Contextual Factors Analysis

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     Nicholas Lacasse

    2/21/2016

    Contextual Factors Analysis

    To effectively teach, teachers must have an understanding of their students. To

    understand our students is to understand their community, their cultural backgrounds, their

    families, their strengths and needs, the classrooms and district they are a product of, and their

    opinions on all of these factors that have influenced their growth. Therefore, it is recognized that

    a teacher’s work does not begin in the classroom but in an evaluation of the school and the

    community that surrounds it.

    Poland Regional High School is part of RSU 16 and serves families from Poland,

    Mechanic Falls, and Minot. These are rural communities that have a total population of 11,014

    over approximately 83 square miles of land [10], [14]. Though there is a low population density

    there is still some variation among the towns. Minot has a population density of 88.2/sq mi.

    while Mechanic Falls has a population density of 275.6/sq mi [10], [14]. While I can expect most

    students to live in a fairly rural environment, there will be some level of heterogeneity among

    our students regarding population density. Due to this low population density, it can be expected

    that there will be few students that walk to school. Most students will rely on transportation from

     parents or the school district to make it to school. Mornings with snow could result in many

    students being late as parents (and possibly children) shovel out vehicles and driveways.

    Across the three towns, many of the most significant features appear in Poland: Range

    Pond State Park, Poland Spring Bottling, Poland Spring Inn, and three of the five schools in RSU

    16. The other two towns are intermittently marked by local businesses. In the summer, students

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    may find outdoor recreation at any of the several golf courses or at Range Pond State Park. In the

    winter, they are not far from Lost Valley, where they could ski or snowboard. Other year-round

    entertainment can be found in the Lewiston/Auburn area. These will likely be experiences shared

     by many students, potentially serving as points of engagement and connections to the local real

    world they know. The location of these students put them in a unique position to appreciate and

    relate to both small local businesses and well known franchises. Lessons could be prepared in

    relation to either type of business to engage students.

    There is very little diversity in this region. The communities served by RSU 16 each have

    approximately 97% of residents identifying as white [10]. Furthermore, no minority composes

    more than 2% of any of those communities [10]. Between a fifth and a quarter of households in

    the community are husband-wife households with children under the age of 18 [10].

    Approximately 30% of households have individuals under 18 years of age [10]. This means most

    students will come from a family of traditional structure, but I must be careful to not make those

    assumptions about all students. Students could come from families of many different structures,

    including those with less than two parents. Students with less than two parents or guardians

    could miss school to watch for younger siblings, take on part time jobs to supplement guardian

    income (see: Figure 1), or have excessive duties at home. The unemployment rate of those

    regions all fall around 10% [13], and 34% of high school students received free or reduced lunch

    in 2013 [9]. There are many ways that students’ life at home could impact their health and

     performance in school. To be mindful of this, it would be best to continually promote an active

    dialogue with students and give them means of confidential communication.

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    In September 2013, there were 504 students and 47 teachers, resulting in a student

    teacher ratio of 11:1 [6]. The school uses standards based grading (following the Maine Learning

    Results and the Common Core). Throughout the semester I will need to continually evaluate all

    of their skills to determine their proficiency. The only grades that are final in their school are the

    standards the students have achieved by the end of the semester [8].

    Figure 1 

    Data from [12].

    The classroom is a 500 square foot area that is utilized, on average, by 19⅓ persons each

    class. This means that each person could have nearly 26 square feet of their own space. Student

    space is reduced by the margin the teacher maintains at the front of the room to utilize the

    whiteboard and in practice the single-person desks the students sit at provide them with only 16

    square feet of personal space. Such constraints should not be underestimated, especially when we

    consider that students may be under these physical constraints all day. To maintain student focus

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    and prevent nerves from building, it is important to give students a chance to move and stretch.

    Physical discomfort could lead to further distractions. To prevent physical and mental fatigue in

    the eighty minute class block, I would advise having several distinct shifts in activities during

    each lesson.

    Being on the second floor and near the end of a hallway, distractions outside the

    classroom and inside the school are limited and it is often appropriate to simply keep the

    classroom door open. The open door helps to promote a nonconstrictive environment and helps

    to minimize distractions when students need to leave or enter the room. Due to the vacant

    hallway, we can generally allow students to take a short walk outside of the classroom without

    fear of them being caught up in social activities. The silver-day math one class is from

    11:30-12:50, directly after lunch. Though this may help them focus because they are not

    distracted by hunger or social needs this class is reportedly more chatty [1]. The blue-day math

    one class is the last block of the day. This means special attention to classroom management

    techniques may be needed to effectively facilitate a lesson.

