Repeat to Understand: Improving Math Discussions through Repetition

When students share their mathematical thinking in a group, it's important that everyone's voice feels heard. One effective technique to ensure this is to have another student repeat the thinking of the person who shared. This strategy, which we saw in many Developing Mathematical Ideas (DMI) videos (as part of the Master of Arts in Teaching Mathematics at Mt Holyoke College), was also recommended by my colleague Louisa for my Student Thinking Assignments in the 2021-22 school year.

There are several benefits to using this approach. First, it amplifies the voice of the student who originally shared their thinking and communicates to the class that their ideas are valued. Second, when a student's thinking is repeated, more students have a chance to hear and understand it. In a busy and distracting classroom, hearing ideas twice can help students pay closer attention. Third, repeating the thinking provides an opportunity to check for understanding. If the repetition is incorrect, we can quickly identify any misunderstandings or communication issues.

Echoing student voices by having another student repeat their thinking is a simple and effective technique to use in your elementary math classroom. It promotes inclusion, helps clarify ideas, and encourages active listening among students.

In your next math class, give it a shot and see how it goes. Then leave me a comment and let me know how it worked for you!

Questions to Reflect & Refine

• In what ways could echoing student voices benefit my classroom math discussions? How could it support student learning?
• How might I use or adapt this technique to suit the needs of my classroom and my students? How might I regularly incorporate this strategy into my practice?
• Can I think of any other strategies to ensure that all my students' voices are heard in math discussions?

Ideas that came up based on feedback from others:

• When students are hesitant or afraid to vocalize their ideas/processes, being the "repeater" is actually much lower stakes. They can still be a part of the conversation, but they don't have to vulnerably share their own ideas if they aren't ready to, yet. (Larry)
• This technique is described above in the context of a small or large group, but could also be a strategy students would use in pairs as a way to show their partner was actively listening. The way the technique is used is dependent on the purpose. (Melissa)
• What happens if the math thinking originally shared is incorrect? Do you still have that thinking echoed? (Melissa)
• Repetition is a super important technique. Students teaching, after gaining expertise, can really boost the repetitions. Giving students multiple modeling opportunities advantages all. (Amy)
• This community has potential to build community. (Judi)
• An important precursor to using a technique like this is to lay out norms and expectations for the group. It is also important students know the purpose; to amplify voices, promote inclusion and clarify ideas. This "echoing" technique shouldn't be looked on as a listening quiz, but rather a chance to restate and reframe. (Louisa)
• When students get used to listening to other students' math thinking and sharing their own thinking, the ownership for learning, thinking and teaching shifts towards the students, giving them agency. (Jennifer) 
• This strategy would be useful in other areas as well, not just in the mathematics classroom (Ashley)

Organizing a Representative Classroom Library During a Global Pandemic

The classroom library is the staple of any elementary teacher's classroom. Making sure that students can access interesting texts at their level is an essential component of our pedagogical approach. We want students to improve their thinking and reading skills, but more importantly, we wish that they develop an intrinsic and deep love of reading.

Selecting and organizing the books is a fun and exciting task, but can be a bit overwhelming as there are many factors to consider. I am aware that these factors have been discussed at length by experts with more education and experience than I have. Nevertheless, I'm interested in sharing what was going through my head as I rebuilt my classroom library in preparation for heading back into the classroom this fall.

• REPRESENTATIVE: The books in our classroom's library should both reflect the perspectives and experiences of the students in my class AND give students the opportunity to learn about and from others' experiences and perspectives different from their own.
• ORGANIZATION: The collection should be organized in a way that makes using (finding books and checking them out & in) the library easy.
• SAFETY: There needs to be a system in place so that books can be borrowed and shared safely during this (hopefully) very unique time of COVID-19.

Windows and Mirrors

“Books are sometimes windows, offering views of worlds that may be real or imagined, familiar or strange. These windows are also sliding glass doors, and readers have only to walk through in imagination to become part of whatever world has been created or recreated by the author. When lighting conditions are just right, however, a window can also be a mirror. Literature transforms human experience and reflects it back to us, and in that reflection, we can see our own lives and experiences as part of a larger human experience. Reading, then, becomes a means of self-affirmation, and readers often seek their mirrors in books.” Dr. Rudine Sims Bishop

Dr. Bishop's words help remind me to include books in my library in which students can see themselves and also books that help them see the world from different perspectives. This is one way they can build empathy for others.

In recent years, I have finally woken up to the reality that my book collection lacks diverse characters, voices, authors and illustrators. Statistics show my collection is representative of all available children's literature. Luckily, publishers are taking note and the availability of books that are more representative of the children we teach is increasing.

