Evolutions in Teaching

This month, I'm participating in a blog challenge called Blaugust.  To see the list of participating blogs, click on the logo above. I would encourage to you please cheer on our participants with either a tweet or a comment on their blog during this month. It can be hard to blog on a daily (or even regular) schedule! :)  If you would like to join the blogging challenge, you can still sign-up anytime!

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August is almost over and yet again, I have not made my Blaugust goal - BUT - ultimately, the point of Blaugust is to get me back into the habit of sharing about my classroom and I *have* achieved that, so go me!  Thank you ALL for reading, responding, sharing, and commenting on my posts and the other Blaugust participants.  It's such a great resource of ideas and inspirations for back to school and I appreciate you!.

I've now been back to school for 2.5 weeks and I'm making good progress on my goals!  I have so many blog posts floating in my head, but by the time I get home and get things ready for the next day, I'm utterly exhausted!

But tonight I want to reflect on one of my goals and how things have evolved in my classroom over the past few years. :)


Multiple Choice Mondays - Version 1

Each Monday, my AP students do a MC Monday consisting of 5 questions over material we've learned (or previous content, like ACT style questions).

However, I didn't want them just to do the MC questions and be done - I wanted my students to reflect on their learning.  This is a common theme in my classroom and I often ask students to write / reflect / summarize to help them solidify the material.  So on Mondays they do their MC and put it back into their table folder.  The next day, the reflection part on the back is their warmup.  For the first 1 (or maybe 2... I don't remember), this was the back of the MC Monday.  The Analysis at the top had a place for the correct answers, whether they got it right or wrong, the type of error, and whether they needed to study that concept.  The bottom was a reflection grid (inspired by the assessment grid that @pamjwilson has blogged about before), with various prompts.  Overall, I liked this, but kids would often write the same thing week to week and weren't really using the grid the way I had envisioned it, so back to the drawing board...


Multiple Choice Mondays - Version 2

So the following year (Year 3 I think?), I changed it...  I had discussed some of my frustrations with the grid with my neighbor teacher and she was having some of the same issues.  Both of us really liked having a place to ask questions and have a dialogue with our students, but decided that maybe we needed to be a bit more specific with the other prompts.

As a result, Version 2 was born, with the prompts asking about which questions they felt most confident about (and why), and least confident about (and why).  We tried to impress on the students that most / least confident is NOT about getting the answer right, it's about how you felt regarding the material.  However, that was an uphill battle as even at the end of the year, I was still having to make the speech about "Remember - confidence is NOT about the answer - it's about the question!"  I did have some great comments and questions from my students on the "I have the following questions..." prompt, but I was disappointed in the most / least confident prompts, so back to the drawing board - AGAIN...


Multiple Choice Mondays - Version 3

I'm really hoping that the third time really is a charm...

During the teacher work-days, I *still* hadn't figured out how I wanted to change the MC Monday Reflections, but I knew that it needed to happen.  I popped by neighbor teacher's room to see if she had any brainstorms and she was as stuck as I am.  Both of us wanted to keep an area for students to ask questions, but that was about all we knew.  I mentioned to neighbor teacher that I really wanted to incorporate more vocab review into the class with "Terms Tuesday / Words Wednesday" and wondered about using the MC Monday to help drive that.  Thankfully, she loved the idea and our latest version was born.  The Analysis box got simplified a bit with the last columns being combined into a spot for students to write themselves notes, then the general reflection area that combines multiple prompts into one, and finally the Terms Tuesday / Words Wednesday box.

So this week was our first MC Monday and I *LOVED* it!  It was so much fun to do the vocab and I think they really enjoyed practicing their retrieval skills to see if they could recall the words we had learned so far.  I'm super excited to see how this plays out over the year, but we might have a winner - plus, it helps me meet my vocabulary goal!  YAY!


If you have suggestions on how to improve this further, please let me know :)

Summer Book Review: 101 Strategies

Anyone that knows me well knows that I often have my nose stuck in a book.  It is definitely one of my favorite past times and during the summer, I can frequently be found on the back patio with a book.  (Of course, that often leads to my mom teasing me about having a great tan on the front of my legs and the back of my legs being a bright white!)  Thanks to the #MTBoS and some great clearance sales at Half Price books last week, I have at least 25 edu-books in my to-be-read pile plus an uncountable number of fiction books waiting on my Kindle.

