Action Research - Planning for the Final Project

Planning for The Final Project

Requirements & Timeline for the Final Project

The final project for the Educatore School of Education's Masters in Education degree is an action research project, where, by completing the project, students are able to increase their knowledge of an educational topic of their choosing while improving their teaching, and developing skills they can use for future activities. The final product may take many forms, but it must:

• be original work that requires critical analysis;
• include an analysis of previous research done in the field;
• require some application that involves the collection and/or analysis of data;
• include an analysis of findings;
• focus on some aspect of globalization or international mindedness relevant to education in general or your specific situation;
• be in the form of a written report (in Word format).

While there is no limits on the length of the report, it must be comprehensive enough to meet the above and generally runs between 20 and 30 double spaced pages and broken down into the following sections:

• Introduction & Statement of Problem/Question;
• Literature Review;
• Proposed Methodology;
• Analysis of Results;
• Summary & Consideration of Next Steps/Action Plan;
• References;
• Appendices (if necessary)

This will be done throughout the months of November, December, and January, with completion expected by no later than the end of January.

Action Research - A Summary

According to Sagor (2001) action research is "a disciplined process of inquiry conducted by and for those taking the action.  The primary reason for engaging in action research is to assist the “actor” in improving and/or refining his or her actions".  Rigsby (2005) makes it even simpler by stating that "action research is a fancy way of saying let's what's happening at our school and decide how to make it a better place".  

While much of the details of action research have been highlighted in the above section covering the requirements for Educator's MEd program, Padak & Padak (2017) unpack the four stages of action research by asking researchers to think about the following questions/ideas for each section:

1. Identifying questions to guide the research.  Think about what makes a good research question (Is it important?  Is is directly related to the issue/problem?  Is it answerable?);
2. Collecting information to answer the questions.  The key thing to remember here is that any information that can help answer your question is data and can be treated as such.
3. Analyzing the information that has been collected.  Think about this section like this:  when the data no longer brings surprises, you know that you have collected enough.
4. Sharing results with others.  Research can lead to more research and therefore it is key to share so that others learn and you get feedback for perhaps further study.

Ideas for Action Research

The first ideas that come to mind for my topics would be:

1. The impacts on monocultural settings on non-national student socioemotional development.
2. An exploration of the teaching of international mindedness and measurement of understanding, application, and attainment of true international mindedness.

More might come to mind, but for now these are the ones that jump out for me and my context.

Potential Challenges & Successes

Obviously, as a father of 2 who has a full time job and it currently looking for a new school to work at in the 2018-2019 school year the greatest challenge I can see is finding the time to get this done.  In addition to time, as I am living in a foreign country, finding the research for Korea in English will also present a sizable challenge.  As for the successes that I see in this process, or at least the things that I think will make it easier for me.  Since I currently work at an International school and wish to focus either on cultural impacts on education or how we can better promote international mindedness in an IB school, I would think that I have fairly easy access to the base for data.  Additionally, since my school is an IB World School I would like to think that there would be a sense of cultural diversity and understanding at the school as well as a basic understanding and practice of international mindedness.

References:

Guidelines and Rubric: Final Project. (n.d.). Retrieved on November 19, 2017 from https://docs.google.com/document/d/1HENDXgi7azEuAJiwYTWzdhE07p9jRnYHL6nDwg5N_Oo/edit

Padak, Nancy & Padak, Gary. (2017, September 28).  Research to Practice: Guidelines for Planning Action Research Projects. Retrieved November 19, 2017 from http://literacy.kent.edu/Oasis/Pubs/0200-08.htm

Sagor, Richard. (2001). What is Action Research. Retrieved November 19, 2017 from http://literacy.kent.edu/Oasis/Pubs/0200-08.htm

Rigsby, Leo. (2005, March). How is Action Research Defined? Retrieved November 19, 2017 from http://gse.gmu.edu/assets/media/tr/ARRigsbyppt.htm

International Schools. What the heck are they?

International Schools.  What the heck are they?

