Getting Students to Reason, Justify and Write in Math

I recently wrote a blog post Reflecting on My Journey through Common Core.  This year I have put a lot of thought into getting my students to the next level and not only preparing them for the Common Core way of thinking, but also preparing them for High School, College and Career.

We are now in the 3rd quarter of this school year and it is amazing to see the growth that my students have made this year as mathematicians.  This is the first year that my students are not afraid to learn.

In the past years my students would shut down when they struggle because the math becomes to hard. Over the summer I did a lot of research and thinking.  It was my goal this year to change that.  I blogged throughout the summer about my ideas and how I could get my students to persevere through their struggle in math.  It was my goal this year to change the mindset of my students.

I wrote a motivational letter to my students that they keep as the first page of their Interactive Math Notebook.

The students did a motivational "sticky note" prompt in the 2nd quarter to remind them about perseverance.  :o)

My students are successful this year because I sold them on the idea of learning from the beginning of school.  They are now eager for the product every day. :o)  Don't get me wrong.  It is not easy. As the Math continues to get harder, and they reach that "Struggle", I have to sell them on the product again, and encourage and motivate.  This is a continuous process, that I will continue to do throughout the year.  But because the foundation was set from the beginning it is a much easier struggle to get through. For all of us.  :o)

I am so proud of my students. This is the first year that my Students are not afraid to write in Math. More importantly, my students are not afraid to think.  :o)

This is the first year I have explicitly incorporated the Math Practices into my teaching methodology and refer to them throughout the day. Over the summer I did a lot of reading and research and realized that incorporating these regularly is crucial in helping my students to be successful in Math.

Emphasizing the Math Practices has helped my students understand why I put an emphasis on being precise and justifying their reasoning. Again, the key to this success was selling them on this idea from day one.
 
Justifying their reasoning is not only done verbally but through writing as well.  I created a Problem Solving Guide for my students' IMN to help them with their Writing about Math.

My students justify their reasoning and write a lot in my math class.  They write in the Solve It! PROVE It!  They write in all of their Team Tasks. All of their Concept Quizzes require them to write justifications.  They write during the Worthwhile Wednesday TASKS.  And they write to justify on their Benchmark Performance Tasks.  :o)

Here are some examples of how my students write in my math class. :o)

Writing to justify their reasoning in Solve It! PROVE It, Collaborative Team Warm-ups:

 Writing to justify their reasoning in Collaborative Team Tasks:

Writing to justify their reasoning on Worthwhile Wednesday Tasks:

And they write to justify their reasoning on Benchmark Performance Tasks:

My students don't only write a lot in my 8th Grade Common Core Math Classes, they also write a lot in my 8th Grade Common Core Math Support Classes.

Writing and Justifying in my (1:1 iPads) Math Support Class

The 8th Grade Common Core Math students are very fortunate this year if they have my 8th Grade Math Support.  My 8th Grade Math Support students actually write more in my Math Support class than they do in my Math 8 class.

I have blogged a lot about how I use iPads in Math, my favorite apps and how I use them in my 1:1 math classes.  We are now in the 3rd quarter and not only are my students not afraid to write in regular Math 8 class, they are not afraid to write in my Math Support class.

In my (1:1 iPads) Math Support class my students do a "Blast from the Past" Math Support daily warm-up on Edmodo.  In this daily warm-up, students solve a problem and justify their reasoning by leaving a typed written response.

The Math Support students also do a daily "Ticket Out the Door" Reflection Response on Edmodo.

In my Math Support class I use Showbie for "Paperless" Tasks.  In my Math Support Class students also justify their reasoning in all my "Paperless" Tasks that I create.

Students also leave a "Comment" after each Assignment in Showbie, summarizing and reflecting on the Assignment.

I love using Socrative for self-paced activities in Math Support. In these self-paced activities I am able to incorporate writing through justifying in the assignment.

Or by adding a "Sticky Note" response into the Socrative Assignment....

Students in Math Support also write in End of the quarter reflections

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There is still work to be done to get my students to write better in math and to have better written responses.  But the first step is getting the students comfortable with writing in math.  And I have achieved that goal.  This year I have created an environment where my students are not afraid to write and reason in my Math Classes. :o)

Next year, I hope to build on what I have learned this year. I am excited to see my students take my ideas of incorporating reasoning and writing in math to the next level. :o)

Thank you for stopping by and reading my blog about my students and writing in math.... :o)

Implementing My Cup Strategy with Collaborative Teams

I am so excited to finally find time to implement an idea I have had since last summer.  I came across this great idea one night in a Twitter Chat.  That is why I love my Twitter PLN.  I love sharing ideas and learning ideas from other great teachers. :o)  

Most teachers use Green, Yellow and Red cups for this strategy, but I am always doing things "Outside the Box". So..... I had to find cups that went with my classroom colors.  I was so excited to find hot pink, teal and lime green cups.  {:o)}^2

I am using this strategy with my Collaborative Teams.  The Task Manager will be responsible for determining which cup should be on the top of the stack.  Each Team will get a set of 3 cups, (pink, blue, green) and a copy of the Team Task Cups Guide.  