A few days ago, a tweet from Kathryn Freed caught my eye:

Kathryn's tweet started me thinking about some of the vocabulary books that I had in my "Summer Reads" pile.  This upcoming year, I will be teaching AP Statistics and Geometry, both which are heavy on the vocabulary.  In Geometry, I anticipate several ELL students as well, so I wanted to work on strategies to help all students be more successful academically.

One of the books in my pile happened to be "101 Strategies to Make Academic Vocabulary Stick", which I received as part of my ASCD membership:

Note:  If you love to read edu-literature, I highly recommend joining ASCD.  For $69 a year (or less if there happens to be a coupon), I am a "Select Online" member, which gives me access to the awesome Educational Leadership magazine plus 5 free e-books per year

Overall, this book had a very nice organizational structure.  Chapter 1 dealt with the various types of memory structures in our brains before diving into the actual strategies, which the author had split into 3 chapters.  Chapter 2 included strategies for introducing and encoding new vocabulary, then Chapter 3 worked with rehearsal strategies, and Chapter 4 dealt mainly with review and retrieval strategies.  Many of the strategies were interchangeable throughout the "make it stick" process.  Finally, Chapter 5 wrapped it up with how to assess vocabulary retention and how to plan for successful vocabulary instruction.

The book had some really good take-aways, which I'll get to in a minute, but my biggest disappointment was that "academic vocabulary" was rarely used to mean "content area vocabulary", rather it was more in line with what I would consider "SAT type words".  This is definitely a book I would recommend to my AVID colleagues as well as my ELA friends because I know that in our AVID classes, we really work hard on academic reading & writing and "owning" those words so that kids are comfortable using what the author calls "Tier 2" and "Tier 3" words while speaking and writing.  The strategies in this book would be extremely useful  for any teacher that wants to develop a vocabulary-rich classroom.

With that said, here are some of the strategies and ideas that I will definitely use:

Open with a Cloze - 
I've done this before, especially in AP Stat.  In this strategy, you create sentences that leave out a key word and try to have students complete each sentence.  I often use this during AP Review to remind them of all of the vocabulary we have learned throughout the year.  I typically provide a word bank to help students out.

WKWL - 
This is a modification of the typical KWL chart, but with the extra "W" for Word at the beginning.  I've never been a fan of KWLs to be honest, mainly because of the "Want to know" heading, so I will probably modify this as a pre/post idea of WKL - Word, What we Know about the Word, What we Learned about the Word.  I think this could be a great strategy in Geometry because often we have words that kids have some familiarity with from previous courses.

Vocabnotation -
I'll admit, this is a strategy that makes me wish I was teaching AVID again!  Vocabnotation is basically Annotation for Vocabulary.  While reading a test (AVID Weekly, anyone?), have students circle the words they don't know, underline and draw a line from a word to a student created definition written in the margins, note (with a musical note) any important words, and draw arrows to words that connect in the text.

Dump & Clump - 
I'm pretty sure I've used this strategy at some point, although I don't recall using this name.  It may be related to one of the strategies from the AVID Critical Reading strand.  Give each small group a piece of chart paper, markers, and a topic.  Have the students brain dump words, ideas, etc onto the chart paper individually, then as a group, clump the words and ideas into subtopics.  Finally have the group write a summary sentence for each subtopic.  I think this could be a useful strategy when preparing for a test to activate their prior learning.

Out of Sorts - 
If you ever take a peek into my cabinets, there's no doubt that I'm a huge fan of card sorts.  However, the author talks about using card sorts with more of a word / definition / picture / example matching activity.  One thing I've never done though, is have the students glue or tape their card sort to their notebook, so I will probably try doing that in Geometry.  I think this could be easily adapted to a Desmos card sort as well.

