their own learning and in self-assessment will help the learner engage in reflection and develop their metacognitive skills.

### Adjusting Instruction on Field Experience and Interpreting Linear Models

When formative assessment process is included into classroom practice, it can provide information which is required in adjusting learning and teaching as they are still taking place. It is notable that the process of formative assessment will serve as practice for the students as well as a check for understanding in process of learning (Torrance, 2012). Formative data would guide me as the educator in making decisions with regard to future instruction.

The formative assessment will help me in: identifying the current state of the skills and knowledge of the learners, making the necessary and appropriate adjustments in instruction so that the learners meet with success, and notifying the learners of their progress to assist them in setting goals. It is worth mentioning that I could utilize the formative data in adjusting my teaching strategies and match the learners with suitable learning conditions and materials. In essence, the information that is obtained following formative assessment could help me, the educator, determine the following: (i) whether the learners require alternative materials; (ii) how to group the learners. (iii) I will also be able to determine the duration of time to assign to particular learning activities; (iv) which learners are actually ready to advance; and (v) which concepts should be taught again to particular learners.

# Part D: Post-Assessment, Data Analysis and Project Reflection

• Post-Assessment

The components of assessment include the following: (i) analyzing scatter plots; (ii) drawing and finding equation of line of best fit/regression line (linear model) – these two components of the assessment basically assessed new math skills which the students have gained as a result of the lesson. The components also assessed how the students apply the new math skills and processes covered in the class. The 10 students were also assessed on the following skills: finding slope and y-intercept from a linear graph, finding the slope from two points on the line, their ability to identify slope and y-intercept from an equation in slope-intercept form, and finding the equation of a linear model from two points on the line.

(iii) Communication and collaboration: this component of assessment assessed the communication skills of the students as well as how a student cooperates with others and relates with fellow students when given group work. (iv) Critical thinking and problem-solving: the students were assessed on how to reason effectively, which entails using different sorts of reasoning – for instance deductive and inductive – as suitable to the situation. They were also assessed on how they utilize systems thinking; that is, analyzing how parts of a whole interact with one another to create overall outcomes within complex systems (Saavedra & Saavedra, 2011). Furthermore, they were each assessed on solving various sorts of non-familiar problems in both innovative as well as conventional ways, and how they are able to identify and ask important questions which elucidate and explicate different viewpoints that result in better solutions (Shaw, 2014). (v) Research and information literacy – this component entailed assessing the students on how they properly complete a performance task that involved collecting data and writing a report following the data analysis. It is notable that this performance task required the students to engage in team work and research.

## Field Experience and Interpreting Linear Models Data Analysis

Math skills: Each of the 10 students in the class was able to successfully learn math skills, although with varying degrees of success. For instance, the student with ADHD diagnosis and the one with celebralpalsy had difficulty grasping the lesson materials and contents and needed assistance regularly unlike the other 8 students. The results reveal that out of the 10 students who were selected, 9 of them demonstrated excellent application of math skills and process that were covered during the course of the lesson; that is, they were able to properly apply the new math skills. These students were able to correctly analyze scatter plots, and draw and find equation of line of best fit/regression line. The student with ADHD diagnosis did not apply the new math skills according to expectations.

The results also demonstrated that 5 out of the 10 students had some difficulty in finding slope and y-intercept from a linear graph. Two students had trouble finding the slope from two points on the line. Three students had trouble in identifying slope and y-intercept from an equation in slope-intercept form and 1 student had difficulty finding the equation of a linear model from two points on the line.

Communication and collaboration: all of the students demonstrated effective communication and teamwork particularly during the performance task which required the students to work in team work and carryout a research. When conducting the performance task, the students effectively organized themselves into 3 small groups: two groups comprising 3 members each and one group comprising 4 members in total. It is worth mentioning that communiation in these groups was satisfactory as each group member contributed to the group effort.

Critical thinking and problem-solving: the students were able to learn new critical thinking and problem solving skills. This is because they demonstrated different kinds of reasoning as apt to the situation, they reflected critically on learning processes and experiences, and interpreted information and drew conclusions basing upon the best analysis. They also solved various sorts of non-familiar problems in ways that were innovative and conventional, and effectively identified and asked important questions which clarified different views and led to them making better decisions.

Research and information literacy: the students carried out the research and completed the performance task within 5 days. The assessment revealed that the students effectively learned new skills. For instance, the students properly observed and drew best fit line on scatter plots, they successfully engaged in finding the equations of the line of best fit with the use of 2 methods and they properly utilized the line of best fit/linear model in analyzing data. In completing the performance task, the learners researched and gathered data regarding a real life scenario. They successfully and effectively researched, collated and organized a scatter plot of data that showed the rise in sea level over the last 100 years. They fit a trend line, found the equation of the trend line and utilized it in predicting sea level in the year 2020 or any other year after 2020.

# Field Experience and Interpreting Linear Models Project Reflection

In this assignment, the desired outcome has been achieved. This is partly because only 10 students were included in the lesson, which is a relatively small number that enabled personalized learning and effective instruction to take place during the lesson. Moreover, the desired outcome was achieved because the selected learners fitted perfectly into the situation considering that they had a wide array of problems since the students ranged from those who are English Language Learners to English as a Second Language learners to a student with ADHD diagnosis to student with celebralpalsy condition which significantly affected the students’ walking and speech. All the students completed the lesson successfully since none of them opted out during the course of the lesson. This was essential for the attainment of desirable results. Even so, it is important to note that one student was a little troublesome perhaps due to the condition that he had: the student with celebralpalsy was a bit slow in comprehending the lesson contents in comparison to the other learners, but in the end he also attained the outcomes which are considered desirable taking into consideration his condition. On the whole, the assessment helped to find out the readiness of the 10 selected students for the lesson ahead. It has been established that 8 out the 10 students, or 80% of these students, are actually ready to move on with the lesson ahead, whereas 2 students, or 20% of all the students, require remediation.

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