To identify and purchase diverse books, We Need Diverse Books (WNDB) is a phenomenal resource. Specifically, I'd encourage you to check out:

• Their OurStory book-finding app (available through any browser or as an Android app)
• Walter Award winners and honoree
• Resources for Race, Equity, Anti-Racism, and Inclusion

"Classroom Library Organization Made Easy!"

In the past, I've organized my classroom library by level because I'm an advocate for helping students find books that are a good fit by their reading level. But I have realized recently that paying too much attention to a book's relatively arbitrary reading level is problematic for a variety of reasons.

For now, I'll stick to organizing my library like a book store, by topic, so kids can find what interests them easily. Helping students understand when a book is "just right" for them will have to be an important part to teaching them how to use the library at the beginning of the year.

Regardless of how I set it up, I knew that I wanted to utilize an app to catalog all my books, something I've never done before. After much Google searching and blog reading, I found that despite some flaws, Booksource Classroom is a fabulous app.

Pros:

• It is FREE!
• The app lets you scan books' barcodes as a way to add them quickly to your library
• The web interface has loads of features that help you audit your library (for diversity, for reading level, etc)
• Families and students can log-in independently to look at what books they have checked out and which books are available

Cons:

• The app and the web interface don't match. The app is good for adding, checking-in and checking-out books but other than those actions, you're better off sticking to the browser version.
• The app doesn't recognize about half of the barcodes that I scan. I wonder if this is because they're outdated? Are my books too old?! I've found a pretty easy work-around though: I look up the current ISBN on Amazon and then use that number to add the books on the web interface. Super slick!

Staying Safe

The pandemic has forced us to rethink the way we "do school" and interacting with our classroom library is no exception. Here are two changes I'm making to make sure my students and I continue to be safe:

• Online Browsing Only. Rather than allow students to physically go through the library in search of a book, I'll have them browse the online catalog through BookSource to find a book that interests them. That way, the only books they'll touch are the books they'll keep to read.
• Book Quarantining. The Preservation Administrators Discussion Group of the American Library Association (PADG) has shared that preliminary research suggests that the COVID-19 virus can only survive on paper/cardboard for 24 hours. To be safe, I'll set up a return system where books returned one day won't be checked back in for 3 days.

Personalized Labels

I had these stickers made at Label Value. The base price is $25 for a roll of 500. Discounts apply when you order multiple rolls. The greater the number of rolls, the greater the discount. I bought 2 and the price was knocked down to ~$20 / roll. Hopefully 1,000 labels is enough! Ha!

Favorite Books

As I scan and label books in my classroom library, I come across many books that I love dearly. 

Wilfrid Gordon McDonald Partridge by Mem Fox is my favorite. 

Personalized Messages

As I open up the inside cover of my books to put on the labels pictured above, I find these personalized messages from people in my life who have gifted me these wonderful books. These messages are so dear to me.

"AJ" aka Aunt Judy

From 2011, when I first joined the third grade team at Kaposia Education Center.

Hidden Surprises

I know this might be an unpopular choice, but I've decided to recycle the dust jackets on the picture books that come with them. I feel like they'll end up getting damaged or lost anyway and I'd rather not deal with that. I only do this, however, if the artwork on the jacket is identical to the art on the front of the book. If that's not the case, I leave on the dust jacket.

As I was taking off this book's dust jacket the other day to see if the art below was an exact match, I discovered this hidden surprise that Yuyi Morales snuck in, and I was so tickled to have found it! Can you spot the difference?

Organizing a representative classroom library in the middle of a pandemic can be daunting, but it has been fun thinking about all the possibilities and putting it all together. It is a constant work in progress though and through continual reflection and hopefully some feedback on this post, I'll be able to continue to add to and improve upon this important staple of my pedagogical approach.

What are you doing that I can't allow?

Almost 20 years ago, I was a 17 year-old high school student heading to southern Colorado to spend my summer working at a camp in the Sangre de Cristo Mountains. As a "camphand" I was preparing myself to clean toilets, wash dishes and do anything else necessary to help the camp run smoothly.

During our 2-week staff training at the onset of the summer, I learned not only how to be a camphand, but also how to help campers who where showing behaviors not allowed at camp. NOTE: I also learned how to drive a stick-shift on the side of a mountain in an old rusty truck nicknamed "The Beast"; but I digress.

That summer, I learned and practiced using a standard set of 3 questions that can help a child self-regulate and independently identify an alternative behavior that is responsible, respectful and safe.

These 3 questions have served me well since because:

• They are quick.
• They give power to the child, without embarrassment or condemnation.
• They keep me calm in the face of a behavior that is irresponsible, disrespectful and/or unsafe. 
• Just like Dr. Sharroky Hollie suggests, these 3 questions help validate and affirm the child, while building and bridging between the students' home culture and language with the school's culture and language.

