# Tag Archives: course structure

## Year 12, Day 0

This week teachers headed into school to prepare for next week and students’ return. This will be my twelfth year!

My teaching this year will include more computer science than ever before:

• AP Computer Science Principles (full year)
• AP Computer Science A (full year)
• Foundations of Computer Science  (spring)
• Computer Integrated Manufacturing (fall)
• Precalculus independent study (fall, three students, three separate periods)

I’ll also be working with our new engineering teacher and our librarian+new-computer-science-teacher to help them with their lessons, and collaborating with two geometry teachers around standards-based-grading.

Extracurricular activities and competitions:

• Coding Club (app development, cybersecurity, & more)
• Women’s Transportation Seminar’s “Transportation You!” Mentoring Program
• TRAC bridge builder competition
• CyberPatriot competition
• STEM Competition
• possible (in my mind, I want to do each of these this year): Cyber Movie Mondays, Saturday AP & PLTW study groups, Girls Who Code club
• probably several others…

Ongoing projects that will occupy some of my time this year include:

• Comp Hydro (teaching hydrology and flooding through computational simulations & modeling, in partnership with the Baltimore Ecosystem Study)
• MyDesign (engineering design process app and learning management system, in partnership with NSF & the University of Maryland)
• Internet of Things project to measure air quality and other environmental factors in schools (in partnership with Cool Green Schools, Johns Hopkins University, and Morgan State University)
• Continuing work toward my Master’s Degree in Computer Science (taking “Artificial Intelligence ” course this semester)
• Baltimore City Engineering Alliance, a nonprofit 501(c)(3) we created to provide opportunities to Baltimore City students to further their engineering education, and for which I am treasurer

School starts for students on Tuesday, after Labor Day for the first time in my twelve years here teaching in Baltimore. Wish us luck!

Filed under computer science, engineering, math, teaching

## Tracking or Not?

[Note: this started as a comment on BmoreSchools’ “Tracking by ability…gifted? average? mediocre?“, but grew so long that I thought I should make a whole blog post out of it.]

### Classroom Intellectual and Knowledge Diversity

At my school, classes are not tracked, for the most part. There is an occasional honors class, and AP courses have some prerequisites, but I’d estimate that 95% of the classes are untracked.

I personally have never taught a tracked class. Though there is a bit of self-selection for those students who choose engineering as their career pathway, I still have students in engineering classes who hate math with a passion, and others who don’t like building things or hands-on activities. Students whose math and reading skills are on a 3rd grade level. And there is not self-selection for most math classes I have taught.

This means every class is likely to have students with learning disabilities and an individualized education plan (IEP), students without an IEP who are slow to learn new things, students who are very quick to learn new things, students for whom English is not their primary language, students with behavior problems, students who come with full memory of background knowledge taught in prior classes, students who don’t remember what we did in class yesterday much less what they ‘learned’ a year ago, students who don’t show up and therefore don’t have a clue what we did in class yesterday or last week. And everything in between.

Teachers are encouraged and expected to “differentiate instruction”, that is, meet the students where they are at and bring them to the next level. This is accomplished by providing supports and scaffolds for struggling students to climb up and reach mastery (or at least a few steps closer to mastery). While also challenging the most advanced students with higher-level thinking tasks related to the same topic.

### My Experiences

I’ve been mostly pretty happy accommodating learners at different levels in my engineering classes. While on some days, I may lose some students when we delve into the deeper math behind an engineering concept, there is enough hands-on activity accessible to students at all different entry points to keep everyone engaged and learning for the majority of the time. (That’s not to say I don’t wish they all had better math skills coming in.)