Here is the Team Task Cups Guide I created:

Here are links to the Team Tasks Cups Guide if you would like a copy to use or to edit.
  Word doc  or  pdf


That's all for now.  I will blog again with an update after I implement the new strategy. I hope it works. :o)  Thanks for stopping by and checking out my blog... :o)

Reflecting on My Journey through Common Core

                                   
I am linking up with Passion in Portable Land and her Remember, Reflect and Goal Set Linky!!!
                                 

The Importance of Reflecting
Reflecting on my teaching is something I do everyday, pretty much all day.... One of the reasons I created this blog was for me to journal and reflect on my teaching.  I am hoping that not only can I learn from my journey and reflections, but I can learn and share with others as well.....

Learning about Common Core
This is my third year teaching 8th Grade Common Core Math.  It was four years ago that I first heard of  the new Common Core Standards.  Our district wanted to get a head start on the transition to Common Core, so our Math Department started getting training and planning days. We spent a lot of our planning days researching, planning and attempting to create curriculum.

Teaching 8th Grade Common Core Math (Year One)
Our first year of teaching Common Core was rough.... Our curriculum was all over the place because we were not familiar with the standards. Our first year of teaching Common Core was full of frustrations because the students were not understanding the concepts and were not making the connections.  The biggest problem was that the students were what seemed to be "unable" to think.  :o(

The planning and pacing for our first year was guided by our training instructor and put together by us without much knowledge of the Common Core Math Standards.

This is the order of our Math 8 Common Core Units for year one:
Unit 1 - Rationality and Exponents
Unit 2 - Functions
Unit 3 - Bivariate Data and Statistics
Unit 4 - Linear Relationships
Unit 5 - Geometry

I learned a lot that first year of teaching Common Core.  I realized that everything we taught was taught in isolation and pretty much out of order. I realized why the students were not making the connections I was hoping for.  So that summer, I spent the entire summer redoing the pacing, lessons and creating new curriculum.

Teaching 8th Grade Common Core Math (Year Two)
I put a lot of thought into the order of the pacing and how I could pace the curriculum so the students would make the connections between the concepts.  The first thing I realized was that our Numbers and Rationality unit would be better taught in the 2nd semester. I knew that the concept of square roots and exponents would help the students make the connections with the geometry concepts. The other changes I made were how we taught the concepts that were related to linear relationships.

This is the order of our Math 8 Common Core Units for year two:
Unit 1 - Linear Relationships
Unit 2 - Functions
Unit 3 - Simultaneous Equations
Unit 4 - Bivariate Data and Statistics
Unit 5 - Rationality and Numbers
Unit 6 - Geometry

Another change I made the second year of teaching Common Core was starting "Teams" with my Math 8 students. I had used "Teams" with my Honors Algebra and Geometry classes and had such great success,  I knew I had to implement that same strategy in my Math 8 classes. I was nervous about doing "Teams" with my Math 8 students, so I didn't start "Teams" until 4 weeks after school started.  I wanted to get my students used to my rules and procedures first.  I wanted to be comfortable with it.... :o)

For the Math 8 warm-ups we did a "Blast From the Past".   Each student had a notebook.  Even though the students were sitting in teams, they did the "Blast From the Past" individually.  I would then call 5 students to the board to show how they solved the problems.  I realized after the first half of the year, that it really was more of a "Time Passer" for many students.  I was lucky if they even simply copied the problem down, yet alone solved it.  So for the second half of the year I changed the way that I did the "Blast From the Past" problems.  I had the students do the problem as a "Team" on a "Team" whiteboard.   Wow, what a difference.  I encouraged them to discuss and solve the problem as a "Team".  This definitely worked well considering I started this strategy halfway through the year.

The "Blast From the Past" and the "Do It With Me" and "Now You Try" problems were really the only things the students didn't do as a "Team".   I created a lot of "Team Tasks" which really helped the students to discuss and work together.  I have previously blogged about the structure of my "Team Tasks".  This structure is key to the success of collaborative teams and the students' learning.

The second year of teaching Common Core went a lot better than the first year.  I had a great group of students that were willing to try and weren't afraid to "Think".  The curriculum was flowing. The students were engaging in discourse and seemed to be understanding the Common Core Standards so much better than the year before.