    There are a set of windows along the wall to the students’ right. Fortunately, they look

    into an uneventful wooded area and do not strongly contest student focus. However, the room

    shares a partition wall with another classroom. The partition allows enough noise through that if

    the adjacent classroom is being loud, but appropriately so, it can be easily heard in our

    classroom. At best, it is masked by our own students. At worst, our students are silently working

    on summative assessment. A potential way to combat this is to use sparingly, if at all, strategies

    which require silence in the classroom.

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    All students at the high school are issues iPads. Though many of them have a separate

    graphing calculator, many students will use Desmos or the very capable TI  - Nspire  app on their

    iPads. This means that we always have a powerful array of portable tools and can easily conduct

    class outside of the classroom. These tools give extremely diverse ways to conduct the

    classroom. It allows us to move the classroom to different locations. It allows us to let students

    download useful videos for use at home (if they don’t have access to the internet) or watch the

    videos directly online (if they do have internet access).

    The classroom is also equipped with other standard tools such as rulers, meter sticks, and

     protractors. Such ease of access means I can incorporate them into my lesson plans without

    concern. Students also have access to personal whiteboards of various sizes. These can be

    utilized in team activities where responses are necessary, or as an impromptu decision if several

    students are without writing implements.

    The Poland Regional High School Course of Studies  reports that students have seven mandatory

    student led parent-teacher conferences throughout their four years at the high school and that

     parental attendance is at 95% [8]. However, Michael Hayashida, a teacher at the school, reports

    that there is very little parental involvement and he expects to receive no emails from parents

    each week [1].

    According to Piaget’s theory of cognitive development, most students of this age are

    equipped to deal with the abstract reasoning required for success in a freshman mathematics

    classroom [7]. However, many of them still lack finer executive functioning skills. It is not

    uncommon for a student to ask for a pencil, or to pull an important paper, crumpled, directly

    from their backpack – if they are capable of finding it at all. To encourage healthy organizational

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    habits I must be a model of how to be organized as well as demonstrating how my organization

    helps me accomplish things more efficiently. Related to this is a standard named  Habits of Work  .

    It accounts for turning in homework, being positive in the classroom, staying on task, and being

     prepared. Most students (25) score higher in the content standards than their Habits of Work  

    standard. The school uses a 4 point scale for their standards based grading. Twenty-three of the

    students have Habits of Work   scores below a 3.0, and seven show a significant deficiency with

    scores below 2.0 (see: figure 2).

    Figure 2

    Data from [2].

    Observations of the classroom have indicated that the low scores in the  Habits of Work  

    standard are not due to insubordination or unruliness. Instead, it appears that the deficiencies in

    this standard are caused from not completing homework, and occasionally detracting from the

    learning environment by distracting others or not supporting a positive learning environment.

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    Throughout my unit, I will need to emphasize the importance of the completion of homework

    and take extra measures to ensure its completion. These extra measures will likely include

     bringing students to my room during their academic support block to have them do the

    homework there. In efforts to support a positive learning environment I will offer ample praise

    and be quick to correct any behavior that detracts from the positive environment. 

    Math 1 encompasses the fundamentals of algebra, functions, geometry, statistics, and

     probability. Though the first half of the academic year was largely centered around algebra and

    functions, skills from those two domains will appear frequently throughout the second half of the

    academic year. During my time there, students will learn about geometry, statistics, and

     probability. I will be teaching the unit on probability.

    Students attend Math 1 every other day. The two sections we have are placed on opposite

    days. This alternating schedule gives time to make adjustments to the lesson after its first

     performance. Furthermore, for students, it maintains the traditional schedule of alternating class

    and homework. The composition of the two sections of the course are comparable – each have

     proportional representation of students of all ability levels. Across both sections there are 39

    students. Most students are making satisfactory progress toward their learning goals earning in

    the 3-3.5 range. A few in each class are advanced and are earning in the 3.5-4.0 range. A few in

    each class also fall below the 3.0 mark and require additional support to be successful in the

    classroom. The class average in each standard is higher for blue day students than for silver day

    students (see: figure 3). Stronger statistical techniques are required to determine if there is an

    actual difference between the groups. This diverse group of learners will require deliberate

    differentiation. There will need to be opportunities for students to have extended amounts of time

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    Students are familiar with slope intercept form and are able to construct lines in slope intercept

    form that model a data set or create the slope intercept form from a graphical representation of

    the line. Students also have some familiarity with point slope form. They have experience with

    factoring constants and single variables from equations but do not have experience with factoring

    quadratics or larger polynomials. Their experience in factoring was within the context of solving

    linear equations and inequalities. These skills were put to more specific use in their unit on linear

    modeling.