For example, the robotic arm activity we’re doing now is tiered in such a way that builds up students’ knowledge, from basic controlling of the arm, to recording and teaching positions, to basic programming, to figuring out coordinates and roll angles, to more complicated motions with the arm, to programming with variables and subroutines, to communicating with another machine. Not every student I teach will make it to the most advanced level of skill in programming the arm–some don’t fully understand variables in algebra, so attempting to build on that prior knowledge with variables in programming may not work. However, every student will work her/his way up the ladder of activities, each one building on the last and extending the knowledge a bit further. And, with the help of some of my advanced students who act as peer tutors, I can make sure every student in my class has experience working with complicated programming techniques like variables and subroutines. And I can push the quicker students to try out other programming techniques, to improve their program’s efficiency and clarity, to apply and adapt their programs to more settings, and/or to help teach other students the programming techniques (which can really cement the concept in the tutor’s mind as well as helping the tutee).

Math class is somewhat harder to differentiate. If a student misses a few days, they come in and may be lost because of how much each activity builds on the previous one. And, as SmallestTwine writes, many students don’t have the confidence to work and explore on their own, so providing the sequence of tiered activities like I do for the robot arm is not possible for most students in math, the way it is easier to do in engineering.

Similarly, it’s tough to be teaching how to solve quadratic, exponential, logarithmic, and trigonometric equations in Algebra II to students who don’t have familiarity and comfort with solving linear equations. Of course I review solving linear equations as a whole class, and then individually with some students as needed. But tracking students would make it easier for me to continually push and challenge those who are comfortable with a previous topic, or extensively remediate those who are lacking prior concepts or skills.

### Thoughts

My worry with tracking is that it can exacerbate inequalities. Students held to lower expectations (like those tracked into the lowest and most remedial math class) will not learn as much as they could if held to higher expectations. A famous study showed that teachers told to expect higher performance from random students actually led those students to outperform their peers.

So I would tend to avoid tracking whenever possible. But on the other extreme, when prior knowledge in a classroom has such a broad range as to make effective instruction nigh-impossible (e.g. 2nd-12th grade reading levels in the same room might be pushing it for an English class), or when students are in a class for which they have not mastered any of the prerequisite skills and knowledge, no one is being well-served. Tracking may be necessary in these types of situations.

__________________________________

Thanks again to my support group of local education bloggers in this month of daily blogging:

Filed under teaching

## SBG Update

OK. I haven’t talked much about Standards-Based Grading (SBG) since last September. I’ve changed some things about how I implement SBG, which I shall describe here, along with how things went.

### Geometry, Fall 2010

Here’s how I set up my Geometry class procedures–SBG-related, anyway–for my fall semester class. We had thirty-two skills, which were mostly assessed in class three times each. I converted students’ SBG grades into a percentage for reporting out by first averaging them and then using a cubic relationship (the third one from this post) to match that average to a traditional percent scale.

The students pretty much did not initiate any re-assessment. Less than five skills were retaken outside of class time. I think for the most part they were confident that, between the next two in-class retakes, they would improve just by being in class and doing the daily assignments and warm-up reviews. But even if they didn’t improve (or even regressed), the students did not seek out help nor did they come in to re-assess. They were content just to let the 1 or 2 be averaged in. And mostly their scores were high, in the 80s [those who attended class anyway].

### Algebra 2 with Trigonometry, Spring 2011

For several reasons, including combating this apathy about un-mastered skills, for my spring Algebra 2 with Trigonometry (A2T) class I made a major change in how I converted SBG skills grades into percentages. Instead of averaging grades and then scaling, I set cut-offs of how many skills need to be mastered to earn a particular grade. Rubric here. This was also in part prompted by criticism of averages as being antithetical to the nature of SBG by the Science Goddess and @mthman.

Other than this big change in grading, I mostly kept the same procedures from fall to spring. There were more skills (blog posted here in draft form, final form here), so we only visited each skill twice in class via our weekly quizzes.

Many more students re-assessed this semester. But many waited until it was too late to seriously improve their grade. For this reason, and because we only assessed each skill in class twice instead of three times, grades were generally lower this semester than in my fall geometry class.

And there were still a few students who seemed lackadaisical about their lack of skills mastery and never came in to re-assess even though they were failing or scraping by with a D-. Perhaps I didn’t motivate them well enough by extolling the glories of SBG and how it revolutionizes grading? Can anyone refer me to a motivational-type speech you use with your students about how SBG helps them?

