*How does a math class look/operate/function that is NOT based on direct instruction? What does a typical day look like? How is direct instruction infused in when needed?*

Background on my question:

Andrew Stadel in January had posed a question on Twitter about finding and implementing tasks. Since then, I have been pondering on and off how I would change how I currently teach. I do quite a bit of direct instruction. I know that I should be looking at other options and not relying on DI so much. However, I find that when I ponder how my class would change, I feel completely clueless. And when I start to really think seriously about it, someone (usually an adult) says something to me like “You do such a great job of explaining to your students.” Usually this is prefaced or followed with an explanation of what the person has seen in another class and what was lacking that I seem to provide. And then every fiber of my being says, “See – you shouldn’t take that out of your class.” But yet, I keep coming back to making changes in my class structure.

I know there are things I could be doing differently, but I don’t know **how** to. I teach based on how I was taught. Granted, that was a long time ago and it worked well for me. I’m sure it still works well for motivated students who are usually at the top of their class. I want to make sure that whatever changes I make benefit as many students as possible and in particular help those students who generally would fall in the middle and bottom.

I know I should be integrating rich tasks into my class – how does that work? When you have students who are not used to doing rich tasks and are used to being taught to, how do you help them make the adjustment (especially students who have tended to struggle with math)? I have so many questions going through my head it is hard to articulate it all. The more information and detail you can provide would be helpful.

I’m not looking to flip my classroom, meaning that I am not looking to move the “direct instruction” portion out of my class time. There are many reasons for that but the main one is the lack of available internet for many of my students. I am looking to minimize the amount of direct instruction and to provide it in a meaningful, natural manner. So how does that look?

I appreciate you taking the time to read my questions and I even more appreciate those of you who will take the time to respond. Every bit helps. Thanks.

]]>20 | I can describe the center of the data distribution (mean or median). | S-ID.2 |

21 | I can describe the spread of the data distribution (interquartile range or standard deviation). | S-ID.2 |

22 | I can represent data with plots on the real number line (dot plots, histograms, and box plots). | S-ID.1; N-Q.1; N-Q.2; N-Q.3 |

23 | I can compare the distribution of two or more data sets by examining their shapes, centers, and spreads when drawn on the same scale. | S-ID.2 |

24 | I can interpret the differences in the shape, center, and spread of a data set in the context of a problem, and can account for effects of extreme data points. | S-ID.3 |

25 | I can read and interpret the data displayed in a two-way frequency table. | S-ID.5 |

26 | I can interpret and explain the meaning of relative frequencies in the context of a problem. | S-ID.5 |

27 | I can construct a scatter plot, sketch a line of best fit, and write the equation of that line. | S-ID.6a; S-ID.6c |

28 | I can use the function of best fit to make predictions. | S-ID.6a |

29 | I can analyze the residual plot to determine whether the function is an appropriate fit. | S-ID.6b |

30 | I can calculate, using technology, and interpret a correlation coefficient. | S-ID.8 |

31 | I can recognize that correlation does not imply causation and that causation is not illustrated on a scatter plot. | S-ID.9 |

I will be honest with you all, dear readers. I pretty much had to create stuff from scratch. I have pulled some problems from various places on the interwebs, but I could not tell you where stuff came from. I don’t have many activities here. Just trying to find practice problems to meet what I felt the standards were looking for was a challenge. All of my note files are formatted for an Interactive Notebook. They are set up for 2 to a page, landscape (5 1/2 inches by 8 1/2 inches).

Please feel free to use and adapt what I have published here. If you take something and make it better, I would greatly appreciate a link back to this blog post as well as a link to whatever you can created. I hope you find the materials helpful!

(Many of these are labeled with the Learning Target (LT) designations from above – you may want to look at the table to help you know what goes with what.)

Learning Target 20 Examples – Examples used in class for LT20 (I can describe the center of the data distribution (mean or median).)

Learning Target 20 Exit Slip -Exit Slip for LT20 (I can describe the center of the data distribution (mean or median).)