    The skills the students learned in the algebra, and functions units were heavily relied

    upon in the unit on linear modeling. The linear modeling unit took the mathematical skills and

    focused on application in real world contexts. This means I can expect some level of competency

    with problem solving and word problems, as well as the ability to transfer skills to new contexts.

    Confidence in their problem solving abilities are bolstered by a series of problem solving tasks.

    The tasks include a mathematical problem within some context, and an accompanying typed

    report on the issue, their process, and their solution. Though linear modeling in classrooms is

    typically formed around perfect models that entirely describe a simple theoretical scenario, these

    students have gone further by examining relationships that are nearly linear. Through the use of

    their technology (predominantly graphing calculators, or iPad apps) they are able to perform

    linear regression. Their skills in linear modeling are well established and they have recently

     begun a unit on exponential equations. Despite students fairly solid mathematical skills, there is a

    split between students enjoyment of mathematics and numbers. The split is unfortunately skewed

    to the right, as seen in figure 4.

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    smooth, if slightly less informative than a platform that offers reports with feedback for specific

    student success. The success with the Kahoot! prompts future use of the tool. It will be a quick

    and engaging way to get students warmed up for the class. Their familiarity and excitement for

    technology also suggests the possibility of non-traditional, technology centered, summative

    assessment. The minor challenge associated with this is that there is a student without an iPad,

    and a student with an iPad but without internet access. In class, this can be remedied by allowing

    students to temporarily use the iPad of a faculty member (myself, my mentor teacher, or the

    special education teacher). The unit on probability will be able to make use of the Numbers app,

    especially during the section on probability distribution tables.

    The students at Poland Regional High School are very skilled in the traditional academic

    sense as well as with their technological skills. Their organizational skills leave something to be

    desired, but most of them still find success in spite of their poor organization. Their familiarity

    with word problems, applications of content, and problem solving experiences will allow me to

    engage them with their interests. By shaping a lesson’s content to be within the context of their

    interests, it will help to engage them and fortify their learning experience.

    Through the implementation of a student survey I have discovered many of my students

    interests. Throughout the two classes, there is significant interest in outdoor activities, sports, and

    the arts. Each of those major categories are represented fairly evenly across the classes. Across

    the survey, students listed, collectively, counting multiplicity, a total of 96 interests. Some of the

    most frequently listed interests include: hunting, fishing, soccer, drawing, friends, music,

    animals, basketball, reading, sports, and video games. Collectively, those represent 49% of all

    listed interests. An important consideration is that even though a student may not have listed a

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    specific interest, it does not mean they are not interested in that thing. In that sense, this

     particular data serves as guidelines and not as strict rules. These larger collective interests could

     be useful topics to design problems around.

    Sports of any kind (namely soccer, and basketball for this group of students), and video

    games have especially obvious ties to probability. Both often use probabilities in percentages or

    decimals and it is natural to wonder about the likelihood of a series of events occurring or if at

    least one of two things will occur. It can be assumed that there are likely some cultural

    commonalities between our students. For instance, it is likely that our students have played many

    games that involve chance: Monopoly, Parcheesi, Scrabble, and many more. These can be a

    springboard to understanding or serve as motivation for students.

    Though these topics may have general appeal to many, it is notable that some students

    may be left out or require a topical connection they care more deeply about to become engaged.

    This is particularly applicable to students who tend to care less about their academic

    responsibilities, or are very distractible. By meeting them on their own ground, I can make a

    student who normally struggles feel like an expert, and I can deeply engage a student who

    normally finds it difficult to be motivated to learn about mathematics. These singular but potent

    interests listed by students include: slavery, civil war, cars, Egypt, racing, and technology.

    Students interests in these topics may influence their content knowledge, and how they perceive

    new content knowledge. For instance, the car enthusiast in the classroom may not think he

    knows much about algebra and ratios, but has an intuitive sense for gear ratios. It is likely that

    the interests students have listed relate to the style of thinking they perform. A visual thinker

    may be more likely to appreciate drawing, and a logical learner may be more likely to appreciate

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    do not learn best through verbal explanations, it also indicates that students need support and

     practice at developing their verbal skills.

