By now, you probably know that I am teaching all new courses this year. Over the last five years I taught only fifth grade, but this year I will be teaching three sections of sixth grade and one section of pre-algebra which is all seventh graders.
After using standards-based grading (SBG) with my fifth graders last year, I knew that it was going to take a lot of work to develop standards for two separate courses. Well, it is done! Ch..check!
A1 Number System Decompose numbers into expanded form according to place value. Decompose 3,213 into expanded form.
A2 Number System Recognize that in a multi-digit number, any digit represents 10 times as much as the same digit in the place to its right and 1/10 of what it the same digit represents in the place to its left. In the number 23,488, how many times as large is the value of the first 8 as the value of the second 8?
A3 Terminology Use appropriate language to describe parts of multiplication and division equations. What are the terms for the different parts of a division problem?
As you look these over, keep in mind that I teach at an independent school that does not follow the common core state standards. So, if topics seem out of place or absent, that may be the cause. If you notice a glaring absence, though, I would still like to hear it. I can always add topics in if they are appropriate.
Sixth Grade StandardsJust get in touch with me if you would like a copy of these in a more accessible format. Say, a spreadsheet.
The first thing to notice is that there are only 22 standards. Already this simplifies the process for students and parents. The downside, though, is that there are some standards that hold some pretty deep and rich ideas.
For example, "D4 - Convert between fractions, decimals, and percents" covers a lot of material. Some of this is review from their fifth grade year, and last year I had this set of content broken into at least five separate standards. I will have to be keep an eye on standards like this one to be sure that they are specific enough. If not, I can always rework them during the year after talking it over with students.
The second thing to notice is that I provided a very general overview of the standards (column 2) separate from a detailed description of what is covered (column 3). My hope is that students will have an easier time understanding what the standards cover by referencing column 2.
The CMP3 curriculum made writing these standards incredibly simple.Just on the incredibly unlikely chance that someone who helped author the CMP3 texts reads this, I want to say "Thank you!" The CMP3 teacher's guides are incredibly helpful. The simple but detailed analysis of the mathematics covered in each module is amazing. When teaching a new unit, I have two go-to references for the content: the CMP3 teacher's guide and Math Matters. I know some studies have shown that TG's aren't always used, but I DEFINITELY use these, even when I am not using the curriculum. The front of the Teacher's Guide has a list of the ideas covered in the text as well as the common core standards that are covered. I just combed through those and combined related topics into individual standards. It helps that I have taught a lot of this before (albeit when I was a young noob teacher).
Pre-Algebra StandardsJust get in touch with me if you would like a copy of these in a more accessible format. Say, a spreadsheet.
Creating the pre-algebra standards for the seventh grade course was a much more involved process. The text for the course is Larson Pre-Algebra seen to the right.Not the Florida version shown here. We use the regular version which has a female soccer player on the cover.
As I have noted before, this text is about as traditional as they come. Each section introduces a super-specific skill, teaches an algorithm in one or two examples, then has students practice applying that algorithm multiple times. There is no big list of ideas or content to cover in the front of the text -- this may be because I only had access to the student edition -- so I had to pull the big content ideas from the text.
I started by making a list of each section in the book and what algorithm or content each section addressed. From there, I started combining related sections into groups. Related ideas were sometimes multiple chapters apart. For example, "solving one-step equations by multiplying both sides" was section 2.6. But, if the value you needed to multiply by was a fraction or decimal, you had to wait until chapter 5. It seems insane to me to separate those ideas at all, since they are not really different conceptually. So I combined them into a single standard.
After getting a rough list of standards from the text, I reorganized them and added detail about what meeting them would look like. In the end, I ended up with what I think is a pretty good list. Having never taught this course, though, I am sure that there will be some changes as the year progresses.The last four standards are topics that the course does not need to cover, but that ARE in the text. I added them there for reference, but I will likely not get to them.
Since I will not be following the (illogical) progression of the text, I have officially decided that my pre-algebra course will not be organized into units.
At first I was pretty nervous about the idea of having no larger organized unit structure. When will I have tests? How will I pace myself? But then I remembered that I have been trying (for years) to have fewer and fewer big tests. A unit-less structure will support that as there won't be any predetermined time for a unit test.