Learning Target 21 Notes - Notes used in class for LT21 (I can describe the spread of the data distribution (interquartile range or standard deviation).)

Learning Target 21 Practice Problems – Practice Problems used for LT21 (I can describe the spread of the data distribution (interquartile range or standard deviation).)

Measures of Spread and Center Survey Project – An in-class project I had students do to demonstrate understanding of measures of Spread and Center.

Learning Target 22 Examples – Examples used in class for LT22 (I can represent data with plots on the real number line (dot plots, histograms, and box plots).)

Foldable – Data Plots on the Number Line. Set to print double-sided landscape.

Learning Target 22 Practice Problems #1 - Practice Problems Set #1 for LT22 (I can represent data with plots on the real number line (dot plots, histograms, and box plots).)

Learning Target 22 Practice Problems #2 - Practice Problems Set #1 for LT22 (I can represent data with plots on the real number line (dot plots, histograms, and box plots).)

Learning Target 23 Notes - Notes used in class for LT23 (I can compare the distribution of two or more data sets by examining their shapes, centers, and spreads when drawn on the same scale.)

Learning Target 24 Practice Problems – Practice Problems for LT24 (I can interpret the differences in the shape, center, and spread of a data set in the context of a problem, and can account for effects of extreme data points.)

Learning Target 23 and 24 Practice Problems – Practice Problems for LT23 (I can compare the distribution of two or more data sets by examining their shapes, centers, and spreads when drawn on the same scale.) and LT24 (I can interpret the differences in the shape, center, and spread of a data set in the context of a problem, and can account for effects of extreme data points.)

Learning Targets 22-24 Review 1

Learning Targets 22-24 Review 2

Learning Target 25 Notes – Notes used in class for LT25 (I can read and interpret the data displayed in a two-way frequency table.)

Learning Target 25 Exit Slip - Exit Slip for LT25 (I can read and interpret the data displayed in a two-way frequency table.)

Learning Target 25 Practice Problems – Practice Problems for LT25 (I can read and interpret the data displayed in a two-way frequency table.)

Learning Target 26 Notes - Notes used in class for LT26 (I can interpret and explain the meaning of relative frequencies in the context of a problem.)

Learning Target 26 Exit Slip - Exit Slip for LT26 (I can interpret and explain the meaning of relative frequencies in the context of a problem.)

Learning Target 26 Practice Problems – Practice Problems for LT26 (I can interpret and explain the meaning of relative frequencies in the context of a problem.)

Learning Target 27 Notes and Examples – Notes and examples used in class for LT27 (I can construct a scatter plot, sketch a line of best fit, and write the equation of that line.)

Learning Target 27 Exit Slip – Exit Slip for LT27 (I can construct a scatter plot, sketch a line of best fit, and write the equation of that line.)

Learning Target 27 Practice Problems #1 – Practice Problem Set #1 for LT27 (I can construct a scatter plot, sketch a line of best fit, and write the equation of that line.)

Learning Target 27 Practice Problems #2 - Practice Problem Set #2 for LT27 (I can construct a scatter plot, sketch a line of best fit, and write the equation of that line.)

Learning Target 27 Practice Problems #3 - Practice Problem Set #3 for LT27 (I can construct a scatter plot, sketch a line of best fit, and write the equation of that line.)

Learning Targets 25-27 Review

Learning Target 28 Examples - Examples used in class for LT28 (I can use the function of best fit to make predictions.) **NOTE – I had students create their own lines of best fit.

Learning Target 28 Practice Problems – Practice Problems for LT28 (I can use the function of best fit to make predictions.) **NOTE – I had students create their own lines of best fit.

Learning Target 29 Examples - Examples used in class for LT29 (I can analyze the residual plot to determine whether the function is an appropriate fit.)

Learning Target 29 Notes – Notes used in class for LT29 (I can analyze the residual plot to determine whether the function is an appropriate fit.)

Learning Target 29 Practice Problems – Practice Problelms for LT29 (I can analyze the residual plot to determine whether the function is an appropriate fit.)