Affix Organizer - 
This graphic organizer is somewhat similar to a Frayer model.  The author intended it as a way to think about prefix / suffix with words that have the same prefix / suffix and to compare those words. In my head, I started thinking about how I could use it more as a graphic organizer such as:

Enriching the Vocab Experience - 
This strategy was a fun little memory test.  Each student gets a blank piece of paper.  The teacher says the first vocabulary word and the students write down related words / ideas, but NOT the actual word.  This allows students to make deeper connections.  After 10 or so words, ask students to flip over their paper and see how many of the original words they can regenerate.  This reminded me of "Taboo" in reverse :)

Frayer Model for Self Reflection - 
This was probably one of my favorite take-away ideas from the entire book and it had nothing to do with the students!  When thinking of vocabulary instruction, most of us are familiar with the traditional Frayer model of Word, Definition, Characteristics, Examples, and Non-Examples.  In Chapter 5, the author challenged teachers to use this model as a structure for self-reflection.  As an example, the author had used the term "Vocabulary Instruction" in the middle spot where we typically would put the word.  Then for the four corners, she asked teachers to self reflect with "Current Habits - When do I teach this? How do I teach this? How often do I teach this?"; "Facts & Characteristics - What strategies do I use to teach this?"; "Examples - Best lessons"; and "Non-Examples - Worst lessons"

Overall impressions:
I'm glad I picked up this book.  It was a quick and easy read, but still provided a lot of food for thought.  I will definitely recommend it to my ELA / AVID colleagues and if I ever have the chance to teach AVID again, I know I will be re-visiting this book! :)

#Made4Math - Knowledge Rating Chart

Sorry that my Made4Math project is a bit late tonight, but I've been at the AP reading since last Tuesday and days of the week really mean nothing here! :) To give an example, I had at least 3 people lined up to send me a reminder to call my dad yesterday for Father's Day because all I knew of yesterday was that it was "Day 5". To make matters a bit tougher, the internet at the hotel is severely lacking plus the only computer I brought with me is a Chromebook, which I'm just learning to use! So tonight after the reading, I came home to work on my project and had to figure out how to use Google Docs and take a screenshot on the Chromebook in order to share this with you! :)

One of the books that I picked up a few years ago at Half Price Books (LOVE that place!) was the book Algebra Out Loud by Pat Mower. Since one of my goals this year is literacy, I brought the book with me on the trip and have been reading through it trying to figure out ideas to use in Statistics. One of the activities is a Knowledge Rating Chart, so I did some research and found some great examples on Math Equals Love. If you don't follow Sarah's blog, please go do so now! I'm lucky enough that I live near her, so we've met up several times and that girl is amazing! I wish I had been half as good as she is after only 2 years of teaching!!

Anyway, after reading Sarah's blog and talking with her on twitter, I came up with this Knowledge Rating Chart for AP Stat:

The idea is that students will put an X in each box if they feel confident in their ability to do that task. I am thinking it might be a good "temperature check" during the sampling chapter to make sure students are on target with their knowledge.

The End is Here :)

I've come to the end of my Literacy book - what I thought would be a fast read (< 100 pages) has taken me a week to read. Of course, taking the time to annotate the book (my AVID buddies would be SO proud of me), blogging about what I've earned, and of course spending LOTS of time on twitter learning about a multitude of things have slowed me down a bit. And while I can easily burn through a lengthy novel in a day or two, professional literature just doesn't flow at that same level :) However, I am eager to move on to my other books (especially those about assessment & Standards Based Grading), so I'm trying to get this one finished up. As such, this post will not be as lengthy as the previous posts (which is probably a good thing!)


Make a Picture! Make a Picture! Make a Picture!
Chapter 4 was about Graphic Representations in the math classroom. While this chapter was an enjoyable read, with several vignettes, I really didn't learn much. Of course, I am a VERY visual learner, so maybe I already knew this chapter's information from experience.

The main theme of this chapter was that student drawings allowed us to catch a glimpse of student thinking processes, which can be extremely helpful for students who cannot fully explain verbally where their confusion lies. Through the power of a diagram, teachers may find that what makes sense to our more mature thought processes does not make sense to our students based on their prior knowledge. One example in this chapter was about quadrupling a recipe that called for 1 1/4 cups of flour. Without prior knowledge of how "cups" relate, the student answered that they needed 8 total cups of flour in the new recipe - 4 big ones and 4 small ones. I'm not much of a cook, and as a kid, I rarely spent time watching my parents cook, so I could have easily had this same misconception when I was younger. As teachers, we have to be careful that we don't assume that students have prior knowledge about everyday things and having the students draw a picture can help us pinpoint these problems.