Going unit-less is also more respectful of the nature of mathematics. If mathematics is a web of ideas that are connected in amazing ways, adding arbitrary units will only disguise this nature. Solving 1-step and 2-step equations should not be separated into different chapters or units. The ideas in pre-algebra build on each other, and I want my practice to reflect that.
Creating lists of standards is exhausting. But, I cannot think of a better way to prepare to teach a new course. When I first got the news that I was teaching pre-algebra in July, I was pretty overwhelmed. I am comfortable with algebraic content, but I was not even sure what content was covered.
Taking the time to outline what ideas I want my students to master forced me to engage deeply with the course content. It helped me to see connections between ideas as I grouped algorithms, skills, and concepts into standards. And, it helped build my confidence as I prepared for the course.
With the start of the school year only a few days away, I am excited to help students, new and old, discover the beauty and interconnectedness of mathematics. I cannot wait!
I've got just three weeks to go until school starts back up. This has been, by far, my busiest summer of work. I have lots of things I want to do and am teaching two new courses. Here is where I am at currently on my to do list.Note: New items are marked with asterisks. Others have been adjusted or removed. Struck-through items are completed.
Develop ≥9 challenge problems - I think I have found enough problems but I am looking for a bit more variety. I have designed 5 of them and posted about 2.
What big projects are you all working on this summer! What can you share?
Those of you who have tried using standards-based grading in their classroom know that it can be a difficult transition for parents and students who are used to percentage or letter grades. This summer I wrote a sample letter teachers can use to introduce the ideas behind SBG to parents.
I worked HARD to keep the letter short and accessible, so that more parents would read more of it.Not a knock on parents -- they are just busy with the whole having children to care for thing. I also focused on how SBG is different on a single assessment as opposed to how it works for an entire term since many school still mandate an end-of-term type grade.
There is a growing movement in education to abandon tradition percent and letter grading for a new system known as standards-based grading (SBG). The goal of this letter is to help the reader understand the motivations for this change as well as how SBG works in my classroom.
Why should we abandon traditional grading methods?
Research has shown that there are a number of issues with traditional grading practices that negatively affect students. Percent and letter grades attempt to summarize a student’s progress with a single value (ex: B+ or 86%). While simple to understand, single-value grades have been shown to be unhelpful and often harmful to students.
Imagine working hard to prepare for a math test. While taking the test you feel pretty good about most of the questions, though there are a few that you find difficult. A few days later, your teacher returns the test. “87% - Good Work,” is written at the top. You feel good about the grade but want to know how to do better on the next test. Based on the feedback, what would you work on improving for future assessments? Unfortunately, there is no way to know from the feedback you received.
How do traditional grading methods affect students?
Feedback is provided as a means for helping someone improve. When feedback does not accomplish this goal, it ceases to be beneficial and becomes only judgemental. Because traditional grades do not provide useful feedback, students often see grades as fixed and representative of their intelligence instead of their learning. Moreover, presenting feedback as a single value leads students to compare themselves to their peers. The end result is that students are thinking about how to earn higher grades instead of how to better understand.
“When students are sent a label telling them where they stand compared to other students, rather than where they stand in their learning of mathematics, it offers no helpful information and is harmful to students.” Jo Boaler - What’s Math Got To Do With It?
SBG attempts to address the above concerns about traditional grading methods by giving students detailed feedback on every assessment without a letter or percent grade. Research has shown that traditional percent or letter grades, even when accompanied by comments, lead students to develop unhealthy mindsets about learning. Moreover, students who have access to SBG are more confident, learn more, and take greater ownership of their learning than those students graded traditionally.
Students are given a set of learning goals called standards, and their progress is monitored in terms of their ability to meet those standards. All standards are content-based. In other words, they do not include things like behavior, attendance, or effort. A sixth grade standard, for example, is “Place fractions, decimals, and percents on a number line according to their value.” This is something we want all of our sixth graders to learn how to do.
Every assessment, whether test, quiz, project, or interview, will cover one or more standards. The feedback each student receives specifically addresses how well they are meeting each of the standards. This presents a clear picture of what learning goals each student has met. When students want to do better in class, they simply try to meet more of their standards. Doing well no longer means getting a high grade, it means learning more of the mathematics that is covered in the course.