#MTBoSBlaugust - Solitaire on a Circle Game

I love to ask students to play games. Playing games is a great way to develop problem-solving skills as well as skills in reflection and persistence. While a lot of games can be played electronically these days, there is something to be said for actually sitting down on the floor with some kids and building structures, manipulating shapes, or rolling dice and moving pieces around a board. 

Strategy games are particularly good at helping develop problem-solving skills. I like games that  look simple, but require students to predict,  look for patterns, analyze mistakes, take risks, and learn through  failure. 

Students can play games against others or themselves. I like to have students begin with "solitaire" type  games or puzzles. After they have played several rounds or examples, I have them put their heads together and reflect on their strategies, failures, and successes.  Then I ask them to return to their games to try again.

One puzzle I like is called Solitaire on a Circle. It was conceived by Alexander Bogomolny, a mathematician and web developer who created this as a web-based puzzle. When Java applets were no longer supported on the web, I adapted the puzzle (with permission) for use in the classroom.  

Students look at the pattern in one of the example problems (there are 8 provided) and  place 10 two-color counters on the circle mat. The goal is remove all the counters from the circle. Students begin by removing one yellow counter. When they do this, they must flip any adjacent counters. Play continues  in this way until all counters have been removed or no remaining moves are possible.

If you want to try this with your students, you can download a PDF version for print and play. If you want to try a digital version, download a copy of these Google slides.

That's it for day 5 of #MTBoSBlaugust. I hope you'll come back tomorrow to see what else I have to share. 

#MTBoSBlaugust - LEGO Ordinal Numbers Activity

I spent the 2019-2020 year on sabbatical in second grade. I'm not exaggerating when I say it was one of the best years I've spent in the classroom since moving to Richmond in 1994. I'm still mourning the loss of a full year with the kids, but I still learned so much. I will be forever grateful to the second grade team who became my friends and mentors.

One of the things I enjoyed about my time was creating activities for math instruction. They didn't always hit the mark, but I learned a lot from those experiences. One of the first activities we tried was a LEGO ordinal number activity. While planning for the unit, most of the resources we looked at were worksheets, but we wanted something that required them to apply their knowledge of ordinal numbers. 

The activity I developed required students to use LEGO bricks to build towers. Once the towers were assembled, students identified the color of bricks in certain positions. Here are some sample pages of the tasks and student recording sheets.

This was a very challenging activity early in the school year, particularly with the multi-step directions. There are 6 different task cards and a challenge activity, but most students only got through two examples during their partner work. I wish we could have revisited this later in the year as we continued to review concepts taught. I think student performances would have been different.

If you would like to try this with your students, you can download a PDF version. If you want to edit to change brick colors or numbers, you can download a Word version. All I ask is that you keep the attribution in place.

That's it for day 4 of #MTBoSBlaugust. I hope you'll come back tomorrow to see what else I have to share.

#MTBoSBlaugust - Visual Notebooks

In the spring of 2017 I decided to have students keep a visual notebook for a class assignment. Prior to this, other forms of journals or notebooks included interactive notebooks, double-entry journals, important books, and commonplace books.

I keep a visual notebook along with my students each semester. (I could call these sketchnotes, but because students also  solve problems and complete reflections in these notebooks, I was looking for a more comprehensive term.) Most students are overwhelmed by this assignment in the beginning, but they ultimately embrace the challenge and create notes that far outshine my own. This is particularly satisfying because many of them enter class with a fear of or dislike for mathematics. 

On the first day of class, students receive this visual notebook overview. 

Good mathematics teachers typically use visuals, manipulatives and motion to enhance students’ understanding of mathematical concepts. National organizations, such as the National Council for the Teaching of Mathematics (NCTM) and the Mathematical Association of America (MAA) have long advocated for the use of multiple representations in students’ learning of mathematics. However, for many students in mathematics classes, math is presented as an almost entirely numeric and symbolic subject, with a multitude of missed opportunities to develop visual understandings. 

Recent research indicates that teachers who emphasize visual mathematics and who use well-chosen manipulatives encourage higher achievement for students, not only in elementary school (Reimer, 2005) but middle school, high school and college (Sowell, 1989). 

To engage students in productive visual thinking, they should be asked, at regular intervals, how they see mathematical ideas, and to draw what they see. Drawing mathematical ideas helps mathematics users of any level, including mathematicians, to formulate ideas and develop understandings.

Studies show that we understand things more deeply when we see them from multiple perspectives. Drawing what you have understood from a reading passage, drawing the science experiment you have just done or drawing the detail of an autumn leaf are all examples of engaging with the same learning from a different angle. Compared with writing alone, adding drawings to notes to represent concepts, terms, and relationships has a significant effect on memory and learning (Wammes, Meade, & Fernandes, 2016). Additionally, the benefits of drawing were not dependent on the students’ level of artistic talent, suggesting that this strategy may work for all students, not just ones who are able to draw well.

Reimer, K. & Moyer, P. (2005). Third-graders learn about fractions using virtual manipulatives: A classroom study. Journal of Computers in Mathematics & Science Teaching; 24(1), 5-25.

