I haven't posted in a long time. I've been studying and trying to learn more about number sense and how to teach number sense. I teach older students, and it seems like number sense is either strong or weak in students before they get to me. What can I do to strengthen number sense later in students' academic careers? When a student is in middle school and does not have good number sense, how do we fix it? If we do not build up number sense, all other mathematics learning will be an uphill battle at best.

Do I teach these students the skills they should have learned before age 6 or 8 now? How do I go about that without making them feel marginalized? Surely most of them would realize that these are skills that their peers already possess. Number sense is such an important foundation for mathematics that I cannot in good conscience ignore these deficits. How do I build these students in a supportive and nurturing way? I want to show these students that they can succeed. They spend enough time believing that they are stupid. I do not want to add to that. I do, however, want to help them fill in the gaps in their understanding so that they can be successful as soon as possible.

I truly believe that if I can build these skills in my students who lack them, they will find success in math classes in general far easier to attain. Am I being naive? Surely it is not "too late" for these kids to get the skills they need. I mean, after all, people can learn to read as adults, so can't I teach a person number sense in middle school? I'm sure going to try.

For those of you who might not be sure exactly what I am seeing, I have a few examples. One student, when asked "If I take two-thirds away, how many thirds remain?" had absolutely no clue what the answer was until I drew a picture for him. Another has to count the faces of a cube each time to figure probabilities using dice. He doesn't "just know" that there are six sides on a cube. Students with poor number sense don't really understand that fractions, decimals and percents can all represent the same thing. When changing 6 1/2 into a decimal, I had a student write 6.12. He can't remember that .5 is the same as 1/2. He has to take 1 and divide it by 2 to get the decimal equivalent, and he's not sure enough in his division skills to do that reliably. He has learned some number skills, and memorized some basic facts and procedures for doing basic arithmetic, but it is not at all intuitive to him. When he looks at a problem, he has no idea if the answer should be closer to 2 or 20,000, so he never looks at his answer and thinks, "That doesn't make sense. I must have made a mistake." This is because none of the math makes sense to him.

Ok, everybody, I'd love some feedback on this. I would love some strategies for nurturing number sense in older children. I'd love to hear where I'm spot on and where I'm way off base.

Made 4 Math Monday!

I finally made something for Made 4 Math Monday. I've been interested in the examples I've seen on twitter and on blogs about using larger whiteboards in class. I have a class set of the individual white boards, and I like to use them for quick formative assessments in class. I like the idea of using the larger whiteboards for group work. I hope to use them for both collaborative problem solving sessions and for the mistake game.

So I bought three marker board/wainscoting boards from Lowes, and had the guy cut them each in half. That gave me six nice sized boards. Then I took colored duck tape and edged them. I chose purple and yellow because they are my school's colors. Here they are:

Student Portfolios

Once again, I'm going to do a brain dump to see if I can flesh out my thoughts, this time on student portfolios.

I want to create e-portfolios for my students next year. I teach 6th, 7th and 8th graders, so I would also like for the portfolios to follow the student from year to year. I would ideally like for the students and the whole middle school team to be able to acces them and add to them. I've thought about Evernote, but I don't know how to do that without having pro accounts for everyone. I'm really looking for a free alternative.

I could set up a free Evernote account to share with the rest of the team with notebooks for each student, but I don't know how we would avoid going over limit each month. With 4 or more teachers adding content to 60 student accounts, we would likely go over limit fairly quickly. I suppose I could allow students to upload without giving them access (read: password and therefore access to everyone's student files) by having them email straight to the Evernote account, but I'm not really sure how that feature works. Would it work well. Would the notes added this way wind up in the correct notebooks or would I be creating a ton of work for myself. If it would be cumbersome, it might be easier to have students email content to me directly and I could put the information into their notebooks for them.

Then there is the issue of what to do with the portfolios once the students leave our school. Ideally, I'd like to be able to give them their notebooks when they leave, but you cannot transfer ownership of an Evernote notebook.

Most of my thinking on this has centered around Evernote, mainly because I use it and love it, although I'm sure there are other options out there. I need to put this out to my Twitter people, as they are a knowledgeable and resourceful group.