The one thing that we can all agree on about the definition of international schools, is that there is no one clear, accepted definition of international schools.  There have been many attempts to narrow down what is an international education and those definitions have evolved over time.  Hill (2016) in how he describes that there needs to be an understanding that there is a difference between international education and international school, a view of which I am in complete agreement.  In that same article he presents criteria and descriptors that allow one to kind of rank or put a numerical value on how international school is, however this, to me, and many other researchers seems far to simplistic and not truly reflective of what an international school is.  According to ISC Research (2017), "an international school delivers a curriculum to any combination of pre-school, primary or secondary students, wholly or partly in English outside an English-speaking country, or...[a school] in a country where English is one of the official languages, it offers an English-medium curriculum other than the country’s national curriculum and the school is international in its orientation".  This one idea or definition offered by ISC seems most fitting to me in my experience (as a 16 year veteran of international teaching). It offers the least limiting definition and is the one that fits what I have seen thus far.  That does not, however, diminish the continual confusion of what is an international school.  Take the three below.  Is a DoDEA not an international school?  How about State Department Schools?  And, what makes the Council of International Schools so special?  

International schools have had a long history in global education.  

According to Wikipedia (2017), international schools have been around since the 19th century serving school aged children of families who had to travel for business, government work, and missionary work to name a few.  The number of international schools has grown as a result of globalization to the point where currently there are more than 8,000 international schools worldwide serving over 4.5 million students with over  420,000 teachers (Wechsler, 2017).  Most researchers do not see the demand for international schools slowing down any time soon and predict that the number of schools to double in the next 10 years.  According to ISC Research (n.d.) the most rapid growth for the 2015-2016 school year was in East Asia, mostly due to the growing demand in China for English language medium education.

International education could not be adequately discussed without mentioning the contributions of Kurt Hahn (1886-1974).  Hahn's 1936 paper was well ahead of the times in what one would describe as learning for students.  Hahn's examples of boys in Salem-Gordonstoun conduct and experiences might well be the first documented examples of international mindedness, experiential learning, and the teaching of affective skills.  His legacy is cemented in the founding of United World Colleges and the Duke of Edinburgh Award.  His work inspired many others, most notably Round Square and Outward Bound International.  HIs early schools has a holistic approach that many schools struggle to achieve today, hence why he is still so fondly remembered as a pioneer in international education.

References:

Hahn, Kurt. (1936, March 24). Education and Peace: The Foundations of Modern Society. Retrieved November 3, 2017 from https://drive.google.com/file/d/0BwgYlY1O2AV2VERSQVVpZFNVOFE/view

Hayden, Mary C., & Thompson, Jeff J. (1995, September).  International Schools and International Education: A Relationship Reviewed.  Retrieved November 3, 2017 from https://drive.google.com/file/d/0BwgYlY1O2AV2dFNNOERaMl9lQUk/view

Hill, Ian. (2015, November). What is an ‘international school’? Part 1. Retrieved November 3, 2017 from https://drive.google.com/file/d/0BwgYlY1O2AV2UHhHa25ta1JvakE/view

Hill, Ian. (2016, April). What is an ‘international school’? Part 2. Retrieved November 3, 2017 from https://drive.google.com/file/d/0BwgYlY1O2AV2ODAxbGQxRl83dWs/view

ISC Research. (n.d.). Demand for international education continues to expand globally. Retrieved November 3, 2017 from http://www.iscresearch.com/news/isc-news/isc-news-details/~post/demand-for-international-school-education-continues-to-expand-globally-20170427

ISC Research. (2017). What does ISC consider to be an international school?. Retrieved November 3, 2017 from https://www.iscresearch.com/about-us/the-market

KurtHahn.org (2017).  Retrieved on November 3, 2017 from www.kurthahn.org/

Wechsler, Alan. (2017, June 5).  The International School Surge.  Retrieved November 3, 2017 from https://www.theatlantic.com/education/archive/2017/06/the-international-school-surge/528792/

Wikipedia. (2017). International School. Retrieved November 3, 2017 from https://en.wikipedia.org/wiki/International_school

Analysis of Teacher Evaluations

Evaluation Practices in Schools

A Contrast of Evaluation Systems for Teachers.

There are multiple ways in which schools and districts evaluate its teachers.  From the collaborative, & mentoring style to the state evaluations connected to standardized testing.  Much debate about teacher evaluations have taken place over the past few decades, in particular in the United States with the inclusion of the No Child Left Behind Act.  While this is not applicable to my context overseas, there is no less of a debate of the effectiveness of teacher evaluation practices amongst international schools.  I would like to take some time here to discuss two such school practices that I have experienced over the course of the last 10 years.

