Remediation is hard

i wish I had a magic wand,  a perfect solution....the WAY!

It would be so much easier....

Remediation is a matter of understanding the student,   It's a matter of knowing how best he/she/ze will see the concept most clearly.

I've known teenagers for whom subraction still makes no sense.   Division, fraction and number sense confusion is so common as to assume that it's confusion should be expected.

I love my kids, but I ache that I cannot possibly help all of them have experiences to clarify all the misconceptions, never mind successfully develop a full understanding of all the current grade level standards as well.

I do know that disruption and sleeping as well as not doing the work is definitely positively correlated to not participating, not doing homework and not answering questions in math class.

Motivation is a killer for students.  Often-times a student's home life can make our best efforts feel like standing still.  We are not alone in this, the students feel it as well.

It's true that math is sequential, and it builds upon itself.  It's also true that many of our students memorize steps, not understanding the why.  The good news is that continuing to build basic skills and remediating misconceptions does slot in lost concepts and I've seen students with that "ah-ha" look in their eyes.

6th through 8th graders have learned the 4 basic arithmetic operations, they need opportunities to hone these skills and practice them.  My 6th graders practice divisibility, factor trees, do kenken, review vocabulary and skip-count (to practice multiples/multiplication and learn to see linear/arithmetic progression, though I don't share the motivation with them).

My 8th graders need to better explain their thinking (yes, Mathematical Practice #3, construct viable arguments - I'm looking at you).  They need to work on being better at showing their work/thinking so that in time they can be better at those explanations.

Evaluation and remediation....

I wish I had all the answers.   Heck, I wish I could better predict the best questions... Here goes anyway:

I am not great at formative assessment, other than knowing my kids and walking around to observe.  I do have a magnetic red-yellow-green board (of my own design) to simplify the notion of exit tickets.

My method of evaluation includes 2 kinds of quizzes.  Content (at 1 less than, to 1 greater than, the appropriate grade level) and Basic Skills Quizzes, or BSQ's.  BSQ's allow me to individually assess students and set baselines which are useful in establishing individual learning goals for the year.

The true strength of BSQ's, because they require (primarily) pure computational skill, is that they are easy to electronically grade.  Do not be tempted to make these multiple choice.  Use a good App, like Socrative.  I have heard that one of google's apps can do this, and I wish knew how to do it...

Students must "pass" the previous quiz to move on.  I require 8/10 on the + and - quizzes and no less than 70% on the rest, or the student MUST reassess.  Students who complete all required BSQ's get free time while listening to headphones, to read or work on the material for another class ( or to do sudoku or magic squares, etc).

I have a student who got 0 of 10 right on a three digit + three digit number quiz.   Standardized assessment is similarity low.  BSQ scores give me a clue at what level the student is, and let's me know where to start helping him.

I am willing to share what I have with regard to BSQ's to anyone willing to work with me on building a library of these.   Include your email, or email me and we can discuss a dialogue on this topic.

*** dear Socrative.com... Love the app, but wish a few things were different.  When running a quiz, once all students have completed, the % should change from percent completed for each student to percent correct for each student.  Also, teachers should be able to run at least 3 different assessments simultaneously.  More would be better.

Middle school and starting the race behind

ok, new focus....

I have 2 sixth grade classes and 3 eighth grade classes.  I can tell you that the sixth graders are great, but much lower than I would have thought... But they are great kids and mostly willing to work at things.

I need to focus on remediation.   I need to differentiate heavily.  I need to make sure no time is wasted as we can ill afford it.

I wish I could say addition was a given, but I am dealing with the students and deficiencies I am given, so we started skip-counting this week.  The goal is to practice mental math and repeated addition is a good preparation for multiplication facts.  Here are the details.  Skip-counting means that students add the same number over and over.  For example, I tell a student 3.  He repeats it back to me.  Th next student says 6, then 9, 12 etc.   I switch when we reach number times 12.  This week was 2-5, next will be 3,4 & 6,7.

Yet my goals are the 6th grade standards that we all know we will be, eventually, assessed is what I am required to teach

Mistakes happen and students are encouraged to try again.  I am discouraging the culture of smirking and giggling at and correcting (sadly sometimes wrong as well) of each other.  It's a daily battle, but progress is being made.  How can one get students confident enough without making such reactions inappropriate?  This is a situation which must be addressed.

 How do you deal with deficiencies and social skills such as these?

Feel free to respond to this question in the comments...

 Next time, evaluation and remediation.

Dice bias. A statistics activity

There are so many great reasons to use dice in math class.  Strictly speaking, most dice should be non-biased, although students generally don't know what this means or if they do know what it means they don't believe it.

The graph of a die (singular of dice) thrown 100 times should show little bias.  If you continue another 900 times and any previously seen bias still occurs one could make a compelling case that the die might be biased.   Ask your students what the graph of a die rolled 1000 times should look like.