Another new piece is that I had set some prerequisite skills (mostly from Algebra 1 but a few from Geometry) that in my mind are so fundamental and which the main skills of A2T build upon. To promote my students’ review of these prerequisites so that I could help them build new skills upon that foundation, I required that students master these prerequisites before they would score any points for core skills (again see the rubric I used). But many students did not really take the prerequisites seriously. By which I mean, they did not review work from Algebra 1, and make sure all prerequisites were mastered within the first week. Some waited until the middle of the quarter to remediate the prerequisites, others until the last week of the quarter–finally being motivated to fix them then so they didn’t fail.

Is it fair for me to set this separate category of skills without which they cannot earn any points? I thought so, since they should not be in an Algebra 2 class without being able to understand key Algebra 1 material. If it is fair, how can I make the students understand the value of the prerequisites in supporting further learning and make sure to really review and master them the first week? Could I refuse to let them sit for other quizzes (on core A2T skills) until their prerequisites are mastered? Or should I get rid of the distinction between core and prerequisite skills entirely?

I welcome your thoughts and criticisms.

1 Comment

Filed under math, teaching

## Trigonometry with Algebra 2

Since this May may be my last month teaching math (for a while? forever? I doubt my departure from math will be permanent … more on the story behind this later), I thought I’d get into the swing of things and connect back into the theme of my blog by declaring that May is Maryland’s Math Madness Month! [To give due credit: this motto was originally thought up by my father as a way I could get kids excited about taking the Algebra HSAs, coming up now in less than two weeks.]

To kick off the month of math madness, I wish to ask other teachers of Algebra 2 with Trigonometry (A2T): how do you balance covering all of a (full-year or full-semester) Algebra 2 course in a reduced time-frame so that there is room in your course also for Trig?

A2T Collage

I suppose there are two main options for dealing with this addition of new material into an already full course: leaving out pieces of content, or teaching all the content at a faster pace.

This is something I think about every year I guess, but even moreso recently when helping students with their Algebra 2 Twilight make-up coursework and having discussions with the Precalculus teacher about what he will expect my students to bring with them to that class.

The Twilight students had question after question to answer about completing the square, which is a method I don’t cover when teaching A2T. For me, solving quadratics by factoring, “doing the opposite”, and using the quadratic formula is exhausting enough, both in the sense that it exhausts the techniques required to solve quadratics of every form, and in that my students are tired of so many methods without adding a fourth. My students have been know to complain that they are learning something new every day in my class (!).  Am I wrong for leaving out this method? Should I perhaps teach completing the square instead of the quadratic formula since it shows deeper understanding of the math involved? I don’t have enough time to do both (plus the other two methods I mentioned, which are even more fundamental).

Similarly, I treat complex numbers very lightly (last year, with the 9++ snow days, I even skipped them!). And I hear on the web about some Algebra 2 teachers teaching rational functions, which I never even conceived of as an Algebra 2 topic, since gaining an abiding understanding of polynomials is challenge enough.

So I guess that lands me primarily on the side of leaving out content. A faster-paced curriculum would leave more students lost, and I do not have selection criteria for entering the class as some teachers might. Additionally, this relates to my philosophy of math teaching, that it’s better to learn fewer things deeply than to shallowly cover everything. I try to focus my attention on the things that connect A2T to prior math and future math (e.g. “doing the opposite” as equation-solving technique and function transformations), that connect it to other subjects, that engage students with project-based learning, and that highlight big picture concepts and skills.

But it’s still a struggle, and I doubt myself (maybe I really should be teaching completing the square; maybe conic sections are more important than my Olympics research project and should replace it in my choice of topics). Especially since that Precalc teacher is counting on me to teach them certain things they will need when they arrive in that class (and just as the Calculus professor is counting on Precalc teachers to cover certain key topics).