That's all for now.

More thoughts on Next year...

I've found a great resource to help me decide on which standards to teach. Mastery Learning has helped me sort those out. They have the common core broken down into 7th grade and 7th grade advanced (for me, Pre Algebra) and 8th grade and 8th grade Algebra. My 8th grade Pre Algebra will use the regular 8th grade standards. This has eased my stress levels considerably.

Of course, now I have to get all those standards organized and get activities and lessons planned for them. I know I can do much of my planning during the year, but I need to have a large part of it done ahead of time. I'll be largely out of commission in July and the beginning of August, so I'm on the clock despite summer having only just begun.

There is one more thing bothering me. The common core standards for 6th, 7th, 7th Advanced and 8th grades all have somewhere around 30 standards. Algebra has 60 or so. I'm concerned about feeling rushed in Algebra. The high schools my students go to don't take 8th grade Algebra as a credit, so many students re-take it anyway, but a few do go on to take Geometry as a freshman, and that worries me.

There's also the standardized testing that we go through each Spring. My school tests the first week of March. That means that everything I cover fourth quarter comes after the test. Very frustrating! Not sure what to do about that. I need to rearrange some of my content, as my students tend to do poorly on the Geometry sections. Geometry is something I cover fourth quarter. So what do I supplant? It's all important, right? What can I teach after the test? Until next time...

Thoughts on next year, Sbar, and Self-pacing...

Ok, I'm going to do a brain dump to try and collect my thoughts for next year. Since nobody reads this blog, I can feel free to sound as stupid as I want and there will be no one to hide from in shame.

• I want to do standards based grading
• I want to do self pacing
• Iwant to use a flipped model of sorts

Now, how do I do all of that?

I've been gathering information and ideas on standards based grading, and have found the The SBGbeginners Wiki website very helpful.

So I'm thinking that I need to make short videos for each of the major concepts I plan to teach. Then, I need to gather other resources for my students to use: worksheets, textbook references, assignments or groups of problems from the textbook, other videos and explanations online. I'll consolidate these and organize them by standard/concept for the students to utilize to gain understanding and practice.

I'll need to pretest my students. Then I plan to use the results of those to determine what activities and assessments I use with each student, as well as which concepts of which students already have a basic understanding.

At that point, I'll have my students begin with the standard which I determine will be the first taught, and give them options as to how they wish to learn. Some might like to read examples from a textbook (not terribly likely, but possible), while others might want to jump right in with trying to solve problems and ask questions as they come up. Still others will want to watch my videos and/or other videos to get the basic concepts down.

I plan to require that students show me adequate preparation (notes taken, examples copied, and independent work done) in order to "qualify" to take the assessment on that standard/concept. I plan to assess each standard more than once, up to 4 times or possibly more. I've worked out a rubric for those assessments, which will include 3 levels of problems: basic, intermediate, and advanced. My rubric is downstairs. It will have to wait until tomorrow for me to post it, but it is a zero to four scale, four being perfect and zero being no attempt given.

On the occasion that a student does not "pass" a standard, I will require that they show me that they have adequately revisited the standard through practice and error analysis before they will "qualify" to reassess.

I plan to encourage students to work together and teach each other as well as engage in discussions with me about concepts with which they struggle.

I've got my Algebra standards largely mapped out, thanks in part to some of the links and uploaded documents I found on the aforementioned wiki site. I am struggling, however, with exactly which standards to use for my Pre Algebra classes. I have two Pre Algebra classes, one seventh grade and one eighth grade. There are no common core Pre Algebra standards. I'm thinking that I should use the eighth grade math standards, but I want to be sure I'm really preparing them for Algebra. I'm embarrassed to admit that in the past I've allowed the textbook company dictate what I cover. I want to be better at my job, so I want to change that.

I'm sure I've left some things out, but it feels Bette rot have it all down. I'll be working on this all month, so there's plenty of time (gotta be careful with that thought, I'm a natural procrastinator) to get my ideas and lesson structure fleshed out.