Teacher Evaluation at ABC School: The LEAD Process

The process at this school is done in the first year of the teacher joining ABC (Level 1) and depending on the results of the initial evaluation occurs every other year afterwords (Level 2 - clear) or yearly (if there are major concerns Level 3 - probation).  The process includes an initial meeting to set departmental and personal, professional goals.  Three observations occur throughout the year and lesson plans for those three class are submitted and evaluated.  Both the classroom observations and lesson plan observations are evaluated against a set of school-wide teaching standards.  In the final meeting items discussed are:

• Evidence of improvement from the first observation to the final observation.
• Areas for subsequent growth.
• Action plans to address the areas for subsequent growth.

Again, depending on the results the teacher is either put on clear standing (level 2) or probation (level 3).  Probation requires further observations and a detailed action plan, which includes profession development supported by the school to improve the teacher's standing.  Teachers on level 3 have to repeat the same process as in level 1 in their second year at the school.  If the teacher is again placed on probation, the the teacher's contract will not be renewed.  

The process for ABC is one of support, though I would argue that it is a bit too sparse.  Often times people get busy and those three observations are the only ones that occur in support of new teachers.  Overall the process is a fair one, given the school's willingness to support professional development of teachers placed on probation.  In my experience there have been only a few teachers placed on probation and of those few only one that I can recall being not offered a contract renewal.

Teacher Evaluation at XYZ

Very different to what I have observed in my 7+ years at ABC, the teacher evaluation process at XYZ was not very systematic.  It was more of a reactionary approach to poor student performance and parent complaints.  It must be noted that the school was only in its second year when I joined, therefore like many new schools it had its needs and clearly a systematic teacher evaluation system was one of them.  

Since teachers were on one year contracts there was always a sense of fear amongst the teachers that a single complaint or one poor result on an assessment would lead to termination.  In all honesty, you only really saw the principal in your classroom if something was wrong - a poor showing in my opinion.  There was little support from the top in terms of professional development or even suggestions of how one could improve.  The school, due mostly to a mediocre salary and benefits package, employed mostly new teachers fresh out of university.  There was little in the way of school supported professional development.  If a problem was observed with a teacher's practices, the only advice that was given was to "read this" or "watch that video".  Although they made no bones about placing problems in your employment file.  

If you were a good teacher you had no problems, otherwise you were constantly working in fear. Even the good teachers complained about the lack of professional feedback and professional development.  Most left very soon after finishing their contracts.

Proposed Elements on Which I would Like to be Evaluated

As I begin this new chapter in my teacher career and reflect on all that I have learned in the TEACH-NOW program, I would be very excited if a school were to evaluate me on the following elements:

• Understanding Students 
• Technology Integration 
• Classroom Management 
• Planning & Preparedness 
• Assessment & Feedback
• Professional Development and Growth
• Commitment to the School's Ethos

High Stakes Assessments

My Experience with High Stakes 
Assessment in International Schools

Introduction:
Having worked in schools overseas for my entire career I have never experienced the kinds of pressures that many teachers seem to face in the United States with respect to high-stakes assessment.   The idea of having my job security tied to the performance of my students on some government administered tests truly does baffle me.  While there are some clear pros and clear cons pointed out by Munoz (2014), it is obvious that there is a problem with the system of standardized testing as it leads teachers to suppress creativity and problem-solving and move in a direction of teaching to the test in an attempt to save their jobs.  

Being an IB World School, however, does bring with it a couple of examples of High-Stakes Assessments that impact the teacher and the students.  Perhaps not in the way that it does in the united states, but in equally detrimental ways.  My school offers all three programs of the IB:  The PYP, the MYP and the DP.  While the PYP has no high-stakes assessments at all, the other two certainly do, with the MYP recently adding high-states assessment in 2015.  I would like to discuss here the impact that this has had on student learning in my school.

Assessments in the DP:
For years the DP has been grounded in several high stakes assessments:

1. The DP Exam.  This occurs after 2 years of studying a subject and is worth around 80%-90% of the students DP results.
2. The IA.  This "internal assessment" is internally assessed and externally moderated.  While it varies across subjects it is a short term exploration into a topic with each of the 6 DP subjects that the student is interested in.  This makes up the remaining percentage of he students subject score.
3. The EE.  The Extended Essay is a large piece of research that every DP student must complete. While this is not reflected in the subject scores all students must pass this in addition to completing CAS (Community, Action, Service) and TOK (the Theory of Knowledge).