So, A2T teachers, how do you deal with the pressure? Do you teach at hyperspeed, or what topics do you cut? [Other teachers feel free to weigh in too 🙂 ]

Filed under math, teaching

## Principles of Engineering Skills

So I’m thinking of giving a skills list a try in my Principles of Engineering (POE) course this semester too. It wouldn’t be full-on standards-based grading (SBG), since in such a project-driven class I need projects and reports to be the major component to student grades, but I think I can adapt a skills list for quizzes (and occasional outside-of-quiz skills demonstration). I’m tentatively planning 50% projects, 25% skills quizzes, and 25% portfolio–including engineer’s notebook.

Below find my first draft for a skills-based outline of how I intend to teach POE this semester. I will be teaching a mix of ninth and twelfth graders, with backgrounds ranging from Algebra I to Precalculus. This will be tough, as POE is the most math-intensive of the PLTW engineering courses. I must try to teach advanced math applications while not boring my students out of their minds, while at the same time exposing students to the great concepts and societal role of engineering and its subfields.

To all the former, current, and future engineers out there, I welcome your input on the skills listed below. Likewise to engineering high school teachers across the country (for your reference, I’ve mixed up the unit order due to equipment lacks: my order goes Unit 2,4,3,1). Or anyone else with an opinion on engineering education.

While I am constrained somewhat by PLTW’s POE curriculum, I do have some choice in what I emphasize and in which skills I test. Are these skills phrased well? Are they representative of what engineering is all about? Are the major subfields of engineering represented (this is a survey course)? Are there any that are too vague (or too narrow) or seem like they don’t belong?

I’m still welcoming feedback to my Algebra 2 with Trigonometry skills list here for about one more day, so my more mathematically-minded readers may like to head over there to ponder and critique.

### POE Skills List

General STEM Skills

1. Solve equations for a single variable
2. Substitute numbers for variables in algebraic formulae
3. Measure lengths and angles to appropriate precision (given the context of the application and the accuracy of the tool)
4. Use trigonometry to solve for missing sides or angles
5. Apply the Pythagorean Theorem to find unknown sides in right triangles
6. Use trigonometry to find unknown sides & angles in right triangles
7. Use the digital dropbox on TS3/Blackboard to submit work
8. Identify problems to be solved in an engineering context
9. List multiple possible solutions to engineering problems
10. Evaluate each possible solution based on specifications & test results
11. Show knowledge of, and skillful application of, the engineering design process
12. Show knowledge of various careers in engineering and other STEM fields

Unit 2 – Materials & Structures

1. Identify five types of bridges by name, definition, and/or picture
2. Split a force vector into its x- and y-components
3. Calculate the centroid of various shapes
4. Calculate forces and moments acting on various objects
5. Pick appropriate formulae relating to stress, strain, and material testing
6. Analyze stress-strain graphs to determine material properties
7. Calculate bridge efficiency
8. Analyze a bridge for structural and material strengths and weaknesses

Unit 4 – Statistics & Kinematics

1. Collect and analyze data using statistical measures of center and variance
2. Calculate speed and velocity
3. Calculate the effect of gravity on velocity and position
4. Analyze horizontal and vertical components of projectile motion

Unit 3 – Control Systems

1. Create flow charts to represent a process
2. Identify inputs and outputs in a control system
3. Identify elements of a flow chart or RoboPro program and their key attributes
4. Utilize branches in a flow chart or RoboPro program
5. Utilize variables in a flow chart or RoboPro program
6. Interpret a flow chart or RoboPro program
7. Identify open and closed loop systems
8. Demonstrate an understanding of pneumatic and hydraulic power

Unit 1 – Energy & Power

1. Calculate ideal mechanical advantage for each simple machine
2. Calculate actual mechanical advantage and efficiency for each simple machine
3. Calculate gear ratio
4. Demonstrate an understanding of electricity and electrical circuits (series/parallel)
5. Use Ohm’s Law and Kirchhoff’s Laws to calculate resistance, current, and voltage
6. Calculate work, energy, power, and power efficiency
7. Demonstrate an understanding of the laws of thermodynamics and thermal energy transfer
8. Demonstrate knowledge of alternative and renewable energy sources

A total of 40 skills. What do you think?

