A good session last week at the science conference was about productive science talk in the classroom. I think the strategies are relatable to the types of math conversations that we want to have. When you use activities like Would You Rather?, Estimation 180, Which One Doesn't Belong, and others you are developing a culture that includes differing answers and discourse. Students will need to listen to each other, rather than battle to be called on with the "correct" answer.
A quality handout I picked up is called Talk Moves. The sentence/question starters are grouped into four goals that move from individual thinking to thinking with others (synergy!)
These talk moves are a good reminder to me for including variety in discussion facilitation. Two that I am going to emphasize this week are asking students why they agree or disagree with another student's statement (7) and asking students share what another said in their own words (4).
The handout is attached and available at this link for Google Drive: Talk Moves
Matt B. Hawkins
Some people love them and some people hate them, but they are memorable...
I started making math memes during a fraction unit.
Sometimes it seems like the only illustrations we share for fractions are pizza (or other foods!) These memes brought some variety to the table and helped to build connections in a subject area that students approach already confused.
They can help guide us through the steps of a problem, like adding/subtracting/comparing fractions:
Sometimes the references are a little more fun for me and they might not fully grasp the connection:
Lately, students have been finding Harry Potter helpful. I may have learned about the order of operations using the mnemonic phrase "Please Excuse My Dear Aunt Sally," but our class has been thinking of it as spell cast by a young Hogwarts wizard. This was even shared a few times by students as they led their winter conferences!
There are a few meme generators to help you make your own. The problem is that most are blocked by the school's web filter. I used this one at Imgflip, but all that you find in a Google search are mostly the same. You can create them off site and upload the images into your Google Drive to use later.
You can use the Meme Template by Alice Keeler. The template is in Google Drawings, has directions, suggestions, and links to Creative Commons photos. I think the best part of the template is that it is student friendly and another way for students to show what they know in math...or any subject!
Make a copy...make a meme...I look forward to see what you create!
Matt B. Hawkins
Whether you call them word problems or real world problems or something completely different, we find that they are a challenge for students. I also experience that if the problems are taken from the textbook, they are not often connected to the real world our students live in.
Dan Meyer, former HS math teacher and currently of Desmos, shares with some humor in this 2010 Ted Talk how math class can be made over, and more specifically the problems we ask.
His action steps going forward are to:
1. Use multimedia to bring the real world to your classroom
2. Encourage student intuition
3. Ask the shortest question possible
4. Let students build the steps
5. Be less helpful
The best math problems will build as a great story should unfold. If shared right, student will be connecting the pieces and will want to be continuing to each step. This idea and the action steps led to the structure of the 3 Act Math Lesson.
An blog post by Dan shortly after his Ted Talk explains the essential components of a 3 Act Lesson.
Act 1 - Introduces conflict and allows students to notice & wonder, formulate a question, and ask for additional details that would be helpful in answering the question.
Act 2 - Where much of the math happens, students use clues and data to solve the problem.
Act 3 - The answer is revealed!
Most of our math curriculum hangs out in Act 2, do the math and move onto the next one. Previously I have shared about notice & wonder that are important to Act 1, but the reveal in Act 3 is just as important. Dan says that you certainly wouldn't want to sit through Star Wars Episode 4 and turn it off before the Death Star explodes! The third act is a great reward for the struggle in Act 2.
So when do you use the 3 Act Math Lesson? Graham Fletcher suggests a great place to start is pre assessments for new units. The Act 1 is a good hook and more appetizing than a paper pre-test that can further decrease student confidence. During the struggle of the second act, you can formatively assess different student methods and make notes of the current understandings. Finally, Act 3 allows all of the class to wrap up on the same page.
Graham has an awesome collection of 3 Act Lessons, ready to go for elementary. They are sorted by grade level and standard. I always start with his collection, but resources are growing as you can Google search 3 Act Math and find many other great math educators sharing their lessons.
Here are some examples that we are using as a 5th grade team.
Gassed - Multiply with decimals
Sugar Cubes - Divide with decimals
The Final Lap - Place Value (hyperdoc for students)
March is "reading month," which is just around the corner, but I never hear anything mentioned about a "math month." A blog post by Tracy Zager wonders what it would be like if we took a similar approach to math as we do with DEAR, drop everything and read. Her daughter laments that her math class is too focused on timed tests and following text books. She wonders if they could just "drop everything and math."
Hello Math Teachers,
Which One Doesn't Belong is a collection of shapes, numbers, and other math representations that I present as morning work or warm-up before math. Curation is done on the web by Mary Bourassa and is inspired by the Christopher Danielson book of shapes, but I mostly have Sesame Street stuck in my head as I share one of these with students.
Nothing too complex, but it does present a good challenge at first for those students who are sure that there must be a correct answer. Students then have great discussion (argument!) how each shape has a quality that is different than the others. In the subsequent examples, the students know that their claims are important, but must be backed up with evidence and reasons why (good practice for math and science practice standards to argue from evidence).