Sowell, E. J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20(5), 498.

Wammes, J.D., Meade, M.E., & Fernandes, M.A. (2016). The drawing effect: Evidence for reliable and robust memory benefits in free recall. The Quarterly Journal of Experimental Psychology, 69(9). 

I talk a bit about dual coding theory and explain to students that in the context of their own learning and development as a teacher that they must learn to embrace visual literacy as a way of knowing. We then watch the video below and practice making visual notes. We then share our notes and discuss the ideas that stood out for us and the ways we represented them.

Here's an example of my note page.

And here is what my students produced.

Students then receive this single point rubric to guide them as they complete their entries. I also share with them the page of resources devoted to visual notetaking on our class web site.

Students spend a lot of time stressing about the "art" aspects of the notebook. I try to encourage them to keep in mind that their notes are about ideas, not art. I tell them they do not need to be pretty or perfect. It's one of the reasons I notebook along with them, as I draw a lot of stick figures.

Students bring their notebooks to class each week and we begin class in small groups with students sharing and talking through their entries. In this way they are activating prior knowledge, reviewing the content from the previous week, and previewing the work to come. At the end of the semester, they complete a final notebook reflection on their big takeaways from the semester.

Here are some examples of those final entries.

This summer, even though my class was fully online, students still kept visual notebooks. They photographed and uploaded their images for review.  We didn't have opportunities to share and discuss them like I wanted, and I think this lack of sharing really impacted how students viewed their usefulness. I'm thinking hard about what this should look like in the fall and how I can continue to encourage students to doodle their way to understanding.

That's it for day 3 of #MTBoSBlaugust. I hope you'll come back tomorrow to see what else I have to share.

#MTBoSBlaugust - Digital Problem Solving Notebook

I have been teaching some version of a math methods course since I arrived at the University of Richmond in 1994. Over these years the course has changed many times in content and form. As new licensure requirements were recently enacted, we revised our elementary math sequence to include two courses instead of one. Here's the introduction from my syllabus that describes these two courses.

This course is the first in a two course elementary math methods sequence. Both courses offer an in-depth examination of fundamental mathematical concepts and subject-specific pedagogy while emphasizing and integrating state and national standards, problem-solving approaches, use of manipulatives and technology, current research, and learning theory. 

510U focuses on the content of whole numbers and their operations, algebraic thinking in the early grades, measurement, probability, and statistics. 

511U focuses on the content of rational numbers and their operations, algebraic thinking in the later grades, and geometry.  

510U focuses on the pedagogy of guided math, math discourse, and the standards of mathematical practice.

511U focuses on the pedagogy of differentiation and collaborative teaching strategies. It includes a supervised practical experience using a Response to Intervention (RTI) approach that emphasizes using data to make decisions based upon students’ needs, monitor progress, and develop individualized mathematical interventions.

I taught the class for the first time this summer. Because of COVID, it was fully online, a format for instruction I have long avoided. It was a rough 8 weeks. I've thought a lot about the  course and how I can improve upon it for the fall. As we prepare for the semester, the university has asked us to prepare all courses to be fully online, even if we are planning to meet face-to-face. Some students will be opting not to return to campus and will need to access our courses in the same way as students sitting in the  classroom. 

As part of this preparation, I've decided to move one of my traditional paper and pencil assignments to a digital format. I think this will be a good model for preservice teachers to explore as they think about how to deliver online instruction themselves.

I've created this notebook using Google Slides. I plan to use Alice Keeler's terrific Pile of Google Slides to push the notebook to students and update it. Currently, Part 1 of the notebook has 5 entries. Here's a preview.

These are just examples of the direction pages. The notebook opens with a problem solving autobiography assignment. Each week, students work on solving different problem types. Normally, or in pre-COVID days, I would introduce each problem type and solve an example aloud so students could understand my thought processes. Then, students would with a partner or small group to work through some examples together. During the next week, students would tackle more difficult problems on their own and reflect on the strategies they used, where they struggled, and how they worked through mistakes and challenges. When we returned to class the next week, we would debrief the problem type and start on a new one.

This summer my students kept traditional notebooks. We solved problems together on Zoom and they solved problems out of a packet of materials I sent them, but they had to photograph their work and upload the images each week. I think this was pretty cumbersome, so I'm hoping this digital notebook will be easier to use.

I hope others will find this useful. You can download a copy of Part 1 of the notebook. Please feel free to edit and adapt to your own needs.

That's it for day 2 of #MTBoSBlaugust. I hope you'll come back tomorrow to see what else I have to share.

#MTBoSBlaugust - So Much to Share

If you're new here and visiting because of #MTBoSBlaugust, welcome. 

I have been blogging here since November of 2006, so close to 14 years now. I am a teacher educator at the University of Richmond who focuses on preparing future elementary teachers in the areas of math and science (social studies too). In recent years this blog has focused on poetry and children's literature, but math and science are never far from my mind.  Here's a math poem I wrote last year.