Filed under engineering, teaching

## Algebra 2 / Trig Skills

Hi! I’m looking for some feedback on what skills I should use in my standards-based grading Algebra 2 with Trigonometry (A2T) course spring semester. I just threw together the following list as a rough draft, and do expect to edit it extensively over the coming week.

A note on organization: I’m planning to focus on algebra third quarter and analysis fourth quarter (did I miscategorize any skills?). Fourth quarter tends to be the shortest quarter, mainly due to our state standardized tests, so it has fewer skills. The first six skills each quarter are meant to be prerequisite skills from Algebra I, Geometry, or even middle-school math; I will hold students accountable for knowing and remembering these skills, but aside from a miniature review I do not intend to teach skills #1-6. I’ve italicized skills that seem weak or a little too easy, and may be combined with others or even eliminated. I’ve bolded skills that seem more advanced or non-essential and possibly not for every student. I’m toying with the idea of requiring students demonstrate mastery of certain numbers of core skills and advanced skills to earn different letter grades.

ALGEBRA (especially of the second degree)!

1. Graph a line given its equation
2. Determine the equation of a line from its graph
3. Solve a linear equation in any form
4. Solve a system of two linear equations
5. Manipulate algebraic expressions to simplify or expand
6. Substitute numbers for variables in an algebraic expression
7. Convert between scientific and standard notations of numbers
8. Apply the rules of exponents to simplify an expression
9. Find the degree and leading coefficient of a polynomial
10. Determine the end behavior of a function
11. Combine like terms to add or subtract polynomials
12. Use the distributive property to multiply polynomials
13. Use long division to divide polynomials
14. Factor a monic quadratic expression
16. Characterize the shape of a parabola given its equation
17. Graph a parabola given its equation
18. Determine the equation of a parabola given its graph
19. Solve quadratic equations in factored form using the zero product property
20. Solve quadratic equations in vertex form by isolating the variable
22. Solve quadratic equations in standard form by completing the square
23. Combine like terms to get an equation in standard form
24. Apply quadratic equations to physics or other real-world scenarios
25. Plot a complex number in the complex plane
26. Add and subtract complex numbers
27. Multiply complex numbers
28. Determine the magnitude of a complex number
29. Solve quadratic equations with complex roots
30. Add and subtract matrices, and multiply a matrix by a scalar
31. Multiply matrices
32. Find matrix determinants
33. Find the inverse of a matrix
34. Solve matrix equations
35. Solve systems of linear equations
36. Graph linear inequalities
37. Solve systems of linear inequalities by linear programming
38. Plot the graph of various conic sections based on its equation
39. Identify key characteristics of each conic section
40. Explain the relationship among the conic sections

ANALYSIS (including TRIGONOMETRY)!

1. Determine a function’s domain, range, maxima, and minima
2. Determine a function’s zeros and y-intercepts
3. Determine the end behavior of a function
4. Convert between tables of values, equations, and graphs of functions
5. Apply the Pythagorean Theorem to find unknown sides in right triangles
6. Use trigonometry to find unknown sides & angles in right triangles
7. Use laws of sines and cosines to find unknown sides & angles in any triangle
8. Solve entire triangles given three pieces of information
9. Apply triangular trigonometry to real-world scenarios
10. Draw and measure angles in standard position
11. Convert between degrees and radians
12. Find coordinates and slope where an angle meets the unit circle
13. Solve trigonometric equations (including multiple solutions)
14. Use common trigonometric identities
15. Sketch the graph of trigonometric functions
16. Find period and amplitude of periodic functions
17. Plot points using polar coordinates
18. Convert between polar and Cartesian coordinates
19. Plot various polar functions
20. Evaluate exponential expressions
21. Apply the rules of exponents to simplify an expression
22. Identify characteristics of exponential functions
23. Use exponential functions to model real-world scenarios
24. Convert between exponential and logarithmic equations
25. Evaluate logarithmic expressions
26. Apply the rules of logarithms to simplify an expression
27. Solve exponential and logarithmic equations
28. Use logistic growth to model real-world scenarios
29. Identify the effects of common function transformations
30. Graph functions and their inverses
31. Use inverse operations to solve equations
32. Compose functions
33. Discuss the effect of transforming, inverting, and composing functions on domain and range

I’m looking for feedback of any kind now, all the way from how to rephrase a skill better and more specifically, to what quintessential A2T skills are missing that I need to add right away. Also, are there some skills here that I can get rid of entirely? Even with the idea of prerequisite/core/advanced skills, 73 seems like way too many (I had only 32 skills this fall for geometry).