The collection includes examples with money, numbers, clocks, games, and some seasonal pictures that are just fun:
Check out the full collection here: http://wodb.ca/index.html
I use Google Slides to share them with my class, you can access the slideshow here
They even inspire student created examples. Here is one from Mariska in Team 508:
Throughout our curriculum there are activities that utilize rounding and estimation to help show that the answer is reasonable. This seems to be the scaffolding for that infamous last question on every the unit test: The Extended Response.
Examples from 5th grade:
-Explain how you know your answer is reasonable (Unit 1)
-Explain how you found your answers (Unit 2)
-Explain how you know (Unit 3)
-Explain (Unit 4)
-What do you do with the remainder (Unit 5...I like this one!)
I'm guessing that 5th grade assessments are not the only ones that include these questions. The problem with this structure is that the estimation is still disconnected from the real world.
At Graham Fletcher's NCTM session in Chicago he demonstrated that a room full of math teachers were not very good at estimating. With a number line from 0 to 1 trillion and a dot on the far right, he asked all in the room to stand up. He shared that the dot was going to move backwards down the number line and we should sit down when the dot reaches 1 billion. Most in the room sat down at the halfway mark and the rest sat down long before the correct spot.
*Take a moment to draw that number line and mark where 1 billion is.
His message was that we need to be doing number sense and estimation activities daily. Ones that connect to the real world and beyond that final question on the unit test.
The best resource for estimation is from Andrew Stadel. His site is called Estimation 180 and is a collection of pictures and videos that students can relate to (bacon, halloween candy!) The activities build upon one another, day after day, so that students use previous reference points to guide their estimations. Once they are using benchmarks, they are no longer guessing.
A strategy to use while facilitating is to ask students for their range, including a "too low" and a "too high." Ask them to use benchmarks from previous activities or real world experiences to explain their claims. One note from Graham is to not accept unreasonable answers like 0 or "a million." Guide students to stake a claim based on evidence so that their estimations have value.
The day after returning from NCTM, I was waiting at the Harding's deli and the women next to me was eyeing the parmesan chicken. She was asking the weight of one chicken piece. She was worried that one piece would be 1 pound and cost close to $8. I could not have made up her quote, "I'm just not that good at estimating." So I pulled out my phone and asked her if I could take a couple pictures, because I had just noticed an estimation activity!
Graham Fletcher was the presenter at NCTM that I was most looking forward to...and I was not alone. Sharon and I arrived 30 minutes early and we were lucky to find two seats together, the doors were closed shortly after we got settled. The subject of the session was 3 Act Math Lessons and I learned a lot about the structure and delivery of this type of lesson by being a participant. It is a joy to be a student in the room of a stellar teacher. There was much more to learn from Graham beyond the 3 Act strategy, including thoughts on estimation, developing number sense, and whole group engagement.
I will be able to share many notes from this session, but I decided to start with one of the videos from Graham that first caught my eye. After watching the Progression Videos in his Making Sense Series, I knew that he was someone who I wanted to continue to learn with. The videos demonstrate the progression of topics from their introduction to upper elementary. The topics include counting, adding/subtracting, multiplication, division, and fractions. They have been helpful to me, a teacher that has spent all of my time at 5th grade, to see the building of foundations for each student. I have noticed how helpful watching Olivia's progression (through all subjects) has informed my teaching, but these videos allow me to check out the math progression in "fast forward."
Check them out on Graham's page here: Making Sense Series
Hello math teachers,
Welcome back and Happy New Year!
I wanted to share some golden nuggets from the NCTM math conference I attended in December. All the sessions I attended were worthwhile. They included many new activities and strategies to deepen student thinking. I don't want to dump too much at once, so I thought I would share a little at a time. Here goes...
A session by Tracy Zager (@traceyzager) challenged us to slow down our approach and allow time for students to develop math questions themselves. This doesn't mean to completely #ditchthattextbook, but try sharing the context of a word problem with the question removed.
Ask students what they notice about the scenario and then what they wonder.
There is a good chance that one of the things they wonder about is the question that is already in the textbook, but there is more student ownership since they are now answering their own question instead of yours.
A recent example from 5th grade:
One lap around the track is 1/4 mile. Amy ran 13 laps. How far did she run?
We just removed the question "How far did she run?" However, enough of our class is going to be curious to ask that question themselves.
I already wrote much more than I thought I would at the start, but if you are still with me, Annie Fetter from the Math Forum shares this much better than I do. Click on the link below for the short video (only 5 - fantastic - minutes).
This is a reflection post for an assignment in a MOOC for Minecraft: Education Edition. The assignment was to try a mode of Minecraft (Survival, Creative, or Tutorial) and share in the discussion board.
Webinar Assignment #1 – Surviving the Night
I knew little about Minecraft this time last year, but was interested in learning about it to connect with my fifth grade students. To begin this process, I attended a session about Minecraft at MACUL (Michigan's conference for technology in education) and learned about the new release of Minecraft: Education Edition. I began dabbling with Pocket Edition to get my feet wet. I played a lot in the summer with my daughter (age 6) and she got hooked really quick! We spent all of our time in creative mode building some awesome houses, tunnels, and railways...my favorite! I had also tried the tutorial world in the trial version in the Fall and was impressed how it helped me and my students learn the keyboard commands easily, since most of us only had Xbox or Pocket Edition experience. Having tried both of those scenarios, I decided to try my hand at the mode I had been most avoiding...survival!