During the 19-20 academic year I was on sabbatical in a Title I school working with second grade, where I spent a great deal of time creating math games and other resources for my kids. When school closed and we transitioned to virtual learning, I began to create activities using Google Slides and Drawings. My plan this month is to share some of my experiences and the resources I have created.

In the meantime, there are a few posts you might want to check out while you are here.

• NPM Celebrations - Mathematics Awareness Month (2016) - In celebration of National Poetry Month and Mathematics Awareness Month, both in April, this post shares some of my favorite math poems.
• Math Storytelling Day and Doubling (2015) - This is a post about the classic doubling problem told in the legend of the chessboard. It includes a video and some book suggestions.
• Math Storytelling Day and Infinity (2015) - A post that examines Hilbert's infinite hotel, a related children's book, and some poems on infinity.
• Thematic Book List - Biographies of Early Scientists (through Newton) (2015) - Even though ostensibly named for scientists, a number of these titles focus on figures important in the history of mathematics as well.
• Poetry A-Z: M is for Mathematical (2013) - This post provides an overview of some excellent mathematically-themed poetry books.
• Pi Day is Tomorrow! But Should We Celebrate It? (2013) - This post links to two videos  that ask us to  consider whether considers Tau is better than Pi.
• Mathematically Inclined (2007) - This post contains some excerpts worth reflecting on from The Glass Wall: Why Mathematics Can Seem Difficult, by Frank Smith.

Thanks for visiting. I hope you'll come back this month to check out the resources I'll be sharing.

Poetry Sisters and Friends Write Etherees

This month's assignment was to write an etheree with the theme of foresight or summer or both! An etheree is a poem of ten lines in which each line contains one more syllable than the last. Beginning with one syllable and ending with ten, this unrhymed form is named for its creator, 20th century American poet Etheree Taylor Armstrong.

I haven't been able to get the events that have unfolded since Memorial Day out of my mind, so my poem is really about current events.

A Pair of Etherees for Our Summer of Protest

blind

we were

unaware

so unprepared

for 2020

we rang in the new year

with exaltation, high hopes

but life spiraled out of control

we masked up, marched for George and black lives

determined to meet tomorrow with hope

hope

for change

for justice

for peace, we stand

united by loss

by incredulity

and unfathomable love

John Lewis led, so we follow

in his mighty footsteps we step out

to make good and necessary trouble

Poem ©Tricia Stohr-Hunt, 2020. All rights reserved.

You can read the pieces written by my Poetry Sisters at the links below. As usual, life has gotten in the way for some folks, but they'll be back for other challenges. 

• Tanita Davis
• Rebecca Holmes
• Sara Lewis Holmes
• Kelly Ramsdell
• Laura Purdie Salas
• Liz Garton Scanlon
• Andi Sibley

If you’d like to write with us next month, the theme is hindsight and the challenge is to pick one of your old poems to revise and/or write a new poem in conversation with it. You may use any form you like. We will be posting on the last Friday of the month (August 28) and would love to have you join us.

I do hope you'll take some time to check out all the wonderful poetic things being shared and collected today by Catherine Flynn at Reading to the Core. Happy poetry Friday friends!

Poetry Sisters Go Into the Woods

Tanita set our challenge this month, which was to write to the theme of susurrus or an image of thick woods, in whatever form we choose. For a minute I was completely freaked out by the thought that I had to use the word susurrus in my poem. Nope, not happening. I didn't even try. It's a fun word to say, and the kind that would make a line of iambic pentameter sing, but I just didn't have it in me to expend the time and energy to make it work. That means I decided to go with the woods.

The form I chose is the triolet. A triolet is an 8-line poem that uses only two rhymes throughout. The first line is repeated in the fourth and seventh lines, while the second line is repeated in the final (eighth) line. Because of this, only five different poetic lines are written.  The rhyme scheme for a triolet is ABaAabAB (where capital letters stand for repeated lines).

And guess what? As I wrote several different drafts, I actually found a way to incorporate susurrus (or a form of it), although I feel like this poem needs a glossary. Anyway, gauntlet thrown, challenge accepted, and completed! Here's my triolet.

Into the Woods
How baleful the thick night wood
marked only by slivers of light
the wolf to my red riding hood

How baleful the thick night wood
its susurrations misunderstood

As owls awake and take flight
how baleful the thick night wood
marked only by slivers of light

Poem ©Tricia Stohr-Hunt, 2020. All rights reserved.

You can read the pieces written by my Poetry Sisters at the links below. 

• Tanita Davis
• Rebecca Holmes
• Sara Lewis Holmes
• Kelly Ramsdell
• Laura Purdie Salas
• Liz Garton Scanlon
• Andi Sibley

If you’d like to write with us next month, the challenge is to write an etheree with the theme of foresight or summer or both. We'll be posting on the last Friday of the month (July 31).

I do hope you'll take some time to check out all the wonderful poetic things being shared and collected today by Karen Eastlund at Karen's Got a Blog. Happy poetry Friday friends!