Learning Targets 28-29 Review

Entering Data in TI-30XIIS - Directions on how to enter data into the Texas Instruments TI-30XIIS.

Entering Data Examples - Examples I used to have students practice entering data into the Texas Instruments TI-30XIIS.

Entering Data Practice Problems - Practice problems I gave students to practice entering data into the (scientific) calculator.

Learning Target 30 Examples - Examples used in class for LT30 (I can calculate, using technology, and interpret a correlation coefficient.)

Learning Target 30 Notes – Notes used in class for LT30 (I can calculate, using technology, and interpret a correlation coefficient.)

Learning Target 30 Practice Problems – Practice Problems for LT30 (I can calculate, using technology, and interpret a correlation coefficient.)

Learning Target 31 Notes and Examples - Notes and examples used in class for LT31 (I can recognize that correlation does not imply causation and that causation is not illustrated on a scatter plot.)

Learning Target 31 Practice Problems – Practice problems for LT31 (I can recognize that correlation does not imply causation and that causation is not illustrated on a scatter plot.)

Learning Targets 30-31 Review

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At the beginning of the school year, I had such high hopes. I had intended to go through as I planned my courses and do as much of what I “should” be doing – integrating problem solving, much more formative assessment, less me, more my students, interactive notebooks, staying connected on Twitter, reading through blogs and digitally categorizing/bookmarking what I wanted to use and what I did use, etc., etc., etc. A few of those things have happened to varying degrees. But mainly I find myself planning on a much shorter leash than I am used to and because of that, I don’t get to much of that list. And don’t even get me started on blogging. As much as I would like to blog, I have not felt like I have had the time to sit and do it (or being motivated to do it). I have spent most of my break so far just vegging on the couch, playing mindless games and trying to decompress. It is now Tuesday and I go back to work on Monday and I have not touched a single school thing (not that it’s a bad thing). However, I haven’t done much of anything else either. (Well, we did buy me a new minivan and we did go and visit my parents, but that’s about it). With only a few days left before school resumes, it’s time to do something.

However, determining what that something is is challenging me at the moment. Like, I should be working on cleaning up part of my house right now, but I’m sitting here blogging instead. Both are important on varying levels, but I am using one to put off the other. I have come to some conclusions though. The biggest one is this – when making changes, pick one or two things to work on. That’s it. Anything more is too much to swallow and it becomes overwhelming. I have said this to others and thought it but until I really went through it this year (rather uneffectively), I don’t think it really rang true to me. I guess I have to learn it on my own. Right now, I am working with interactive notebooks somewhat effectively and that’s a good thing. It has forced me to re-think (to an extent) of what students should record in their notebooks and it has forced me to re-think some of my base lesson structure. It still has a long way to go, but I am making some improvements. I have been doing a little better with formative assessment but it is still a very conscious process for me. I should probably take some time to really read Embedded Formative Assessment by Dylan Wiliam which I have started twice but never got as far into it as I should have and also go back and do the same with Mathematics Formative Assessment (#75facts). Though, now that I have I written that, I probably ought to switch the order around. That would give me two things to concentrate on rather than the laundry list I started with. I will probably still work on digitally cataloging my resources because some how I need to find my resources again. But I think that gives me plenty to focus on for the remainder of the school year.

I suppose I have procrastinated cleaning long enough. Off to tackle a few other things on my list. Happy New Year everyone!

]]>So, I am making myself a pact and so I’ll stick to it better, I’m making it public. I am going to read blogs more. If something moves me in the post, I am going to make an effort to comment to the author. Michael said that “Every comment on a post is worth ten replies to a tweet.” Not only do I believe he’s correct, I think he’s put too small of a value on a comment. I think I would say it’s worth twenty replies (not that I have ever gotten **that** many replies to a tweet). If someone comments on my blog, I know that something they read was valuable to them because they took time to respond on my blog, where the comment will be part of the post and others can read it. That’s way more permanent than a tweet, although you can go back and find tweets (but not always easily). Plus, since it’s longer than 140 characters, I believe the person really put some honest thought into what they had to say in response to my writing. I know how much it means to me when people comment on my blog, especially when I am asking for comments so I can ponder what others have to say. So, if I value people taking the time to comment on my blog, I should do the same to show my appreciation to others who blog. So, I’m going to do it. Of course, to do that, I need to start reading through the backlog of posts I have in my Digg Reader.

