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.
i need about 15 pages including reference page
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
FIELD EXPERIENCE PART 2
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
- 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
FIELD EXPERIENCE PART 2
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
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
FIELD EXPERIENCE PART 2
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
FIELD EXPERIENCE PART 2
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
FIELD EXPERIENCE PART 2
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).
FIELD EXPERIENCE PART 2
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).
FIELD EXPERIENCE PART 2
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
FIELD EXPERIENCE PART 2
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
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
FIELD EXPERIENCE PART 2
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.
FIELD EXPERIENCE PART 2
(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.
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
FIELD EXPERIENCE PART 2
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
FIELD EXPERIENCE PART 2
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.
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
FIELD EXPERIENCE PART 2
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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