MATHDave

Grading Activity - July 27th
Next term I am certainly going to wrestle with the ideas for and against grading homework. I have had such a low amount of participation and so much cheating suspicion, that I'm wondering about the value of attaching a grade to it. However, I do see the homework as being valuable practice that I want to encourage the students to do. In addition, I would like to get around the danger of students doing the problems wrong over and over, so I'm trying to figure out a way to solve that too.... maybe giving the answers and looking for the process? Maybe more worked examples within the problem sets? Maybe waiting longer before giving homework on a subject: Typical day would be warm up on what was learned two days ago, practice what was learned yesterday, learn a new skill, and homework on what was learned 2 days ago?

I am confident in my ability to grade quizzes and tests. I think I am in a subject (math) that more easily lends itself to objective grading techniques.

Reflection Activity - July 25th
I think that one of the harder scenarios to deal with is the one where the teacher does not have access to the computer lab when they need it. With this in mind, I purposely have relied very little on computer lab use in the past - but I can see the value in it and actually want to be able to have a computer lab portion of the unit I'm planning right now. I suppose that the best way to deal with it is to try and design the unit in a way that the computer lab portion isn't particularly "time dependent". By this I mean that it could fit into more than one place in the unit. One of the easier scenarios is the absent student. Since this is such a common occurrence, every teacher must be prepared for it. I simply would have the absent student read a summary of the section(s) that they missed and would give them time to complete the work equal to the time they missed. I also would make myself available during lunch and before/after school to assist if the student did not have the reading comprehension ability to understand the material on their own. Any extra work time available during class would also be a moment to check in with that student's understanding. But ultimately it is on the student to catch up after an absence - the teacher can only do so much...

Please post a 1 paragraph explanation of valuable 3 insights you've gained from your discussion or discussions with your content advisor.
Meeting with the content advisor has been the most valuable part of this course for me. I have struggled in the past courses trying to apply what we're learning to a secondary mathematics environment, and I was looking forward to getting insights on how best to present "math specific" concepts.
 * I have benefited a lot from being able to discuss math-specific tests with her, and she was able to bring in an interesting variety of tests that teachers at her school give.
 * She also provided some great examples of performance assessments and some ways to structure their implementation and grading.
 * I liked hearing about how math classes operated in a different district and the different expectations that her school was able to have.
 * I also benefited from her insights into different ways to approach the difficult topic of the "order" to teach concepts. There is more than one progression of topics a class can follow, and all methods have advantages and disadvantages.
 * She had good ideas for some "fun" math activities - - I really need to build my toolbox of these!

Session 10: Overview of Unit Plan
Main Topic
 * Analyzing and Graphing Data

Essential Questions
 * How can data be represented with graphs, and what are the advantages and disadvantages of different types of graphs?
 * How are the graphs of one-variable data different than those of two-variable data?
 * How can data be represented using matrices, and how can matrices be manipulated mathematically?
 * How can data sets be described and summarized?
 * How can someone use data sets and graphs to make conclusions and predictions?

Objectives
 * Find the minimum and maximum values and the range of a data set.
 * Calculate the mean, median and mode of a data set and articulate the similarities and differences between them. Use reason to decide when each measure is appropriate.
 * Describe data set using quartiles, interquartile range and five number summaries, and use this information to display data in a box plot, and interpret the meaning, utility, and limitations of box plots.
 * Create pictographs, bar graphs, and dot plots to represents data, and interpret the meaning, utility, and limitations of each of these representations.
 * Create histograms and stem-and-leaf plots, and interpret the meaning, utility, and limitations of each of these representations.
 * Test conjectures with the aid of graphs.
 * Plot two-variable data on the coordinate plane using scatter plots, and describe and interpret data represented on the coordinate plane using appropriate vocabulary.
 * Represent two-variable data with matrices. Multiply a matrix by a number and add or subtract matrices and interpret the meaning of those operations.
 * Use appropriate technology to display and organize data and perform calculations.

Common Core Mathematics Standards Addressed
 * Represent data with plots on the real number line (dot plots, histograms, and box plots).
 * Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
 * Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
 * Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
 * (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
 * (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
 * (+) Add, subtract, and multiply matrices of appropriate dimensions.

Session 8: Overview of my thoughts regarding late work
While I taught last year I started by accepting late work whenever people would turn it in, and had a point penalty that increased as the lateness increased. I then had a "bottoming out" of the point penalty at 50%. I allowed students to make up missed quizzes due to absence anytime without point penalty, and tests were to be made up on the day the student returned from an absence.

I didn't like getting the flood of work at the end of the term while students tried to boost their grade, often using work copied from classmates that DID turn their work in on time. So I changed my policy to stop collecting late work for a unit when we have the unit test, and made the point penalty time-line more severe. This discouraged those students who were blatantly "playing the system" because they tended to only care about their grade just before the marking period was finished - too late to turn in much late work and have much effect.

