MathBits is an online publication of the Minnesota Council of Teachers of Mathematics. I encourage you to explore it!
Below are links to a few recent postings (some middle school specific) along with some tantalizing snippets of the content of each one:
10 Favorite Math Blogs (Oct. 29, 2017)
submitted by Sara Van Der Werf, MCTM Past President
"Here are some of my favorite Minnesota Math Teacher Bloggers. You need to follow each of their blogs. They all have some fantastic things to say. (In no particular order)…"
Updated MCA Samplers and TE Items (Jan. 6, 2018)
Submitted by: Angela Hochstetter – Math Assessment Specialist, MNDOE
Ann Page – Math Assessment Specialist, MNDOE
"This article will answer the following two questions:
Highlighting Mistakes (Nov 30, 2017)
submitted by Amy Wix MCTM VP for Junior High / Middle School
“It used to be that when I handed back an assessment to my 6th graders, they would look at their score and be done. A few years back, after attending a presentation from Rick Wormeli, I revised my teaching to include standards based grading and the chance for re-assessing on any of the standards until they were met. This along with using some of the resources from Jo Boaler’s YouCubed site has helped me in my journey to promote growth mindset with my students…”
Meaningful Relationships (Oct 29, 2017)
submitted by Amy Wix, MCTM VP for Junior High / Middle School
"So how do we build those relationships with our middle schoolers? Let’s face it--their personalities can change by the hour sometimes! Here are a few things I’ve tried- some are the obvious types, others are stolen from #MTBOS folks that are so willing to share…"
This post brought to you by Carol Lucido, the K-8 District Math Coordinator
What if we knew beyond a shadow of a doubt that a particular practice would increase student learning in a profound way? What if this practice had no price tag and was readily available to teachers at all sites? What if we already had time set aside in our calendar to devote to this practice? This exists: we know what to do, it costs us nothing, and we have time set aside to do it.
The practice I am talking about is the powerful practice of developing and giving a common formative assessment, and then analyzing the collected data in Professional Learning Communities.
A Snapshot of How This Might Look in Practice:
My PLC teammate and I meet to discuss what we will be teaching and assessing coming up. We agree to focus on the Prioritized Learning related to creating a strong argument with text evidence.
We agree on a formative way to assess this skill: we’ll both use an outline format called a fishbone analysis. We decide how we're going to score it using the Proficiency Scale that aligns with the Prioritized Learning.
Individually, we both teach the lesson, give the assessment, and score our students' work.
Individually, we look for trends (areas of student success, student struggle, pockets of students who have excelled, pockets of students who seem to have really struggled, etc). Then, we each collect a high, medium. and low example of student work to bring to a future PLC meeting.
Together, we bring our student work to the table and analyze collective trends using our Proficiency Scale.
We create a reteaching and reassessment plan, as well as decide how we're going to continue to challenge those students who have already found success.
We repeat the process. Focusing on the plan created in 'Step F', we loop back to 'Step G.' Eventually. we bring student work back together again and look for new trends, improvements that still need to be made, or additional needs that have arose. The cycle continues until the whole class has mastered this Prioritized Learning and/or until the course comes to a close at the end of the year (or semester, in some cases).
Using and analyzing common formative assessments in this way is a research-affirmed practice. PLCs who engage in this practice consistently see higher student achievement and less of an achievement gap in their classes.
If your PLC is beginning this journey or deepening your practice and would like support, please reach out to any member of the secondary Curriculum and Instruction team. We’d love to help support your work!
This post brought to you by Heather Willman, APOSA overseeing Secondary Curriculum and Instructional Coaching
The History Center of Olmsted County is a valuable resource right in your own backyard. The History Center is here as a resource for the community, and it can help Rochester Public School teachers by offering supplemental services to the classroom as well as be a resource for the students themselves and their families. Today, the History Center of Olmsted County actively serves Olmsted County and SE Minnesota by offering a varied presentation of educational and outreach programs, special events, museum exhibits, a research center, and archives. It also offers endless options and opportunities to visit its beautiful 46 acre grounds. There is, frankly, something for everyone.
Below is a sampling of what the History Center has to offer:
These programs, brought into your classroom by a History Center employee, are each structured to support your students' specific needs and your classroom schedule.
Tours of the Four Historic Buildings
Arrange a bus to come out , or suggest that students come on their own with their parents/guardians, to visit history firsthand by touring a historic building.
Summer Day Camps
Students might enjoy the days of summer by stepping back in time.
An important part of the programming at the History Center of Olmsted County, Living History makes history more engaging. To bring history to life for the public each summer, they hold the Living History Fair--a weekend of interactive events from the 1800s. Young visited often find these activities quite engaging.
Young and old, community members often enjoy these seasonal events.
Plus, the History Center is open to all guests: consider dropping by for a visit! They are open Tuesdays-Saturdays, 9:00 AM to 5:00 PM.
If you would like to know more about how the History Center can support you as a teacher, your students, and their families please reach out to me. I'd love to help you make arrangements or to help you answer any questions.