But I also miss the act of blogging. Taking the time to sort through the many thoughts in my head and putting it to computer. When I take the time to do that, even if I don’t have a definite end in mind, it helps me figure out the answer I am seeking (eventually) if I have a question, or it helps me sort out all the things that are bouncing around in my head. Twitter tends to be about connecting with others (or at least it does for me) or seeking quick answers and advice. Blogging, for me, is about reflecting on my teaching practice and sharing what’s happening in my classroom. If sharing that helps others, so be it, but in all reality, blogging tends to be a rather selfish act for me. Most of the time, when I take the time to reflect, I become a better teacher. And in the long run, that’s not only better for me, it’s better for my students. As a teacher, isn’t that what we all want – what’s best for our students?

So, I’m going to make more of an effort to blog more often and comment more often (but don’t go expecting these twice-a-day posts like I’ve done in the last week now, okay?). See you around – more often!

]]>We had about 25 minutes or so in class to work on this. Many students got through 6 or so. When I printed the cards, I printed them on colored card stock and used a different color for each type (problems in one color, answers in another color, and graphs in a third color).

Students in both classes worked fairly well. I had hoped they would get through more problems. I think the most anyone got through was eight. In fact, I was a little nervous that they would get through all twelve and still have additional time. Part of that may be that we spent more time than I had expected reviewing homework from the previous night. The file has twenty-four sets (problems, answers, graphs) and I mixed up the problems in the baggies so that each pair would not necessarily have the same problems. I am contemplating having students work on the problems again tomorrow for additional practice, but I think I will wait until I see the results of an entrance card as they come into class and make a quick decision at the beginning of class. Since I already have the cards ready to go, it would not be a big deal to have them practice again if the entrance cards show they need the additional practice.

]]>How many of you have #EmergencyLessonPlans that say some thing like, “Ss will visit @DailyDesmos.com, pick a challenge, and…” #mathchat

— Desmos.com (@Desmos) November 13, 2013

I thought about this tweet for about a second and realized that it would be the perfect solution to my sub plan problem for Calculus. Here is what I put together for them:

I was hoping for more out of my Calculus students. They pretty much went for the easier ones and only turned in two. Granted, I wasn’t there for their last period Friday afternoon class, but I am guessing that it did not take them a majority of their 50 minute class period. I would like to use this again, but I definitely need to do some tweaking. Regardless, I did want to share it. Maybe it will inspire someone out there to do something similar with their classes.

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To get an idea of what the community is interested in hearing about and/or learning about we set up a Google Doc (http://bit.ly/TMC14-1). It’s an open GDoc for people to list their interests and someone who might be good to present that topic. If multiple people were interested in a session idea, he/she added a “+1” after it. The doc is still open for editing, so if you have an idea of what you’d like to see someone else present as you’re writing your own proposal, feel free to add it!

This conference is by teachers, for teachers. That means we need you to present. Yes, you! What can you share that you do in your classroom that others can learn from? Presentations can be anything from a strategy you use to how you organize your entire curriculum. Anything someone has ever asked you about is something worth sharing. And that thing that no one has asked about but you wish they would? That’s worth sharing too. Once you’ve decided on a topic, come up with a title and description and submit the form.

If you have an idea for something short (between 5 and 15 minutes) to share, plan on doing a My Favorite. Those will be submitted at a later date.

The deadline for submitting your TMC Speaker Proposal is January 20, 2014. This is a firm deadline since we will reserve spots for all presenters before we begin to open registration on February 1, 2014.

Thank you for your interest!