    The least represented intelligences in the classroom are logical, and naturalistic, both

    appearing in the top three just below 7% of the time, and students scoring above 30 raw points at

    3.5% and 13.8% of the time respectively. Though this may seem to indicate that connections to

    nature may not be intrinsically motivating for students, it is important to recognize our previous

    conclusions. Though connections to nature may not be intrinsically motivating to many, it can be

    deeply motivating to a few select students.

    Figure 6 

    A raw score of 40 is the highest possible for any category. Data from [3].

    The most significant information gathered from the multiple intelligences survey is the

    significant representation of kinesthetic and visual/spatial learners. In particular, 93% of students

    have either visual/spatial or kinesthetic in their top three intelligences. These results indicate that

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    the implementation of manipulatives to further instruction will be essential to the engagement

    and success of this class. It also suggests that I should investigate appropriate strategies for

    including these intelligences in assessment. For example, allow students to convey their

    understanding through sketches, by making physical model that describes their ideas, or even a

    video that allows them to express their understanding through manipulatives. With the use of

    their iPads, these all become easy feats that can be seamlessly integrated. The results of the

    multiple intelligences survey is supported by additional questions posed to the students during

    the survey.

    A free response section of the survey asked them to list something a teacher can do that

    would prevent them succeeding in the classroom, and two things a teacher could do to help them

    succeed in the classroom. Students were largely in favor of group work and access to their peers,

    with 41% of students reporting such preferences. Other common items listed as being helpful for

    their success included individual work, teacher support, the option to listen to music, and hands

    on activities. To promote these self-reported supports, I will emphasize the use of manipulatives

    and provide diverse groupings (individual, pairs, small groups, class discussion). It is typical in

    the classroom for students to listen to music if the setting is appropriate. Due to this well

    established routine, it will be easy to implement into the classroom. Cooperative learning

    strategies such as the think-pair-share will be implemented to encourage the diverse groupings

    that students desire.

    The quality most cited as undesirable was a teacher that talks too much. This reinforces

    recent professional development at Poland Regional High School that focuses on the ratio of

    student to teacher talk. Students reporting this quality accounts for 25% of all reported

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    hindrances. To combat this, I should reduce direct instructional time when appropriate and

    replace it with group discovery or other cooperative learning strategies that keep students as the

     primary agents in the classroom. The next most common complaints include not explaining

    things well, going too fast, or going too slow. Though these are vague, blanket statements that

    are often cited as difficult to work with, I propose two solutions. To combat poor explanations,

    formative assessment will be a continual process. Exit tickets will check for understanding at the

    end of lessons and methods such as 1-2-3 (a self-reported representation of understanding) will

    inform and influence instruction. To prevent going too fast or too slow, it is important that

    students stay the primary agents in the class and differentiation is incorporated. Developing

    extensions of content will be critical to maintain engagement and academic rigor in all students.

    The student survey that was conducted has given me powerful insights into my individual

    students. Having two sections of math 1, the survey results are split between the two blocks (H

     block and D block). Most students participating in the survey, but others have managed to elude

    it – some intentionally, others innocently. Unfortunately, the students that would elude the

    survey are the same students who would elude other homework and duties. It is therefore

    difficult to get them to take the survey at home, and inefficient for us to make them do the survey

    in their academic support block where academic instruction takes precedence. The vast majority

    of students have taken the survey. The results of the survey can be found in addendum A and

    addendum B.

    The overwhelming majority of students scored highly in kinesthetic, interpersonal,

    intrapersonal, and visual/spatial intelligences. Immediately, this informs me I should be using a

    variety of grouping strategies to satisfy these students interpersonal and intrapersonal

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    intelligences. The kinesthetic and visual/spatial intelligence is an indicator that hands on work,

    graphic organizers, drawings, and diagrams will help them understand ideas. Nearly half of the

    students are interested in or participate in sports. Relating the content to sports provides both

    real-life examples, motivates content, and engages students with their own interests.

    We are all each of us a product of our environment. To understand ourselves or others we

    must also understand their environment and their perception of it. The students at Poland

    Regional High school are residents of rural Maine, and many of them hover near the poverty

    line. There is significant variance in the amounts of support students receive at home and access

    to the internet or technology should not be assumed. Though most are able to think abstractly, a

    significant portion of them also lack executive functioning skills that help them be successful in

    the classroom. Their impressive grasp of technology and strong algebra skills will be relied on in

    our unit on probability and give us access to many different avenues of exploration. The

    students’ widespread love of games of all kind (sports, video games, board games), their

    appreciation of hands on activities, and their aptitude for group work provide the perfect

    combination of attributes to kick off a unit on probability.