Any time you encounter a child showing an unexpected behavior at school you consistently ask these 3 questions:

1. What are you doing that I can't allow?
2. Why can't I allow that?
3. What will/should you do instead?

It is important to understand that children will most often answer with "I don't know" or "I don't remember" at least at first. If you encounter this, BE PATIENT! Calmly tell them that that is okay and that you'll give them time to think.

If after giving a student the appropriate wait time you believe that they truly don't know how to answer these prompts, take the opportunity to make it into a teachable moment. Again, this is the Build & Bridge part from Dr. Hollie.

Remember: All behavior is communication. Perhaps a student is running because they think it is a more efficient way to move down a long hallway. Maybe they are talking to an adult in a way that seems rude and disrespectful, because that is the way they've learned to communicate in order to be heard. If a student doesn't know how to read, we help them learn. We also have the responsibility to teach them the skills necessary to be able to demonstrate expected behaviors in school. 

Note: In a recent communication with my former camp director , I learned two things:

• This technique is known as (or based on) "Perception Check". Even after doing a quick Google search on "Perception Check" I'm unable to identify to whom this technique might be attributable. 
• The technique actually involves 4 questions, with the fourth being  "WHAT do you feel you need to do now?" I feel like this question is appropriate when some sort of reparations are called for.

Teaching writing authentically: the WHAT, the WHY, & the HOW

This post was written collaboratively by elementary teachers enrolled in the Alternative Pathway To Teaching program at the University of Minnesota in partnership with Teach For America. The post was edited & stitched together by Ryan Higbea, one of their instructors. As part of CI 5214: Elementary Education Content and Pedagogy IV, teachers are working to understand writing and genre instruction in the elementary school. This post is a synthesis of chapters 1, 2, 4 & 6 of Reading and Writing Genre with Purpose in K-8 Classrooms by Duke, Caughlan, Juzwik, and Martin. Page references throughout the post refer to this text.

Introductory Thoughts

by Gwen

Teaching writing with purpose allows students to see connections between the writing they are learning and their daily lives, while explicitly learning key skills. Genres are not taught in a specific sequence but rather reflect the mixture of text types they’ll see in their daily lives. Writing with purpose allows students to become motivated to write and will engage students to work hard and become more curious about their writing.

The 5 principles (p. 3) that help guide writing instruction are:

• Create an environment that welcomes all communication
• Introduce, through exposure, different types of text
• Explicitly teach genre features.
• Explicitly teach genre-specific or genre-sensitive strategies
• Offer ongoing coaching and feedback

These principles are designed to engage students at different levels to learn these main types of texts: narrative, informative/exclamatory, and persuasive.

What are narrative texts?

by Hannah Bates

Narrative texts share stories about a variety of experiences, for a variety of reasons. Narrative writing is authored by people who have knowledge about a particular experience and can be fiction or nonfiction. It's important to teach narrative writing to empower students to write about their own lived experiences, or historical experiences that have affected them.

When teaching narrative writing, create meaningful assignments that are "larger" than the students themselves. Make them collaborate about something meaningful that will allow them to truly engage authentically. Use mentor texts and modeling to expose students to the components of narrative. Teach genre features, such as setting, plot, details, language, etc. Teach strategies for effectively making sense of narrative texts, like visualizing or rereading for clarity, (p. 22-51).

In the Minnesota Academic Standards for English Language Arts (ELA) K-12, the third benchmark in the writing strand (x.6.3.3) is related to narrative writing.

Narrative – the HOW

by Sarah Ehlen

In my own classroom, after explaining the “what” of narrative, using mentor texts in a variety of narrative types has been crucial in teaching the “HOW.” Young students are natural storytellers, filled with experiences and stories to share. By reading mentor texts and highlighting published authors' “craft moves,” students are able to see different methods of bringing stories to life on the page.

Exemplar mentor texts (like On My Way to Buy Eggs by Chih-Yuan Chen) exposes students to different aspects of narrative writing and gives them an anchor when they want to try a new element of narrative writing themselves. A set of mentor texts is necessary, as well as a variety of paper choices, illustration tools and writing instruments. Students of all stages of writing development should have access to writing materials that allow them to test out craft moves and tell their own stories. Older students, should also use different forms of technology.

Once students begin reading, publishing and sharing their writing, other ELA benchmarks are addressed (x.8.1.1 for example).

The WHAT of Informative/Explanatory

by Callea

“Informational and explanatory” is a broad genre that consists of many sub genres, including but not limited to:

• Textbooks
• Newspaper articles
• Magazines
• Journals
• Websites
• Letters
• Informational pamphlets

Authors of these texts use strategies that we should teach students to use:

• Research by reading texts, interviewing and observing
• Preview texts by skimming and scanning
• Make clear and concise notes
• Summarize
• Capture the gist
• Organize information

The intended audience should be the driving force behind deciding what type of informational text the author will create.