We played with dice in class.  First I had students roll a single die 100 times and then that die was passed to another student who did similarily.   Students were asked to keep their results to themselves and they were asked to describe if they thought the die was biased or not.   After the whole class' data was brought together the case for the die not being biased was easier to make.

Next had students roll two dice and collect the sums obtained.   There is a definite bias int Ensues which will be found.  Some sums are more likely and others much less likely (and surprisingly some are impossible, like a sum of 1).  We rolled, collected data and graphed results (which forms a wonderful curve that gets lots of attention in statistics classes, but is rarely generated in such classes)

Amazon crayola air dry clay

I went out and bought air-dry clay and had students make themselves two six-sided dice.   Students were told to make the dice as carefully as possible and they were left to dry (happily they dried sufficiently in 24 hours to make the next part of this possible, though next time I would likely have students paint their dice with clear nail-polish, and let them dry a second night, so they were less likely to crumble... Though this wasn't a big problem for most of the students)

We again did the collecting of sum activity and noticed that our graphs weren't quite so pretty.  After collecting 100 rolls from their own dice, students were asked to predict what the sum of rolling the two dice would be given the bias of their handmade dice.

Expected value is one of the harder concepts for students, at least mine.  In my class, students themselves came up with the term and a good working definition as well as a reason for the term itself..  Win-Win in my opinion..

An apology to my readers

short and sweet, I'm sorry.

There have been a number of difficulties in my life this past year which have prevented me from updating this blog as I have wanted.  I won't say they are done, but I can say I now have more time and a corner has been turned.

Also, for the past 9 years I have taught high school math, but as of this September I am easing back to middle school.  This mean that my blog will have a different focus.  I do still have a couple high school ideas I want to share, though.

Made for Math Monday * Foldable for introducing matrices

I don't think this is a very difficult topic for most students, but I do occasionally have a couple who struggle and could use a little more time working on the basics of matrices, so I made a foldable to keep most of the class busy while those students got the time they needed to process and absorb the material.

First, take a 8.5 x 11 sheet of copy paper and place it in the landscape position (wider than tall).  Fold in about 1-1.5 inches on both sides.  Next, while the sides are folded in, fold the entire paper in half both ways (lengthwise and width-wise)  I found the template for this foldable a while ago and just hadn't before used it.  Now that I have use it, I'm trying to figure out where else I can use it! (funny thing is I didn't even realize it was for matrices until I wrote the blog posting).

Here are 2 versions of the front of the foldable I did.  I like that the foldable has 4 pages within, each one having a little pocket to hold something

The RED CLOCK thing I did was a mnemonic I did to try and help the students remember that in defining the dimension of a matrix that it does ROWS and then COLUMNS


I told the students to make the time a number that meant something to them.  We just started a new trimester and I only know about 25-30% of the students from last trimester.  This gives me a way of connecting with a new student and the students a way of personalizing the foldable.









Next, here are pages 1-2.  I would like to point out that I had students label each part as one would label the elements of a matrix (a (sub) 11, a (sub) 21, etc.

 As we did the foldable I didn't give any instruction on how to perform any of the operations.  We put the foldables aside and did examples of adding, subtracting and multiplying by a scalar.

For homework they were to write instructions on the pages a (sub) 12 [adding matrices] a (sub) 13 [subtracting matrices] and a (sub) 14 [multiplication by a scalar] as well as make up 4 addition, 4 subtraction and 4 multiplication by a scalar problems - on half-index cards, which fit wonderfully in the pockets.  Students will quiz their partners as I check the assignment on Monday.

I'm just not a very good test taker

I must hear these words at least 3-4 times I give a test. (I'm just not a good test taker).

I've come to realize that this doesn't actually mean what the student is trying to say.

After hearing this from a number of students, I peeked into their other grades and found that many of these same students were doing quite well in other subjects but struggled in math.  Upon asking them about their test-taking skills in these other areas the overwhelming response was that those other tests are easier.  Yet I have students who will still say that they are poor test takers even on assessments with very high class averages.

I'm convinced the "I'm not a good test-taker" comment is more a cry for help from students who are struggling but who lack the skills necessary to improve their scores alone.

Essential skills for studying in math

• you must know what material will be assessed
• you should know what kinds of questions your teacher will likely ask (multiple choice, constructed response, etc)
• you should identify your own weaknesses and focus your study there
• you should NOT wait until just before the test

What better students will frequently do in addition:

• make up practice questions
• even if you just take a problem worked out in class and just change 1-2 numbers and work that out
• find another student in that class and discuss the examples
• better yet, challenge each other with the additional examples you've made
• Seek out assistance _online, IRL, etc...

Any other strategies you can suggest?