For our DP teachers and students the results are highly important and more and more universities are looking to these results to gauge university readiness.  Students are accepted and/or rejected based on these scores and that places a lot of pressure on students to perform on the day of the exam.  It places pressure on the teachers to ensure that all the content is covered and they they have given the students ample practice to complete old exams in order to prepare them for the real exam.   As you might conjecture, teaching to the test is very common.  

The eAssessments in the MYP:

In 2014 the MYP switched its assessment practices from an internally assessed - eternally moderated model to one where the students will have to complete five on-screen exams, two portfolios and the personal project along with service and action to get their MYP Certificate.  Granted, this does not mean too much in terms of university acceptances like in the DP, but in a culture where face is very important and certificates are highly valued, there is the added pressure on teachers and students in the MYP to do well.  Since the work has a more conceptual framework, teaching to the test like in the DP is not that common, but it has placed the need to use sample on-screen exams as a baseline to create their own assessment, which in some ways is taking away from the opportunities for creativity and inquiry within the MYP.

A South Australian Perspective:

I have recently finished leading a workshop on Inquiry at a school in Adelaide Australia.  I was surprised to see that even in Australia there were set standards and high-stakes tests that the students have to take.  What was more shocking was the impact that the tests had on teaching and learning.  There was a  burning desire of the teachers in the workshop to teach more inquiry and 21st century skills, but they felt bound to continue to ask the questions in the same way that the test does.  The feeling was amongst teachers was that if they wanted the kids to do well, then they had to teach to the skills necessary on the test and clearly there was not a deep level of inquiry or 21st century learning skills on the state exam.  Clearly this was impacting the teachers by limited how and what they could teach as well as the pressure on the students to do well and get into a good university.

Conclusion:
What I have learned in all of this are a few things:

1. There are pros and cons to high-stakes assessment that cannot be overlooked.  Far too often we only focus on the negative.
2. Regardless of the system or country you are in, there are high-stakes assessments, and they are impacting how we teach and the social emotional well-being of our students.

References:

Munoz, Roberta. (2014). High Stakes Testing Pros and Cons.  Retrieved [Jan. 29, 2016] from https://drive.google.com/folderview?id=0B5rGfc4UZHoXQzYyX0I0MlktZWs&usp=sharing

The International Baccalaureate.  http://www.ibo.org

The South Australian Curriculum Standards & Accountability Framework.  http://www.sacsa.sa.edu.au/index_fsrc.asp?t=Home

Planning Assessments

Introduction

For this assessment I will be focusing on my 10th grade MYP PreCalculus class who are working towards mastery of the Common Core State Standard: HSS-ID.C.7. Interpret the slope (rate of change) and the intercept (constant term) of a linear fit in the context of the data.  

This blog entry, for  the TEACH-NOW Module 5, Unit 2, Activity 2, is focused on an objective that was developed in Unit 1 - By the end of this unit, when given a set of raw data, 10th grade math students will be able to consistently represent the data as a scatter plot that is appropriately labeled and includes an appropriate scale.  (Based on the December 13 virtual class discussion, the objective was slightly modified to fit my school's context since we are an MYP school and do not use percentages).  

As a means to track student progress towards the reaching the standard, I have designed the following four formative assessments that lead to a larger, more comprehensive summative assessment:

Formative Assessment #1

The students will collect measurements of each others arm span and height.  It will be recorded and share in a single Google Spreadsheet.  The students will make a copy of the spreadsheet for their own analysis.  In their own copy of the Google Sheets the students will create a scatter plot. After successfully completing the task in Google Sheets, the students will repeat the task in MS Excel, Apple's Numbers, and their TI-nSpire graphing calculator.  For each program the students will receive verbal feedback from their peers and the teacher as to the appropriateness of the scatter plot.

Formative Assessment 2

Using the same data and scatter plot as in the first formative assessment task, the students will use the features in Google Sheets to properly label each of the axes, include a title on the graph, and a legend.   This will  be repeated in MS Excel, Apple's Numbers, and their TI-nSpire graphing calculator.  For each program the students will receive verbal feedback from their peers and the teacher as to the appropriateness of the labels, titles and legends.

Formative Assessment 3

Using the same data and scatter plot as in the second formative assessment task, the students will features in Google Sheets to create a line of best fit, linear regression equation and r-value (correlation coefficient) for the data.