Team TMC – Lisa Henry, Lead Organizer, Shelli Temple, Justin Aion, Mary Bourassa, Tina Cardone, James Cleveland, Cortni Kemlage, Jami Packer, Anthony Rossetti, and Glenn Waddell

]]>**1. What hooked you on reading the blogs? Was it a particular post or person? Was it an initiative by the nice MTBoS folks? A colleague in your building got you into it? Desperation?**

I don’t know if I can pinpoint a particular post or person right now. When I first started on Twitter in 2009-2010, I remember seeing people tweet out their blog posts and I would follow the link and read it. I really started reading them in the Summer of 2010. At that point, I was starting to think about Standards Based Grading (because it seemed like everyone I was following was talking about it). I remember reading Kristen Fouss’ blog and, of course, Dan Meyer’s blog for math. I think what really got me going was reading Matt Townsley’s Blog because at the time, I was looking for how someone was implementing Standards Based Grading in his/her classroom.

**2. What keeps you coming back? What’s the biggest thing you get out of reading and/or commenting?**

I think the biggest thing that keeps me coming back is that I know what is being blogged has been classroom tested and written by classroom teachers. I can relate to the struggles and triumphs that other teachers face. I know that what they are sharing is genuine. When we were in college (and for me, that’s a while ago), everything seemed to come from professors, many of whom were rather far removed from the classroom. It might work, or it might not. At least I know from reading someone’s blog that they have tried something and what worked (and possibly what didn’t work). If you continue to read in the comments, many times you can find other teachers’ suggestions of how to change the activity to work in your own classroom.

**3. If you write, why do you write? What’s the biggest thing you get out of it?**

I started writing a blog in June, 2010 because it seemed like “all the cool kids” were doing it. At the time, I really needed someplace to hash out how I was going to do Standards Based Grading in my classroom. It is extremely difficult to get those thoughts out 140 characters at a time. Blogging allows me to more fully form my thoughts and think through situations. Many times, I will find that by blogging, I will eventually figure out the answer to a question in my mind. I think the biggest thing I get out of blogging is a safe place to share what is happening in my classroom with other like-minded teachers. I am one of three high school math teachers in my district. No one else teaches the same classes that I do. Other Algebra 1 teachers can read my blog and share what has worked for them in the comments. Other math teachers can share that they are going through something similar to what I am and share how they have worked through it. I cannot get that in real life from my in district colleagues. Blogging and reading blogs has helped me to be a better teacher. By sharing what is going on in my classroom, if I can help someone else as someone else has helped me before with their blog post, I am not only helping myself be a better educator, but also helping someone else improve as well. And if it doesn’t help someone, oh well. It at least helped me to get it out and think through the situation.

**4. If you chose to enter a room where I was going to talk about blogging for an hour (or however long you could stand it), what would you hope to be hearing from me? MTBoS cheerleading and/or tourism? How-to’s? Stories?**

First of all, I honestly wish I could be there. I am certain that whatever you choose to share will be interesting and beneficial to those who choose to listen and hear the message you are sending. I think that I would hope that the session would be a blend of what is available via blogs and how to blog.

I didn’t begin blogging until I had a chance to read other people’s blogs first. Knowing how to find math teacher blogs that will be interesting and useful to me is helpful because, although there are a lot more blogs than when I first started, I’m not certain that googling “math teacher blogs” is the best way to go. I don’t know (because I haven’t checked) if the resources that we have put together as the MTBoS Community will come up as one of the top choices if someone were to google that. I believe, for many, knowing the resources that are available out there for free, would be valuable. Maybe showing some specific posts from a few blogs? Talking briefly about different reader resources like Feedly, Digg Reader, The Old Reader, etc. so that people know how to check on several blogs rather than having to bookmark them?

When I first started blogging, it would have been helpful to know what platforms were available and a couple of key things about each platform that would help me choose which one to start on. I think I originally choose Blogger because several people at the time were using it and it was pretty easy to use. I switched to WordPress because there are more things I could do to change it than Blogger.