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    Addendum A: Survey Data from D Block  

    Student Verbal LogicalVisual

    SpatialInterpersonal Musical Naturalistic Kinesthetic Intrapersonal

    S1 20 28 33 27 38 31 34 30

    S2 33 29 39  32 39  31 29 39 

    S3 26 21 25 21 19 21 28 33 

    S4 20 23 30 33 31 18 37  30

    S5 25 21 25 29  21 21 25 29 

    S6 18 22 22 27 29  25 24 24

    S7

    S8

    S9 25 28 34 29 21 17 37  27

    S10 18 23 28 25 30 24 32  23

    S11

    S12 24 24 30 32 31 26 34  33

    S13

    S14

    S15

    S16 24 24 24 24 24 24 24 24

    S17 31 29 31 32 40  32 31 36

    S18 23 27 30 30 37  26 37  32

    S19 23 21 34  26 29 22 31 30S20 25 28 36 35 39  26 30 31

    S21 20 28 33 27 38  31 34 30

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    Student Interest 1 Interest 2 Interest 3 Interest 4 Interest 5 Interest 6

    S1 Hunting Soccer Fishing Running

    S2 Technology

    Monopoly

    (b/c/

    strategy

    and math) Photography Music

    S3 Baseball

    Building

    models

    S4 Softball Painting Puzzles

    Lord of the

    Rings

    S5 Basketball Soccer

    Pretty Little

    Liars Camping

    S6 Soccer Swimming

    S7

    S8

    S9 Racing Basketball Working

    S10 Cheerleading Drawing Painting Animals

    S11

    S12

    S13

    S14

    S15

    S16

    S17 Running Gardening Hiking Flute

    S18 Sports

    S19 Video Games Golf Arrow (TV) Nature/Animals

    S20

    Car

    Enthusiast Hunting Fishing Skiing Soccer

    Video

    Games

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    Co-Curricular 1 Co-Curricular 2 Co-Curricular 3

    Soccer

    SRB Golf

    Cooking Baseball

    Softball

    Basketball Soccer

    Cheer Chorus Soccer

    Basketball SRB

    Football Baseball

    Poland Regional Golf

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    Works Cited

    [1] Hayashida, Michael. "Instructional Strategies and Classroom Management." Personal interview. 29

    Jan. 2016.

    [2] JumpRope. Digital teacher grade book. 2016.

    [3] Lacasse, Nicholas. Student Insight Survey. 2016.

    [4] Maine Department of Education; Resident Expenditures by Budget Categories FY 2013-2014 (Per

     Pupil Amounts); ; Retrieved 20

    December 2015.

    [5] Maine Department of Education; Resident Expenditures by Budget Categories FY 2013-2014 (Total

     Amounts); ; Retrieved 22

    December 2015.

    [6] New England Association of Schools and Colleges. Poland Regional Final Report. 2013. Retrieved

    20 December 2015. 

    [7] Papalia, Diane E., and Ruth Duskin. Feldman. A Child's World: Infancy through Adolescence. 12th ed.

     p. 418. New York: McGraw-Hill, 2011. Print.

    [8] Poland Regional High School. Program of Studies and Course Descriptions 2015-2016. 2016.

    ; Retrieved

    3 January 2016.

    [9] RSU 16 Budget Committee. RSU 16 Budget Committee Meeting Minutes RY2014, Meeting 4. 2013.

    Retrieved 23 December 2015.

    [10] U.S. Census Bureau; Census 2010, Table DP-1; generated by Nicholas Lacasse; using American

    FactFinder; ; Retrieved 22 December 2015.

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    [11] U.S. Census Bureau; 2010-2014 American Community Survey 5-Year Estimates, Table S1901;

    generated by Nicholas Lacasse; using American FactFinder; ;

    Retrieved 22 December 2015.

    [12] U.S. Census Bureau; 2010-2014 American Community Survey 5-Year Estimates, Table S1701;

    generated by Nicholas Lacasse; using American FactFinder; ;

    Retrieved 22 December 2015.

    [13] U.S. Census Bureau; 2010-2014 American Community Survey 5-Year Estimates, Table DP03;

    generated by Nicholas Lacasse; using American FactFinder; ;

    Retrieved 22 December 2015.

    [14] U.S. Census Bureau; 2010 Census Gazetteer Files. Retrieved 22 December 2015.