• A textbook for children?
• An informational pamphlet for parents?
• A guidebook for visitors?

Students should get exposure to the text types they are creating and take note of the text features that are predominantly used. These text features can include:

• Information boxes
• Pictures
• Graphics
• Graphs and data
• Paragraphs carefully organized by topic

MN ELA benchmarks related to reading and writing information texts are:

• Informational text benchmarks:
• x.2.1.1
• x.2.1.2
• x.2.5.5
• x.2.6.6
• Writing:
• x.6.2.2
• x.6.4.4
• x.6.8.8

The “How” of Informational Writing

by Will McDuffie

There are five “principles” for teaching informational writing to students (p. 84-108):

• Create a compelling, meaningful environment 
• Introduce interesting topics and graphics
• Design projects around pressing issues
• Provide a real audience
• Follow through (i.e. if you tell students you’re sending their writing to the president, really send it)
• Provide exposure and experience
• Give kids either a teacher model or a mentor text
• Explicitly teach the features of informational texts
• Examples of these features:
• Table of contents, headings/subheadings, index
• Final summary and closing statement
• Frequent repetition of the topic of the text
• Technical vocabulary
• Graphical devices like timelines, diagrams, and flowcharts
• Be influenced by the students’ writing, the needs of their audience, and state benchmarks - not the sequence of mini-lessons from the published curriculum.
• Explicitly teach genre-specific or genre-sensitive strategies
• Strategies for reading and listening
• Strategies for writing and speaking
• Researching
• Planning
• Revising
• Offer Ongoing Coaching and Feedback
• Small group and one-on-one settings

The WHAT of Persuasive

by Freda

The purpose of persuasive text is to influence the reader’s opinion - either subtly or blatantly. Persuasive text is found in many different types in our daily life:

• Editorials
• Blogs
• Magazine articles
• Pamphlets
• Literary essays
• Poetry
• Letters
• Speeches
• Surveys
• Commercials
• Grocery flier
• Campaign flier

Persuasive assignments are often given to students without any real purpose or audience. If students feel their writing has a legitimate purpose and an audience beyond simply the teacher for a grade, they are more likely to be passionate, excited and highly involved in the actual writing because it matters.

Years ago, my son’s teacher challenged her second graders to think of their favorite restaurant and the reasons why it is their favorite (related MN ELA related benchmark: 2.6.1.1). Students wrote a persuasive piece attempting to influence one of their classmates. My son was so excited about this assignment. 

My son picked Smashburger. Students got to share their essays with one another, they were posted in the classroom and copies were mailed to the local restaurants.

Weeks later, my son asked if I would take him to Smashburger for dinner. Upon receipt of my son’s work, the local Smashburger sent coupons to the school as a way of thanking him for his writing. When we redeemed the coupon, I thanked the cashier and she thanked my son for his writing sample!

Now that I am a teacher myself, I think of the extra effort that my son’s teacher went to for this persuasive writing piece to ensure that the assignment had actual purpose to increase student involvement and passion about the writing.

Features that we should teach include:

• Knowing your audience
• Using vocabulary 
• Being creative with arguments
• Beginning with a great launch or “hook” 
• Including rebuttal responses 
• Ending with a strong conclusion

The HOW of Persuasive

by Colin

Several actions MUST be done to teach students HOW to write with persuasion and to support them in their knowledge of a persuasive text. Finding a situation that engages students is essential and once the problem has been identified, find something your students can do to contribute to a solution (p. 142). To identify those problems, think global, act local; in other words, address a real need in their community.

Provide

• Access to resources
• reading texts, watching videos, listening to others’ experiences
• Opportunities to collaborate
• get students talking so they can communicate thoughts and opinions
• Modeling
• model texts from the teacher or the students to show what their work could look like. This will help students produce quality work and meet expected outcomes
• Opportunities to practice
• Give students the chance to communicate effectively, construct arguments with purpose and reasoning, and connect with their audience
• Supports
• graphic organizers (like this one or a bubble map) and support systems can help students structure their arguments

Concluding Thoughts

by Katie

Teachers should keep in mind what being authentic looks like in practice. We may teach the same benchmarks, but we do not use the same goal posts. The needs of students are not necessarily equal. The innately personal aspect of writing necessitates careful contemplation of the needs of our specific students, and just as students must think of their audience when writing, so too should us teachers when planning a project.

The more impassioned by the topic students are, the closer we inch to true engagement. Conversely, without analysis of what an authentic topic means to our specific students, the amount of engagement plummets.

“Children aren’t born knowing”, (p 94), but what they are born with is a need to express, and teaching writing authentically does just that.