The curriculum seemed "Pretty Good"....  But after taking the SBAC Practice Test and Field Test, I knew that "Pretty Good" was not "Good" enough.  Although I knew that we were definitely on the right track, I knew that we were no where close to being rigorous enough....  So that summer I once again gave the curriculum a makeover..... I was determined to get this right.... :o)

Last summer was the summer between years two and three of teaching Common Core.  It was last summer that I started my blog and journaling my ideas for my 8th Grade Curriculum.  I spent the entire summer researching, reflecting, and creating new ideas to add to the 8th Grade Common Core curriculum.

Teaching 8th Grade Common Core Math (Year Three)
I knew that the order that we taught the concepts in the second year was perfect, I just tweaked them slightly.  Over the summer I also created additions to the curriculum that helped the students to make the connections between linear relationships that I was looking for.  :o)  I will blog in more detail about the changes I made that really helped my students with linear relationships...

This is the order of our Math 8 Common Core Units for year three:
Unit 1 - Linear Relationships
Unit 2 - Functional Relationships
Unit 3 - Simultaneous Equations
Unit 4 - Bivariate Data and Statistics
Unit 5 - Rationality and Numbers
Unit 6 - Geometry

We are only half way through year three, but so far this year I have seen my a lot of difference in my students' learning and understanding of the math concepts compared to the first two years.  I can't tell you how exciting that is... :o)

This year I made a lot of changes to my classroom structure.  I previously blogged about my classroom structure and my "collaborative teams".   One major thing I did was to start teaching with "Collaborative Teams" from day one. This year my goal was to "Make Math Social" and really work on the students discussion and discourse.  I have seen the growth in my students this year through that discussion and discourse.  I knew that this change in my classroom structure would also help the students' Growth Mindset and persevering through struggle and that too has proven to be true.  :o)

My students have been doing so well this year and having a lot of success.  Even though I thought that maybe it was because of my new ideas that I had added this year, I wanted to get the students' opinions. So before the students left for break I had the teams reflect on the first half of the school year and think about what classroom strategies helped them the most.

Here is a list of the most common responses I received from the teams.

• Team Tasks because it increased our knowledge of the concepts when working with our team to solve the problems.
• Post It, Prove It because it helps us to explain and prove what we did. 
• Color-coding the guided notes because it helps us see the connections within the concepts and lets us know what is important.
• Worthwhile Wednesday's because it helps us increase our skills individually. 
• Making us be precise because it helps ups explain everything in detail.
• Random groups every week because it helps us to learn from different people.
• Word of the Day because it helps us with the math vocabulary you want us to use.
• Reminding us to persevere because we will always struggle with math problems.
• Your color-coded posters on the wall because it helped us remember the concepts.

• Our great teacher because she would push us to try our best.  This is my favorite :o)

After reading through the students' responses I realized that it was my new ideas that were helping my students and it was nice to have validation by my students that they knew that too.  This validation makes me realize that my hard work IS making a difference.  And my goal is to continue to "Persevere" through my "Struggle" as I make this journey through teaching Common Core.  :o)

Thanks for stopping by and reading my blog.... :o)

The Evolution of My "Post It! PROVE It!" Idea

First of all it is so nice to have time to sit down and write a blog post.... :o)   Time has been my enemy lately...

Wow.... I can't believe the 1st Semester is already over. It has been a busy year so far.  Not only have I been super busy updating and tweaking our 8th Grade Common Core Math Curriculum, creating unique and engaging 1:1 lessons, I have also taken on a few other responsibilities. I have become a member of the Instructional Leadership Corps which is a team of California teachers giving professional development workshops to help other teachers in California with the Common Core Shifts.  I have also become the Technology Lead Teacher at my school and as part of this committee we are designing a technology integration model for our district.

I have been reflecting on the first half of this year and thinking about all the new ideas I have implemented.   Over the summer I put a lot of thought into ideas that would help take my students to the next level and teach them to think critically. One of my new ideas was to implement a daily "Post It, PROVE It".  I have previously blogged about my "Post It, PROVE It"  problem.  This idea was based on doing the daily problem as a team and having one student be the "Recorder/Reporter" and the team would discuss and solve the problem as a team, and then write a written justification as a team.
This is an example of one of my "Post It! PROVE It" problems.

Here are some examples of my students doing the daily "Post It! PROVE It" problems.

The Evolution of My "Post It! PROVE It"
I originally came across this idea and tweaked it because I wanted the team discussion and written explanation to be the center of the strategy.  I started implementing this strategy by having the students discuss and solve the problem as a team, then "Post" their team's answer on the board, and then write the team's "PROVE It" written explanation.....  That evolved into using Promethean Clickers to "Post" the team's answer and then write the team's "PROVE It, written explanation....  I soon realized that students were discussing, solving, "PROVING" and then "Posting" their team's answer....  And this evolved into having the students "Post" their team's answer on their whiteboard with their team's "PROVE It" written explanation.