As math teachers, we often tell our students (particulary with a "word problem") to draw a picture. Using graphics helps with teacher assessment, but more importantly it allows students to make connections between the words and the concepts. For visual and hands-on learners, making a picture may be vital to the learning process because it forces them to slow down and process. For me personally, I am not auditory at all - I struggle in traditional classrooms, in meetings, listening to NPR, because I have to focus so much on what is being said that I can't keep up. :)

Talk it up!
The last literacy strategy of the book is discourse, which is what Chapter 5 is devoted to. This strategy comes easier to me in Stats than in Algebra, mainly due to the nature of the course. Even so, I still came away with some useful jewels of knowledge.

One of the first statements in this chapter says that "discussion and argumentation improve conceptual understanding." Personally, that statement shows itself to me all of the time via my twitter PLN. For example, this morning, I tweeted a question about standards based grading, which lead to a lengthy conversation with several colleagues, a few new blogs to read, and in the end, way more questions than I had started with. This discourse with my peers truly improved my understanding of SBG and allowed me to put the puzzle pieces together in my head of how to implement SBG in the classroom. The free-flowing idea stream that came out of today's discussion was simply amazing, although in the classroom, I could definitely see where this "non-controlled" environment could stress some teachers out. I had no idea where my question would lead me and in the classroom, that can be a scary thought (especially depending on your clientele!)

I have always tried to keep my classroom open for discussion, often asking students "why" in order to get them to explain their thinking. However, I may change that. One teacher that is used as an example in this book uses the word "More?" as a way to keep kids talking about an idea and appending previous student comments. I like that idea because it opens up the discussion to more than just an explanation - it could be any comment about the idea at hand.

The other big idea that I got from this chapter that will impact my classroom is this: "Rich, deep, and argumentative discussions occur when students display their work and present their strategies". I really need to have students tackling more application-rich problems and presenting their findings to the class. Of course, while I know that I need to do it and I really think I would enjoy doing it, I have no earthy idea of where to start, so obviously some research will be required there. I'll get back to you on that :)

A couple of other tidbits I got from this chapter:
- Don't rush to save kids too quickly. Often they will discover and correct errors on their own as they think and explain their reasoning.
- Have students share their methods, esp non-traditional, as it help everyone grow mathematically (I had this happen this year as a student noticed a pattern w/ perpendicular slopes when the equations were written in standard form - love when kids come up with their own algorithms!)
- Don't have kids just memorize vocabulary - they need to process the concept before the vocab word makes any sense to them
- Graphic organizers are great tools, but in order for students to truly expand learning w/ these tools, they need to discuss and share with others in order to clarify thinking

The big ideas...
Overall, I really enjoyed this book. I came away with a lot of ideas on integrating reading, writing, graphical representations, and discussion in my classroom. I know that not all of those ideas will make it into my classroom this year, but that's part of the purpose of this blog - to act as my "holding place" for my "mindful mediation" :) Having these thoughts written down here will help me throughout the years as I reflect back on previous ideas and things I want to change. Now I get to dig through my treasure trove of books from last week to find my next mind-bending adventure....

Writing in Math

Chapter 3 of Literacy Strategies is about writing in the math classroom. I was particulary interested in this chapter because the topic of writing (journals, learning logs, etc) has come up several times recently in discussions with my twitter PLN. While I got some great ideas from this chapter, I'm ultimately left with more questions than answers about how to integrate writing effectively.

We all know writing has great benefits. For the student, they are provided a canvas in which to develop their communication and thinking skills, and for the teacher, an avenue in which to assess how well the student understands and processes a concept. The author of this chapter relates writing as "mindful meditation" and the page as a "holding place for our thoughts". To me, that idea is the basis behind a journal or a blog. I've never been much of a writer, but even I find writing on this blog to be very useful for my personal and professional growth/reflection (aka mindful mediation) and I've often used my blog as a minddump of ideas that I haven't fleshed out, but that I don't want to forget. However, I had never quite put that idea into the classroom.