I think most importantly, be you. If people see you are being genuine, that will go a long way. Your enthusiasm and knowledge about blogs and blogging will shine through and that will spark others to see what is available. I’m glad to hear you’re doing this session at NCTM. Good luck and I hope it is well-received! –Lisa

]]>In one of my classes, they came in with more questions. I answered a couple before the start of class, but then it was time for their assessment. What frustrated me here is that they waited until right before the test to ask questions. No one had emailed me, and even though I had been answering questions on Monday, toward the end of the period, no one had questions. But now that it was time to assess, NOW they had questions. They continued to ask questions during the assessment and I won’t answer questions on how to do something during the assessment on that topic. It is their responsibility to know it at that point.

I have finished grading their reassessments. As Dean predicted, they did not do much better. I will say they did do better on the rate of change material. But as far as graphing goes, they did not do markedly better as I had hoped. I gave them equations in standard form (graph using the intercepts), slope-intercept form, and point-slope form. As much as I am aware that they will have access to technology, I still feel it is important that they are able to graph lines by hand. I am debating how I am going to handle this deficiency. It frustrates me that my students accept that they don’t have the concept fully or even close to fully. I’m not sure how to help them change their attitudes. I am also wondering how I can best help them if they aren’t willing to help themselves.

As I am reflecting on this post (which I typed before I left school today), part of what I am struggling with is determining at what point do I say “it’s good enough” and move on. I know the ideal is that every student would have the concept solidly and we would proceed, but in reality we aren’t able to do that. In most classrooms, even with Common Core narrowing the number of topics but deepening the understanding, I think we would become challenged to touch on everything we are supposed to for our students to move on to the next course.

I’m looking for any thoughts or encouragement you can give. Thanks for giving me a few moments to share my thinking.

]]>I spoke with Max at length today on the way home from school. Part of it was just venting – I was/am so frustrated. I felt like I had set up good practice structures (see this post) and that I had students do meaningful notes in their interactive notebook. I was pleased with the foldable I had the students use for their notes.

But, my students didn’t prepare well enough. As I continued to reflect with Max, I realized that some of my students went through the motions. A couple of them even admitted when they turned in their papers that they didn’t study. With it being the end of the first grading period, this concerns me because although I had felt I had modeled good ways to prepare in class, my students couldn’t or wouldn’t translate that to outside of class. It concerns me also that they didn’t feel it was important enough for them to prepare somehow for the assessment other than what they did in class. It concerns me that what effort they put into homework and class practice time was not enough. Although I am not raising the issues of what I could have done better here (and I am sure there are some things I can improve on), right now, I am trying to figure out how to help them learn how to be successful in my class (and subsequently other math classes).

Ultimately, for whatever reason, they weren’t ready to assess today. Part of what this emphasizes for me is for better use of formative assessment on my end. I am still feeling rather lost on this and I need to fix that right quick. (Now, if I only had the time to do the reading I want to so I better understand this…) After discussion with Max (which I am ever so grateful for today – thank you!), I have decided to do the following:

First of all, there will be a reassessment. I won’t leave these grades in the first grading period – but they will assess again next week and it will go on the second grading period. Secondly, I going to reinforce direction reading (either using this or something similar). For enough of my students, it was clear on at least one problem that they did not read the whole problem and that would have made a difference for several. Thirdly, after I pass back their assessments tomorrow, I am going to have students complete this form.

Max gave me this idea and I think I got pretty much all we talked about putting in this form. I know as I am looking at it that it is going to take up some paper, but I feel that it is so important that my students really look at what they are doing in preparation and be able to find their mistakes. Hopefully this reflection will help them to do both. I am still trying to figure out the last steps before having them reassess next week. I am thinking right now that I will set up problem relays for Friday. What I am now struggling with is whether one day of additional practice in class on their part will be enough or if I need to do further remediation before their reassessment. The other monkey wrench is the weekend/day off in there – if I have just the one day, the reassessment will be Monday (not sure if after the weekend will be good or not). If I add an additional day, it will be Wednesday (we are off Tuesday). I am hoping to get some clarity on this tomorrow.

I am curious about your thoughts on the form. Please leave them in the comments or tweet me. Thanks for “listening” and offering feedback – I do appreciate it!

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