[PS I promise a post up soon reflecting back on what worked and what didn’t from semester 1’s courses, and looking ahead to my plans for the new semester’s courses, including how those plans reflect on SBG and PBL.]

Filed under math, teaching

## Funding Woes

Actually, maybe “funding annoyances” might be a better title.

Annoyance #1: Project Lead the Way (PLTW)

They’ve revamped three of its courses’ curricula in the past two years, and with the new curriculum for each course they are requiring thousands of dollars of extra spending on new equipment. I can see some of the reason behind the new curricula: to make sure their engineering pathway and course content is motivating and engaging to students, while also meeting higher education and engineering industry standards. But stagger the courses out please!! We can’t afford all this new equipment at the same time, even if we weren’t in the middle of a recession!

At recent meetings with teachers from other schools across the city, state, and region, various people have expressed their frustration that PLTW had them buy a robotic arm for an estimated $15,000, that now — less than two years after purchasing it — is no longer part of the curriculum while PLTW is requiring purchase of several thousand dollars’ worth of Lynx Robots instead. Or similar stories for the other PLTW courses and equipment. Additionally, many teachers have mentioned that they don’t yet have the required equipment for a course that began in August, due to a combination of a lack of funds, illogical bureaucratic ordering schedules (see next topic), and several-month-delays in shipping. All in all, though I’ve been a fan of PLTW’s exciting and relevant program since I’ve begun teaching engineering, this was not well thought-out. Annoyance #2: The Perkins funding schedule Who on Earth designed a system wherein you apply for funds (from the federal Perkins grant, which sponsors a variety of career and technical education programs) in April, don’t hear back how much got approved until October, thereby not ordering equipment and supplies until November that actually arrive in December, for a course that began back in August?!?! What’s even worse is when you have a prescribed (though not scripted – ew) curriculum, like we do for PLTW, where we are expected to be using certain equipment and supplies on Day 1 (in August) and specific other equipment on Day 40 (in October), equipment which has not yet even been approved for ordering! What’s even more worse is if you’re teaching a semester course instead of year-long, so your course ends in January, meaning the equipment arrives and you have three weeks left to use it! The short answer, I believe is that Congress (who wrote the Perkins law) is who designed that ludicrous schedule. [I see a lot of heads nodding in understanding now.] But it appears they wrote this education law/grant without talking to a single educator, all of whom could have told Congress that the school year is not the same as the calendar year. That getting supplies in December (80% through a semester-long course, or 40% through the school year) is not a good or sensible time frame. Now, to those who say, then plan ahead and use this year’s Perkins funds to pay for next year’s equipment, I say: Excellent idea! If only we can catch up from using this year’s funds to pay off what was urgently needed last year or at the START of this year and still have some money left over, that would work well. But a few factors get in the way: bureaucratic reality (most schools start behind, and so will never catch up), the need to plan super-far in advance (really ordering things you’ll need a year and a half from now), and PLTW changing the things you need to order (see point #1). The best solution to me would be to (approximately) reverse the timeline. Have teachers and schools submit what they will need for the next year in October, hear back in April, and put in orders in May, for equipment which will then arrive over the summer, be set up, and be ready to go the first day of school! A revolutionary concept, that! This is not perfect: the equipment needs will not be as clear in October as in spring, but hopefully the big equipment needs are somewhat clear, since the teacher is teaching the course (as opposed to April, when that teacher may not have been there if it’s her first year). And the impatient among you might say getting equipment in December is better than not getting it until the school year is out, but at least this plan makes it 100% clear that you are buying for the year ahead, instead of the gray area under the current plan where people think the Perkins money is for this year but don’t get it until halfway through, and then you’re trapped in a bad cycle. Anyway, we teachers have brought up this scheduling issue time and again when meeting with our district office, and while they are not the ones in charge of the schedule (the federal government is), it is a continued point of conflict (though not heated, everyone keeps their cool): how can our district be expecting us to raise test scores (not to mention tie our pay to test scores) when the test will be on equipment, and procedures for using and understanding that equipment, that we do not even have when we are teaching the course? Dealing with my anger issues So, to make a long story short (too late!), we just found out a few weeks ago that we only received 16% of what we requested through the Perkins grant. And what we requested was not frivolous or padding, but required equipment to add a PLTW course and upgrade our existing course curricula. No justification was communicated to me as a teacher for why this was so low, or what specific parts were rejected while delineating the 16% that were approved. Combined with our overall fiscal situation in rough times, this means we have a budget crisis. Even though PLTW may not like to hear me say this, it also means that I won’t be able to keep up with all the new curriculum, and shall try to teach my students with some muddled combination of ideas and concepts from the new curriculum, taught with equipment from the old curriculum plus whatever I can scrounge from our science department, the dollar store, and the local sidewalk. On a positive note, we have also been looking more deeply this year into grants we can apply for. One we are working on right now is the NACME STEM Innovation grant (my math teacher readers, your ears may want to perk up here!), up to$1000 which can be applied toward any STEM-related project at an inner-city school.