In the classroom, I would guess most of us rely on verbal communication, whether that comes from lecture, student responses, etc, yet all of us would like for all students to be engaged in the classroom. The author points out that only one student at a time is able to speak, but if we ask them to write instead, this encourage more participation because the entire class can be involved at the same time. Again, a simple idea, but one that I had never quite thought of. Ultimately, I would like to get to the place of presenting a problem, having students think and write individually, then work with a peer group to refine and edit, but worry about issues like student buy-in and wondering if kids will take it seriously or just jot down random things and not really grasp the benefit of the writing.

One point that the author made that I struggle with is that the thinking involved in writing/explaining is different than the thinking needed for solving a problem. All of us have experienced this issue. Students can find the answer to the problem, but struggle with explaining the how and why of their work. You may have even had a situation where a student could explain a topic (such as multiplication), but has very little computational fluency. There must be a balance between these two types of thinking and I'm not sure where that balance lies. We want students to be successful in both conceptual and computational learning, but how do we find that balance?

Writing in the classroom should allow us to open a dialouge with our students. When presenting them with a task that requires them to explain their thinking, we should take advantage of that opportunity to assess their thought process and any gaps or misconceptions. The teacher taking the time to read and respond to student writing on a regular basis is important in order to help students develop clarity in mathematical thinking and communication. However, that poses another question - where do we find the time? Obviously reading and responding to written responses will take a lot more time than grading a traditional math assignment. Also, many writing assignments may just be an informal assessment, gauging where students are conceptually and are never meant to be entered into a gradebook.

This chapter also provided insight on how writing can help ELD and SPED students develop mathematically. One point the author makes is that for both of these subgroups, there is a need for teacher assistance in organizing their thoughts through structured-response prompts. As confidence grows, the teacher can provide less and less structure until the student is performing independently. In my opinion, all students, not just ELD and SPED, could benefit from this structure as they are learning how to write in the math classroom.

Overall, I leave this chapter feeling convinced of the power of the written word in helping a student learn math and to reflect on their learning. I still struggle with some of the practical questions that come with this idea, such as the time issue, needed balance, etc. I feel like this post is more of a jumble of random thoughts instead of a cohesive review, but that may be appropriate considering that I feel quite lost and jumbled in how to effectively apply this strategy to my classroom. :)

Reading in Math

Chapter 2 of Literacy Strategies (which, btw, is freely available for you to read at the ASCD website), really made me squirm in my seat. When I was a kid, our pastor used to (and still does) get up on Sunday mornings and preach his heart out. More sermons than I can remember had him saying that when he was praying about and researching for that week's message, that he felt convicted, that God had "really stepped on his (the pastors) toes" that week. After reading this chapter, I knew exactly the feeling that Pastor meant. This book really stepped on my teacher toes this weekend and I feel very convicted as a result.

This book is a collection of essays from a group of teachers, and as such, this chapter was much smoother to read, but very deep in content. The big idea of this chapter is this: Ultimiately, the responsibility in teaching a student to read a math textbook lies with us, the math teachers. Granted, we have not had formal instruction on how to teach reading, but their reading teachers probably haven't had formal instruction on technical texts either. Here's a list of ideas from this chapter and my reaction...

Book: Traditional math instruction is training, not education. Students can perform procedures on cue like a trained animal, but have not really learned the mathematics until they can apply it.
Me: OUCH!! If that didn't step on toes, I don't know what will. This idea really knocked me on my rear and I had to step away from the book for awhile to process. I felt very convicted by this statement. How often do we train them for a standardized test, train them how to use an algorithm, without teaching them the true concept beind the computations? I can think of many examples in Algebra 2 this year where, after feeling beat down by pacing, snow days, family issues, lack of sleep, etc, that I resorted to "here's how you do this problem" rather than the WHY of doing the problem. This statement still has the power to knock the wind right out of me :(