Day 1: I did not know how long day would be, so I went to the nearest tree and got as much wood as I could. I then built a simple shelter, 5 blocks by 4 blocks and only 4 blocks high. I had not checked on how to build a door yet, so as the sun went down I closed in my house to be safe. I could not see a thing! When would it be daylight? If I knocked out a block to check for daylight would there be monsters there? If I left a skylight open, can monsters climb? I checked a couple times and saw stars and knew that a door or safe window would be what I worked on next.
Day 2: I crafted a door and collected some more wood. I started to look for sheep so I could make a bed, but could only kill one. The beds had been mostly decoration in creative mode, but I was having a hunch that they could help make the night go faster. The nights sure seem longer than the days!
Day 3: Rain! I made a wood pickaxe and begin trying to mine stone. I am picking away and some sort of gray block is disappearing, but not being collected in my inventory. I try to mine in three different places, but not having any luck. I try to find sheep with the little light I have left and have no luck. I barely make it back to the shelter and have a hard time finding and shutting the door in the dark.
Day 4: I go deeper and deeper to collect stone (my daughter's advice), but it is still not showing up in my inventory. I do find two more sheep and make a bed. The night zooms past and I can get back to work.
Day 5: I try a few more places for stone and try different shades of gray. As I venture farther and farther away from the shelter it is more difficult to make is back before dark. I did not make it this time and stumble around until I fall down deep into something! I wait out the night, surprised that I am not being attacked by monsters, and look up a long way once I have daylight!
Day 6: I started to mine a staircase, but then realized that I had enough resources to build the staircase. That went much faster!
I had to take a step back and figure out why the monsters did not find me. Hmmmm...looks like "normal" is not the default setting. So I survived a few nights, but maybe it was not that hard at all.
I setup a new world with the correct settings and started again....and again....and again. I went about the same process of quick shelter, but tried to get the door with windows and a bed fit into the first day. Problem was once I died outside of the shelter from monsters, I kept respawning at night and away from safety (I learned about setting the new spawn location later). It took me four attempts to finally survive the first night with the monsters, but such a fun challenge! I am still having some difficulty collecting stone, maybe it is the wrong stone or I have the wrong tools. Something for me to keep working on.
This assignment was a great chance for me to explore the Education Edition more and a mode that I have little experience with. While I think I still prefer creative mode, I also think I will go back and keep building more in my survival world. I also enjoyed playing with the camera and portfolio, they are awesome resources to share out what it happening in student worlds. I look forward to the next assignment and seeing how the classroom mode will connect all of us in the classroom!
In preparation for the start of new #goaltime projects and some upcoming Mystery Skype sessions, I wanted to spend some time improving the questions that students are asking. In the move to NGSS, asking questions is the first science practice on the list. When starting investigations, students are quick to get going, but I want to slow them down just a bit so that they begin with wonder and that there is a foundation that drives the investigation. I also see an improvement in their science writing when their claims (CER) are directly related to a question they asked before they started.
5 Clue Challenges
I learned about the 5 Clue Challenge project from Mike Soskil during his Ditch Summit interview. The project is a collection of short videos (2-3 minutes) where a mystery location, person, animal, or object is shared by slowly revealing clues. The videos can be paused for as long as needed to allow time for students to research, discuss, and ask questions based off of the clue. Class discussions turned in directions I did not expect based off of questions students asked or information they found while searching. One example of this was a clue about population of a city when some students found population data based off of city limits and others found metro area statistics. After completing a few challenges on video, I turned the tables and asked student groups to write their own clues that were then presented to our class.
Quantity Over Quality (to start!)
Students began proposals for their new #goaltime projects and I wanted to weave in another element I had learned from Paul Solarz: asking PHAT questions. These are questions that are Pretty Hard And Tough....skinny questions, he says, are those that can be quickly looked up on Google. With the right question(s), students can continue that deep dive into their topic or learning goal throughout the project time.
I created a new graphic organizer and shared with them the expectation to ask a really tough question. I felt really good about the direction of the project, but I failed in facilitating the asking of that tough questions! Some students did not want to write a question they did not know the answer and many simply put the first question they thought of in the blank and moved on. An example was, “why do snakes shed their skin?” This answer could be found in a short time with a Google search, but I got a puzzled look when I challenged him to ask a deeper question. Other students left the question blank because they were paralyzed by the request to write one good question. They may have been thinking through possibilities, but could not recall the ideas they had rejected.
My requests began to change as I conferenced with students, instead of looking for the one PHAT question, I began asking them to physically write 10 questions or more. We reviewed lists and eliminated skinny questions and narrowed down to deeper questions. Students began self-selecting better questions and they were not the first questions on their lists. I look forward to beginning next #goaltime sessions with a longer list of potential questions instead of the pressure to declare one awesome question right away.
How will we know what a good question is unless we have something to compare it to?
What are resources and strategies you use to facilitate better questions from student? Please share in the comments below.