Do you know of any other grants to look into?

Filed under engineering, teaching

## Why SBG?

Though others have written far more convincingly and elegantly about why they use Standards-Based Grading (see dy/dan’s “How Math Must Assess”, Think Thank Thunk’s SBG ManifestoFAQ, and Parts I & II on this post from Take It to the Limit, among many others), I figured I should at least have some explanation for my halfway jump into it this year.

A discussion over in the comments at Sam’s blog got me thinking, and this post was inspired by writing a response there.

Standards-Based Grading means two things to me:

While meeting a constant flow of deadlines is a key life skill, even more important in my view are the following: independent self-directed learning, setting your own goals on your way to a deadline, and keeping trying until you have reached a goal. A math professor I studied with in college would always say that failure is the only way we truly learn anything. Making a mistake (using what we know and failing) opens our eyes and prompts us to learn a new way that will succeed. And this skill: the skill of persistence in the face of failure, and learning from your mistakes, is perhaps the most important skill I wish to teach my students. Even though it’s not on my SBG skills list 🙂, the very nature of SBG and re-assessment seem to promote this continual striving to get better instead of being satisfied with mediocrity.

____________________________________________

I believe this will be my last SBG-details post for a while. I’m hoping to get back to posting more about the content of what I’m teaching in Geometry and Computer Integrated Manufacturing, describing some of the projects we’re doing, and reflecting on how things go. But, for those of you who have liked my last few posts, I do plan on continuing to update my folder over on Scribd with weekly skills quizzes and other relevant documents from my foray into using SBG in Geometry.

Filed under math, teaching

## My SBG Geometry Plans

After some dialogue with gasstationwithoutpumps and some additional thought on my part, I made a few changes to the skills list I talked about last post. Thanks for the ideas and discussion, g! My new, updated Geometry Skills List and personal course guide is posted here. I am mostly happy with it, including the fact that its number of skills is a power of 2! However, I am aware that #12 & #23 are both fuzzy, and I have yet to decide exactly how I will assess them. I’d still be happy of additional input for next year into the makeup of the list, even though the list is mostly set for this year. Or also thoughts on how to (more concretely) assess those two fuzzy skills.