Book: Math texts contain more concepts per sentence and paragraph than any other type of test. The text contains words, numbers, and symbols that must be decoded. The eye must travel in a variety of ways that is unnatural to reading (both left/right, up/down, graphs, charts). While reading, some information is extra and must be discarded by the brain, yet still distracts the reader.
Me: I paraphrased the above of course, but I had never sat down and really analyzed the difficulty in reading a math book. Because, as math teachers, we are (hopefully) math literate, our brains ignore all of the issues that are listed above, but as a young reader, can you imagine trying to tackle that? How overwhelming! This section hit home so much that I had to read part of it to my husband because I had never thought of a math book this way. Another issue that I would add to their analysis is the weight of books - holy moly! Those suckers are HUGE!!! Definitely not the book I'm going to sprawl out beside the pool reading :)

Book: "If we are really trying to help students read and understand for themselves, we must ask them questions instead of explicitly telling them what the text means"
Me: Another big OUCH here. How many of us, when a kid comes up and says "I don't get it", just tell the student what to do, rather than asking questions to lead to understanding? Questions like, "Can you read the instructions to me?" "What does this word mean?" "What is the problem asking you to find?". I try to be good at asking questions, often to the frustration of some students, but there are times, when I'm feeling rushed, or multi-tasking, or whatever that instead of asking questions about what they've read, that I give them too much information. Asking questions is also important because it helps me figure out where a student's misconception lies.

Random other tidbits that I picked up from this chapter:
The language itself poses a huge problem. The same word in Math-speak and in English do not mean the same thing. In addition, small words make a big difference (percent of vs percent off). To further compound the issue, clarity in written and spoken language can create complications for students as well. Vocabulary (or lack thereof) can be a huge issue and graphic organizers can be very useful for students to clarify and organize the information.

Final thoughts:
Like with everything in the classroom, kids learn by modeling. As teachers, we need to model the processes we use to read and decode text. We need to "think aloud" while working through problems so that kids have a working example of how to tackle problems on their own. We need to break down the text into manageable "bite-sized" pieces and ask questions along the way to demonstrate the thinking process.

Gosh, after this chapter, I may have to find something more light-hearted to read... my toes *still* hurt!!!

Literacy Strategies

Okay, so as previously mentioned, I am going to be spending some time in professional reading (but my new novels look awesome too!), and sharing some insight here. The first book I'm reading (about 100 pages, hence why it's #1 on the list) is Literacy Strategies for Improving Mathematics Instruction.

So far, I've tackled Chapter 1. I have to admit that I kept getting distracted and this isn't an easy read for me - I'm really not one for "goobly-gook speech patterns", I'm really a pretty simple-minded person at heart. I tend to like books that are more of a "say what ya gotta say and hush" type of book :) Edu-speak typically irritates me quicker than anything because most of the time I feel like they are either trying to impress me with their vast amounts of knowledge OR they want me to feel bad for not understanding a word they are saying. However, there was one part of Chapter 1 that really stood out to me....

In Chapter 1, the authors really spend time related Mathematics to other languages. It has its "nouns" (numbers, shapes, functions) and "verbs" (modeling, communicating, transforming) and as a "foreign language", we really should approach it more with ELL type-strategies. The authors shared experiences of "use it or lose it" with both mathematics and traditional foreign languages. For myself, I took 2 years of Spanish in HS, yet retained none of it long term. As the author points out, some of that is of course that lack of usage, but could also be attributed to the way I "learned" Spanish. In Spanish 1, we spent a lot of time on nouns and verbs - my teacher had a table at the front with all kinds of stuff - toys, household items, etc and she would hold up an item and name it, we would repeat it, etc. She also taught us verbs - toss, pet, touch, point, etc. This memorization was useful, but ultimately it was just memorization, not a true understanding of the language. (With that said, I *loved* my Spanish teacher - she was amazing at making it fun to learn). Another point made was regarding decoding the language of math, both symbols and words. For example, the same symbol horizontally (=) and vertically (||) means totally different things in math. Food for thought... especially in how to relate to those students learning BOTH the language of english AND the language of math at the same time.

Overall, I think I'm going to enjoy this book. The next chapters delve into the strategies, but I know that I personally have given lip-service to "math is its own language", without really understanding what that meant. They've definitely opened my eyes to issues I hadn't thought about.

Til next time... :)