Session 7: Two new insights from meeting with content advisor
1: The culture of a school has a big effect on the frequency and style of cheating that occurs. In the school I have taught in, it would surprise me for any student to go out of their way to try and cheat on a test. In suburban schools, I'd have to be much more careful about how I administor tests to discourage cheating.

2: I got an interesing variety of mathematics assesments to look at: some cool ideas for ways to structure group work on tests and different alternative assesment activities.

What are the author’s main arguments or points?

 * The author believes that, contrary to popular belief, writing is a useful tool in a mathematics classroom. The process can give a teacher insight into the thinking process of students, insight into the relative success of a lesson, and give students opportunity to clarify their mathematical thought.
 * The author categorized mathematical writing assignments into 4 categories:
 * Keeping journals
 * Solving math problems
 * Explaining mathematical ideas
 * Writing about the learning process

Does he/she support those arguments or points convincingly? Explain.

 * Yes, the author supports the arguments well. She begins by admitting that her attraction to mathematics in the first place was partly due to the //lack// of writing in the content area. She goes on to describe how during the first years of her teaching career she did not assign any writing assignments to her students, but gradually found the value of writing assignments for both her and her students. She sited examples of student writing that gave her valuable insight into misconceptions that may have been missed by simply assigning math problem sets. She also gave examples of interesting class discussion that informed short writing assignments about important mathematical concepts. The task of discussing and writing about the concept helped to cement in the knowledge that was being gained.

How does the information in this reading support what you will do or do in your classroom? Site some specific examples.

 * The publication does give me some good ideas on how to use writing in the mathematics classroom. Separating the task into 4 categories made sense, and the author also gave a long series of "tips" at the end of the article that could help support a new teacher trying these ideas. The author ended the article quoting the NCTM math standards, and highlighted the fact that the standards //require// that students can communicate mathematical ideas effectively. That information certainly supports the notion that writing assignments are valuable tools for the mathematics class.
 * One think that was missing from the article was the role of the teacher as a model of writing. Simply assigning writing does not in itself created better writers. The teacher needs to show what good mathematical writing looks like, and provide feedback on student writing so that students can improve. Maybe a teacher could have assignments where the students have to read 3 or 4 different writing samples on the same topic, and compare and contrast them - discussing what differentiates writing perceived as "good" from writing perceived as "bad".

Outline for Essay:
Looks odd due to abnormalities in cut-and-paste from MicrosoftWord -
 * Introduction
 * o Justification for changes in math instruction: changes in the world on a fundamental and global level.
 * o Introduce the three main topics of the paper
 * § Technology
 * § Cooperative Learning
 * § Equity
 * o Close and bridge
 * Technology
 * o Connect to opening justification
 * o Examples of ways to use (and not use) technology
 * § Technology can be used to //support//new knowledge and save time
 * Like the excel spreadsheet example from article
 * § Technology should not be used to replace knowledge
 * Using calculators to do simple arithmetic
 * o Outcomes of research about technology in math classrooms
 * § Use of spreadsheets and “slider” manipulation help higher level thinking and notions about variable.
 * Also helps make connections between graphs and equations in a MUCH more time-efficient way than traditional by-hand methods.
 * § Use of Computer Algebra Systems in math classrooms had no negative impact on traditional, non-computer based skills, and saved class time for deeper investigation. Also encouraged multiple perspectives on the same problem, and supported symbolic understanding.


 * Cooperative Learning
 * o Connect to opening justification
 * o Examples of what is and is not “real” cooperative learning
 * § Is not
 * Just working in close physical proximity to others
 * Splitting up a large task into smaller parts that each group member is now individually responsible for.
 * § Is
 * 2 to 6 people
 * Mutually dependent
 * Equal opportunity to interact and communicate in various ways
 * Each member is responsible for contributing and is accountable for the work of the whole group.
 * o Outcomes about research on cooperative learning
 * § Facilitates higher level learning
 * § Promotes active involvement in mathematics
 * § Increases mathematical communication
 * § Increases comfort-level with asking for help
 * § Promotes a positive attitude towards the learning experience.


 * Equity
 * o Connection to opening justification
 * o Connection to standards
 * o Description of the definition
 * o Examples of characteristics of equitable classrooms
 * § Classroom environment
 * High expectations for ALL students
 * o Both internal (students beliefs) and external (teachers beliefs)
 * Supportive and helpful
 * Comfortable (especially comfortable to make mistakes)
 * § Equal opportunity
 * For students to have quality instructors
 * For access to particular course offerings
 * § Relevant Curriculum
 * Engaging
 * Appropriate
 * Connected to the world of the student
 * o Outcomes of research
 * § Students do better in classes in which they feel safe
 * § Students are more interested in material that is relevant, and thus learn more in classes that present that material
 * § High expectations increase student achievement
 * § Poverty and outside-of-school environments can be overcome with quality, equitable classroom experiences.


 * Conclusion
 * o Restate thesis
 * o Discuss barriers to implementation of the ideas
 * Discuss implications if barriers are not overcome


 * Represent data with plots on the real number line (dot plots, histograms, and box plots).
 * Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
 * Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).