### A few more details on my SBG (Standards-Based Grading) plan for the semester:

• I decided to steal Sam’s rubric and test it out, see how it goes. I admire it, as well as his thoughts on SBG at various times including his most recent detailed account of his new system.
• I’ve borrowed a lot of Dan’s style in the following documents which I hereby share: a blank skills list handout for students to track their own progress, a more-visually-appealing version of the previously-discussed skills list, and the very first quiz I gave last Thursday assessing my skills #1, 2, 3, 4, 5 and 6. Dan has a bunch of good philosophy and practical tips at that same page of his I linked: his “Comprehensive Math Assessment Resource”.
• Although I didn’t steal handouts from other people, many many other math/science teacher bloggers and tweeps have helped me shape my ideas [and I’m sure will continue to do so as the semester progresses], so a big THANK YOU to y’all as well!
• I plan to teach and assess 2-3 new skills each week, and assess/re-assess each skill 3-2 times, with the latest grade overwriting earlier ones in the gradebook (and of course the option to reassess more times in after-school or lunchtime coach class). Skills will have a quarter-based deadline to reassess by, since that is a date set by the district. I’m attracted to the idea of two perfect scores allowing you to skip the skill question when it rolls around for a third or more time (perfect scores of level 4, not just mastery at level 3); I may try this too.
• To convert a student’s grade on skills into a percentage, I’m planning to go with my third conversion formula discussed in this post, though I do wish to revisit the issue when I plan for An SBG version of Algebra 2 with Trigonometry at the start of the spring semester. I shall give cumulative midterm and final exams, which are factored into the grade separately from the quarter grade of 50% skills quizzes and 50% projects.

Filed under math, teaching

A twitter colleague, @druinok, posed the following challenge, which prompted me a great deal of thought:

﻿

How do you convert from standard-based grades (often on a 1-4 or 1-5 system) into a percent score required by a gradebook or school district, while still maintaining a sense of what the 1/2/3/4(/5) system means?

While the formulas involved may be too complicated for a gradebook, I approached this problem mathematically: can I create a map from the SBG 1-4 system to the grades I believe they should represent? My understanding of the SBG system is as follows, which informed my selected points and function choice:

• 4 = exceeds standard; demonstrates complete mastery and conceptual understanding with no nontrivial errors
• 3 = meets standard; demonstrates mastery of a skill/topic, perhaps with minor errors
• 2 = approaching standard; shows some understanding, with major (or many minor) errors
• 1 = below standard; shows little or no understanding
• 0 = did not attempt

In my conversation with @druinok, she stated (and I concur) that a student with all 3s has met all standards and should receive a B+/A-. All 4s should clearly represent 100%. In my opinion, all 2s should be enough to scrape by with barely passing the class (60% or D); some may argue that since that student has not shown mastery of the standards he or she should receive a failing grade.  A student with a 2.5 average (half twos and half threes, e.g.) should receive a C. A student with 1s should not pass. In my district, the lowest grade we can assign on a report card is a 50, so a 1 average yields this.

In playing around with the numbers, they seemed to fit naturally into a symmetric pattern around 2.5 = 75%. This in turn prompted me to find differences and look for a cubic equation with inflection point around (2.5, 75).

• 1 average = 50%
• 2 average = 60%
• 2.5 average = 75%
• 3 average = 90%
• 4 average = 100%

My first attempt is odd since it reverses the independent and dependent variables (x/y). My second attempt is more understandable and develops the equation $-\frac{20}{3} x^3 + 50 x^2 - \frac{280}{3} x +100$. Its graph is shown below.

I also tried a third attempt with different points (3=85% & 2=65%) since I was slightly unhappy that the above function from my second attempt was not monotonically increasing on the interval [1,4]. Still, my second attempt is closer to my understanding of the 4-point scale.

For what it’s worth, I also tried fitting a 5-point scale to percentages.

Anyway, that was a bit of fun. But the formulas aren’t perfect, and are certainly a bit complex for gradebooks (the original challenge).

So my main point in writing this post was to ask: those of you who are standards-based grading aficionados, how do you handle the conversion to a percent or letter score?

Certainly any solution, whether it be a formula like this or a more holistic approach like “a student must meet all standards with a 3 or higher to achieve a grade of A, etc”, must involve clear and open communication about the grading policy with students & families.