I soon realized that I don't really need the "Post It" part of the strategy.  I realized that what I really liked about the idea that I found was the "PROVE It" part, because I wanted to develop my students written justifications.  The two most important parts are: solving the problem and the written explanation.  So now my "Post It! PROVE It" has evolved again..... Starting after break, it will be called "Solve It! PROVE It".....  I don't know why I didn't think of that in the first place. LOL

This is an example of one of my new "Solve It! PROVE It" problems.

Throughout the first semester I have recorded a lot of video of my students developing their mathematical discourse.  It has been super awesome to see them grow throughout the year.  The day before break I asked my students to list 5 classroom strategies that helped them the most this year. It was unanimous, every team commented on how the "Post It, PROVE It" strategy helped them to explain and prove what they did to solve the problems.  It was nice to have validation that my idea was as effective as I thought it was..  I am so excited to start this new version of my favorite strategy.  :o)

Thanks for stopping by and reading my blog.... :o)

Paperless Tasks and Student Learning Via Showbie

First Quarter Benchmark Week
We have reached the end of the 1st Quarter in Math 8 and the students spent last week completing a Benchmark Assessment, a Writing Assessment and a Benchmark Performance Task.  The idea for our assessment week is to prepare the students for the SBAC test in the Spring.  During this test in the Spring the students will take a multiple choice test and complete a performance task.  Our Benchmark weeks are like practice tests, to help students learn to persevere through struggle and do the best that they can. :o)

The last couple of weeks in my 1:1 Math Support classes I have been helping my students review the Math 8 concepts from the 1st quarter and prepare for the 1st Quarter Benchmark.  The Benchmark Performance Task was based on a real world situation that represents a linear relationship and a proportional relationship.

Here is an example of the Benchmark Performance Task.

Using Showbie in a 1:1 Math Class
If you have read my blog before you know how much I love Showbie.  I honestly believe it is by far the best app for any 1:1 class or BYOD classrooms.  Showbie is the center of my 1:1 Math support class.  I use it to organize the weekly assignments for my Math Support classes.  I use it to give the students links to important resources I want them to use, and I use it as a way for my students to reflect and write after each assignment.  Check out Showbie's Blog featuring my student reflections. :o)

My students also love Showbie. They love Showbie because I create paperless performance tasks, and assessments for them to complete via Showbie.   The students love the annotation feature  in Showbie because it allows them to write directly on the iPad and they can easily erase and rewrite their answers. Showbie also has a "Comment" feature that allows the students to type a written response on my paperless tasks. To utilize this feature I have created a symbol for the students to know when I want them to type a written response.

This is an example of what the students would see when I want them to type a written response.

Here are pictures of my students using Showbie to complete my paperless performance tasks.

Here are some examples of the paperless performance tasks my students did to help prepare for the benchmark performance task.

My "Paperless Performance Tasks" are usually require multiple days to complete.   The best part about Showbie and my paperless performance tasks is the fact that I can give feedback to the students via Showbie.   I look at my students' work every night and leave feedback on their performance tasks so the next day they can see their mistakes and make the corrections that are needed.

Here are some examples of the my annotations on my students' paperless performance tasks.

One of my newest ideas for my Math Support class is my paperless assessments. I love these because they allow me to check for understanding and give the students feedback.  The students take the assessment in class.  That night I can look at each of the students' completed assessments on my iPad and correct them using Showbie's annotation feature and leave a typed response using Showbie's "Comment" feature.  The next day the students can go back to the assessment and make the corrections and then they leave a "Comment" in Showbie explaining their mistakes and what they now understand about the concept.

Here are some examples of a recent CFU  assessment I used to help my students review for the benchmark performance task.

                           

 

 

Here are the paperless assessments I made to use in Showbie if you would like to download them: Writing Equations from Situations Assessments

I did a poll in Edmodo on my students' favorite app in Math Support.  After the students did the poll, they left a "Comment" in Showbie explaining their reasoning.  It didn't surprise me that Showbie had the most votes in the poll.

Here are some of the reasons the students left for why Showbie is their favorite app to use in Math Support class.

I have always known how great Showbie is and everything that it has to offer.  I had my students do an end of the quarter reflection.  In their reflections some of my students explained how important Showbie is to them and how Showbie helps them in Math Support. These are awesome reflections. :o)

Here are some examples of the students reflections.

Thank you for stopping by my blog and reading my post about my favorite app Showbie.  :o)