Formative Assessment 4

Using the r-value from the third formative assessment task, the students will interpret the correlation of the data and how that will impact the appropriateness of the data to make predictions about the relationship between arm span and height.  This task will require no technology, however will be done in groups of three as a discussion.  Students and teachers will offer formative feedback to students in order to ensure that students are making sound, data-based predictions.

Rationale

In breaking down this larger task into smaller task, there is greater opportunity for the teacher to guide the students with formative feedback so that their end product is of high quality.  Since the summative task for this unit is for students to take a large set of raw data and carry our a regression analysis in order to make predictions and subsequent informed decisions on the loaning of money through KIVA, it is important that they are able to display the data appropriately and in a way that is not misleading.  One of the biggest areas of growth for many of the students I encounter in 10th grade is there inability to create appropriate graphs.  In having them do the regression in parts the teacher ensures that they have the right product before carrying out the next task.  In doing so, the overall product will not be impacted by a mistake in the formation stages of the product.

Since the real world uses multiple applications to do this type of work, and since our students have access to all kinds of spreadsheet programs, it is also important that they encounter a variety of applications in the formative stages of the unit.  For the summative, the students will be able to choose the application that they feel most comfortable with.  However, it is noted for the students that the TI-nSpire should be mastered as it is the only tool allowed for tests and IBDP examinations.

Finally, the fourth task is designed as a practice for the summative task, which will ask students to interpret the r-value for the KIVA data and if their predictions are sound or not.

Understanding and Applying Standards (A Reflection)

Activity 1 - Unpacking a Standard

I have had to work with the Common Core State Standards since we adopted them at my school in 2010.  Prior to that all of the schools that I worked at had not adopted any national or international standards.  After working here for the last 6+ years and completing this activity it does shock me that there are schools out there that do not have a set of standards to anchor their curriculum.  I must admit, however, that while I have worked with Common Core State Standards for the last 5 years this is the first time that I have actually taken the time to unpack them.  Unpacking the standards was an invaluable learning experience.  I actually took the time to unpack a standard that I had already worked on a couple of months ago and now find myself wanting to go back and reteach because there is so much more I could have done with it.  From the unpacking the standards activity I learned that it is effective to break the standard down into the how, the what and the why/where.  By doing this is allows me to see the standard in parts and design activities that are scaffolded to meet each part, eventually getting to the bigger picture - the context (or why/where).

Activity 2 - Backwards Mapping

While I have been using this model of unit planning since having attended UbD training in 2009, I have not resisted the trading or attended a refresher since.  Additionally I have never thought of using the concept of backwards planning in my day to day lessons, but in conducting this activity I found myself driven to implement a backwards mapping design to all of my lessons - an ambitious goal I would say.  For me, the value of backwards planning is clear.  If I, as the teacher, know the end goal of the unit (or lesson), then I know what is necessary to complete along the way to achieve that goal.  I can design all of my lessons and activities with a clear purpose.  I can offer formative feedback on the path to the goal that is specific to the big goal for the unit.  By keeping the end goal in mind, I can better deliver a quality unit of instruction and increase the probability of my students reaching the goal for the unit.

Activity 3 - Writing Objectives

It was't until I completed an activity in a previous module that I had ever thought about developing S.M.A.R.T. objectives.  I have heard of, and developed, S.M.A.R.T. goals for the math department when I was the department head, but never S.M.A.R.T. objectives for a class.  What I learned from the previous activity in another module was that actually writing S.M.A.R.T. objectives makes designing teaching & learning activities much easier!  What I learned from the activity for this module was how interdependent S.M.A.R.T. objectives and the standards are and how important it is to first unpack the standard before you develop objectives.  At the risk of sounding corny, a big take away from all three activities for me is that your objectives become smarter if you first unpack your standards and by doing do in corporation with backwards planning, your lessons are smarter and so will be your students.

Standards and Backwards Mapping

Standards & Backwards Mapping

Introduction

When I was first introduced to the idea of backwards mapping it was through a training that my school offered on the UbD model developed by Grant Wiggons and Jay McTighe.  The presenter offered a couple poignant yet effective quotes that have really stuck with me.  The first was, "How can you give directions to a place that you don't know you are going?"  The second was clip from the children's TV show Dora the Explorer.  This clip was in every episode, and was when Dora would ask the children, "Who to we ask when we do know the way to go?"  