This post brought to you by Aaron Saterdalen, Education & Programs Coordinator at the History Center of Olmsted County
Connect with Aaron Saterdalen via email or by calling 507.282.9447
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Math + Football
I recently ran across an interesting article complete with video from Sports Illustrated called, “A Calculated Decision: Why John Urschel Chose Math Over Football.” There’s a powerful message at the end about choosing your own path in life that shines through. Plus, his passion for mathematics is inspiring. This would be a great piece to share with your students or could become the foundation of a great new lesson!
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Minnesota STEM Resource Teacher Center
If you're looking for a resource to help you more fully understand the Minnesota Academic Standards in science and math, then check out the Minnesota STEM Resource Teacher Center. SciMathMN (a non-profit business) and the Minnesota Department of Education created the “frameworks” (resources) to help teachers easily translate Minnesota state standards into classroom practice.
From the login, you can search by subject and grade level to find clusters of standards for your courses. (If you don't already have one, you'll first need to create an account.) Within each cluster, you will find pages of information that will bring you deeper into those standards. It's under these heading that you will find a treasure trove of information:
To get a feel for this resource, click on one of the following hyperlinks for a sampling of standards that you teach:
If you would like to explore or discuss these resources with me, or should you like some help implementing these in your classroom, please reach out to me, Dan Devine, or an Instructional Coach. We'd love to help you!
This post brought to you by Carol Lucido, the K-8 District Math Coordinator
In her book Mathematical Mindsets: Unleashing Students' Potential Through Creative math, Inspiring Messages, and Innovative Teaching, Jo Boaler lists six ways to change a ordinary activity into a rich mathematical task. The use of any or all of the six ways described below will increase a tasks "richness" and will help students to think like true mathematicians.
1. Open up the task so there are multiple methods, pathways, and representations.
2. Ask the problem before teaching the method
3. Ask the problem before teaching the method
4. Add a visual component and ask students how they see the mathematics
5. Extend the task to make it 'low floor' and 'high ceiling'
6. Ask students to convince and reason; be skeptical
Incorporating one or all of these six changes does not need to be difficult. I saw a great example while visiting the classroom of a science teacher earlier this week. He was teaching a chemistry class where he was asking students to find the density of irregular shaped objects. The students were given an overflow cup and a very short list of instructions.
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First, watch the following video of Archimedes
Then, design an experiment to measure the density of 4 irregularly shaped objects
Next, create and design a data table for data collection.
Finally, come up with a way to represent your results.
I have personally seen this same activity presented to students with a full set of step by step instructions that take away the students imagination and opportunity to struggle and learn. This way, the task is wide open for the students.
All six of Jo Boaler's ways for making a task rich can be met with this simple set of instructions and with a purposeful instructional pedagogy that allows all students to enter the activity, use their creativity, and explain their thinking Instead of telling the students what to do. This teacher let them figure out what to do and how to represent their results. He did not have to search the internet for a creative and rich tasks on density, he only needed to make simple changes to an activity in front of him.
If you have traditional STEM task that you'd like to develop into a rich one, please do not hesitate to reach out to me. I would love to help you develop your idea.
This post brought to you by Dan Devine, Secondary Implementation Associate
If I had a nickel for every time a student came up to me after a test, the last week of the quarter, or even after report cards were released and asked “What can I do to raise my grade?” I might have been able to retire before I hit the age of 30. At the time it was easy for me to blame each of these conversations on point grubbing or students who didn’t prepare well enough the first time, but the fact of the matter is that I had created a game for them and they were simply playing by my rules. I realize now that the grading system I used in the classroom was a simple translation of the system I had experienced as a student and as a student teacher. In fact, perhaps like many of you, my very first grade book was primarily set up by my mentor teacher, with very little input from me. I didn’t know any better and there were far more important things, in my mind, to worry about than my gradebook. If I had only taken a moment to ask myself a few simple questions I might have avoided utilizing the following counterproductive and/or destructive grading practices:
So what questions would I pose to my first-year-teacher self? There are four of them—simple in nature, but can be very difficult to answer:
These are the four questions that were posed to the Secondary Grading Committee when they created the Purpose and Beliefs document related to grading, as shown below:
I encourage all RPS teachers to review this document and ask yourself these four simple questions.
In subsequent blog posts, I will be sharing some tips and tricks within some of these key grading and reporting areas. In the meantime, I encourage you to talk about grading and reporting with your colleagues and, if you don’t mind a good dose of passion, contact me and I'll join the conversation!
This post brought to you by Brandon Macrafic, POSA focusing on Career & College Readiness and administrator at CTECH
During the Back-to-School staff development days, the vast majority of our elementary and secondary math teachers attended a training on the 8 research-based mathematics instructional practices from NCTM. Participants had amazing conversations about how to make math learning more powerful for all of our students. The million dollar question now is… NOW WHAT? How does this impact my classroom?
It can be daunting to make sweeping changes to your instruction all at one time. Don’t let that deter you – just start somewhere. Here are some first steps you might try!
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Get to know your students as math learners
Pose some questions and ask students to discuss, write, or even draw a picture about their answers…
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Establish positive norms for your classroom and revisit them often
Communicate ideas such as those suggested by Jo Boaler in Mathematics Mindsets:
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As you begin to plan lessons, try to enhance the use of the 8 instructional practices.
Even small changes can have a great impact. As one math teacher shared in the August training, “I started by just having kids talk more and explain their thinking…and it made all the difference!”
Here are a some things to consider (again, from Jo Boaler, Mathematics Mindsets):
Finally, don't forget to give yourself and your students time to grow into these new practices!
This post brought to you by Carol Lucido, the K-8 District Math Coordinator
I drive a manual transmission. If you know me well, this will not surprise you: I like to have control over as much as I can, which includes being in charge of when and how I shift my gears.
As a teacher, I like to start out in first gear just as school gets going, quickly shift into second, and then progress all the way into fourth or fifth gear by the end of first quarter. By second quarter, I shift into fifth (if my students aren't already there) and then into sixth. Once in sixth, I put my classroom on cruise control: speed down that learning highway at 65+ miles for the duration of the year. Of course, sometimes there is construction and I have to downshift mid-year, but as a whole I like to drive my students to their destination at full speed.
But summer: summer for me is for downshifting. Returning to first gear, regrouping, and maybe revving the engine just a little.
This first week of summer, while teachers are "off for the summer," I have had the benefit to work with teachers as they downshift. As they slow down to enjoy the view, revamp their routes, and then rev their engines a bit before we race off again in the fall.
Summer Curriculum Writing
Our secondary teachers gathered this week to predominantly work on creating formative assessments with their PLCs: formatives that align with RPS's newly developedPrioritized Learnings and Proficiency Scales. These new and tweaked assessments will help our teachers enter the school year with a clear map and full fuel-tank.
Pages on the Patio
The first Tuesday after students went home for the summer was the first gathering of Pages on the Patio (sans patio this week because of weather): 26 teachers gathered off-site to simultaneously read, and later discuss, various professional texts that would enhance their instruction. It was 90 minutes of a low gear cruise control, allowing these teachers to really focus on how their car is driving, the sounds of the road, and the direction of the travel.
Summer is the perfect time to downshift. The perfect time to slow down and take in the views, to revamp your map, and to get ready to rev things up again in the fall. So, will you join me on this summer road-trip?
This post brought to you by Heather Lyke, Secondary Implementation Associate
It has been a wonderful first year at CTECH and the students have had some very exciting experiences. Below, see some examples of field trips, guest speakers, mentorships, hands-on activities, and labs that students have participated in this school year.
Our CTECH students have a lot to be proud of and it has been exciting to see the growth and learning that is taking place at CTECH each day. Again, if you haven’t been out to visit yet, please connect and come see what CTECH is all about!
This post brought to you by Erin Broviak, APOSA overseeing Career and Technical Education
Rich Task? Being that it is St. Patrick's Day, I could blog about the leprechaun's search for the pot of gold at the end of the rainbow or talk of my experience searching for the many riches of the Emerald Isle. Instead, however, this post is about rich mathematical tasks as described in so many journals and websites on mathematical instruction, and as has recently been the focus of many conversations about math here in our district.
Question 1: What is a rich mathematical task?
I performed an internet search using the following query, "What is the definition of a rich task?" The query yielded these webpage descriptors:
When reading these three webpage descriptors I asked myself, What teachers wouldn't want their lessons to encourage students to display their learning, perform tasks that are beyond memorization, and generate enthusiasm for learning? The answer: none.
Questions 2: What are the hurdles that slow a teacher's implementation of rich tasks?
Instead of listing all the hurdles, let's focus on getting over the first one. For me, the first hurdle was always the initial experiment. Once I tried a method and found that it had merit, I would proceed forward towards the next hurdle. What I am saying is that the only way to get over a hurdle, is to take a run at it. I have been encouraged by many classroom teachers who are taking a run at the first hurdle and are trying rich mathematical tasks. Our teachers are incorporating a variety of rich tasks in their classrooms and helping students to struggle productively through the use of these tasks. The feedback that I have been receiving from the teachers has been positive: they often find that their students are engaged in meaningful discussions that help to develop conceptual understanding of mathematical concepts.
Question 3: Where can I find the resources I need to take a run at it?
For your convenience, the Secondary Curriculum and Instruction team continues to add links to many high quality websites containing rich mathematical tasks on this website. You can also check out this PDF that succinctly describes the what, where, why, and how to for rich tasks.
Question 4: So, what's keeping you from giving rich tasks a try?
It is often best to make decisions based upon research, so take the time to look into it and then give it a try...you may just find that pot of gold. Now, Go N-Eiri An T-Adh Leat (Good luck) and Slainte (Good health/cheers) to you.
This post brought to you by Dan Devine, aka 'Danny Boy', Secondary Implementation Associate
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