Most of us either had kids or had been around kids so we answered, "The Map!"  While this might seem childish and inappropriate for a teacher training, it did drive home the idea that if we truly want our kids to reach the end goal, then we must clearly know what that end goal is.

For this activity I will be focusing on my 10th grade PreCalculus class.  The standard that I will be developing my activities and assessment for comes from the common core state standards.  It is:

HSS-ID.C.7. 

Interpret the slope (rate of change) and the intercept (constant term) 

of a linear fit in the context of the data.

The reason that I chose this particular standard from the common core is because it is, for me, and many of my students the one that seems to have the most impact on how relevant math is for our everyday lives and in many of the jobs.  When I have taught them how to do this, its usefulness in the real world and the jobs that make use of this kind of work, the students are often very captivated.  The fact that it allows for the integration technology takes away some of the "math sting" that many students who dislike math or have been led to believe that they are no good at make feel.

Proficiencies for this Standard 

The proficiencies that I use to indicate what students will be able to do at the end of this unit come from the National Research Council's The Five Strands of Mathematics.  The three I would focus on here are

1. Conceptual Understanding - here the students will make the connection to what they already know (slope and constant/y-intercept) to real world applications and technology.  It done as a bi-variate statistics lesson, which I normally do, then they begin to make connections between algebra and statistics.  Tying in a concept like, say, connections, supports retention and limits errors.  By the end of the unit I would hope that the students are able to see the connection between the study of the data and the decisions that we make through the use of real life examples such as in the movie Money Ball (most of my students enjoy sports and particularly baseball).
2. Adaptive Reasoning - I would expect that after the learning experiences the students capacity to think logically, reflect on their learning, as well as to explain & justify their findings would increase.  
3. Productive Disposition - After having been through lessons and activities that were very much connected to real-life examples I would hope that the students would see mathematics as sensible, useful, and worthwhile, in addition to having developed a belief in diligence and their own efficacy.

Assessments Against the Standard

In order to measure the students achievement against the standard, I would conduct the follow formative assessments.  These three formative tasks would be part of a greater number of task that ultimately lead to a summative task for the entire unit.

1. Given several sets of data with corresponding regression (linear) equations and correlation coefficients, as well as accompanying scatter plots and lines of best fit, the students will: 
• discuss the relationship between the "closeness" of the data on the scatter plot and correlation coefficient
• interpret what the intercept (constant) means in the context of the problem
2. Given a (housing purchase) data set along with a corresponding regression (linear) equation and correlation coefficients, as well as accompanying scatter plot and line of best fit, the students then come to a conclusion as to whether it is wise to buy or sell one's home. Key to this task is for students to think logically, reflect on their learning, explain their findings, and  justify their conclusions.
3. As a reflection at the end of the unit the students would write in their ePortfolios a reflective piece on how the study of this unit has helped them to see mathematics as sensible, useful, and worthwhile.  Additionally, students would need to reflect on their own development as diligent, students who are able to produce the desired outcome.

Learning Experiences to Help Students Meet The Standard

The learning experiences for this standard would be connected to the assessments above.

1. Group work with given data sets: Given several sets of data with corresponding regression (linear) equations and correlation coefficients, as well as accompanying scatter plots and lines of best fit, the students will discuss the relationship between the "closeness" of the data on the scatter plot and correlation coefficient in their groups, coming to a consensus for presentation to the class.  Additionally, they will interpret what the intercept (constant) means in the context of the problem.  Feedback will be given to each group by the teacher and peers using a Google Form.
2. Independent work with housing purchase data: All students would be given data from different parts of the world.  Since I only have 17 students in this class, this would not be too difficult.  Each student would be responsible for coming to a conclusion based on analysis of data set along with a corresponding regression (linear) equation and correlation coefficients, as well as accompanying scatter plot and line of best fit, of whether or not it is reasonable to buy or sell a home in that region.  Their work will be presented to a partner for peer feedback (verbal).
3. Quiet reflection writing activity:  At the end of the unit the students will write a reflection on their ePortfolio addressing how the study of this unit has helped them to see mathematics as sensible, useful, and worthwhile.  Additionally, students will to reflect on their own development as diligent, students who are able to produce the desired outcome.  Only the teacher will see this and schedule one-on-one sessions with selected students to see how the lesson have done a better job meeting the above standard.

References

National Research Council. (2001). Adding it up: Helping children learn mathematics. J Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.