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One (Kind) Kindergarten

Hello and welcome back to cycle three of my posts on teaching mathematics in a task-based classroom! This week, I will be talking about how the "formative five" allow teachers to assess tasks in the classroom.

When I am preparing a task for my classroom, I first create a rubric (pictured above). I consider what the goals of the task are: are students generating ideas about how to solve a new type of problem? Are we solidifying understanding they should already have? Are they creating a new representation or algorithm? I do not always use all 4 pieces of the rubric, but instead use the ones that align most closely with my mathematical goals. I define each of these at a beginning, developing, accomplished, and exemplary level.

Conceptual understandings refer to the actual extent to which students understand the mathematics, as evidenced by their work and explanations. Justification and thinking I separate from this, as it refers more to the level of thinking presented in a students answer and in the discussion phase. When developing a rubric, consider the possibility a student is valiantly defending a wrong answer. While their conceptual knowledge might be low, their justification and thinking may still be high-level. I consider the terms and notations (equations, use of correct vocabulary) and the use of tools when applicable (ten frames, hundreds charts, fingers, etc.).

Once I have aligned the task to the mathematical goal, I am ready to think about how I will formatively assess to determine student progress. This is where the "formative five" come into play:

1. Observation: Usually a simple check list, this type of formative assessment allows teachers to quickly assess an entire class or large group. Using the rubric, pick a few things you can check off as you circle the room asking assessing and advancing questions. Prepare your rubric with student names and the few things you are looking for and you can quickly note a YES/NO during the lesson. This is particularly helpful if you want a snapshot of the group of students overall.

2. Interviews: Picking 2-3 key assessing and advancing questions, zero in on students you are seeking to understand better. Record their answers to each, calling back to the rubric to determine how they are developing understandings of the content.

3. Hinge questions: Posed at a key moment in the lesson, a hinge question is given to the whole class. A hinge question can determine whether or not the class is ready to move on, or needs additional time to explore the content at hand. It can be conceptual or procedural. Check these answers immediately and determine next steps.

4. Exit tickets: An old favorite, an exit ticket provides the opportunity for students to show their thinking on a similar problem or problem type that they explored during the task. Graded after the lesson, teachers then determine where the next lesson needs to go.

5. Show me: An obtrusive form of assessment that happens during the lesson. Stop a few students in their work, and ask them to show you their thinking physically, on the current or a different problem. Select these students intentionally.

The task cycle requires many opportunities for formative assessments throughout to determine where the learning goes next. Using rubrics and the formative five can help closely monitor student learning towards key mathematical goals!


Yours,

Ms. M
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Welcome back! I am so glad you are joining in for session two, which will focus ideas for on launching mathematical tasks.

There are several goals when launching a high-quality task:

  1. Eliminate all contextual and linguistic barriers for all students so they can focus on mathematics
  2. Pose a problem
  3. Generate interest
  4. Activate background knowledge
  5. Share logistical information: how long will students have to work? How will they be working (partners, individual, etc.)?



Notice and Wonder
Great for generating interest and for students to be already considering their own questions. 
Show an image, expression, graphic, video, scenario, or representation of a mathematical idea. Draw out noteworthy elements.
Students first see all the things they can "notice" that are obvious from the artifact. Then students brainstorm a list of mathematical questions. When moving into the task, you can select one or more of these questions for students to explore.


Try One
One of the most common concerns raised by teachers is how to launch a task when students don't have the appropriate background knowledge. "Try one" is a great strategy for this because it involves attempting a problem that has similar features or requires a similar thought process as the primary task. This gives students a bank of strategies to try when they approach the task. In order to maintain cognitive demand, ensure the launch is not used to demonstrate how to do the task.



Ways of Seeing
This is essentially a number talk. Show image, expression, graphic, scenario, or representation of a mathematical idea. Pique interest, show noteworthy elements.
http://ntimages.weebly.com/photos.html has many images that can be used to launch tasks, including the one above.

Which One Doesn't Belong? (pictured at top).
Show image, expression, graphic, scenario, or representation of a mathematical idea. Students defend their thinking about which image does not belong and why. There should always be multiple correct answers for best discussion.
Wodb.ca has a ton of images and suites that can be used for this purpose already made!

Three-Read Protocol
This is a launch for word/story problems. The key element of this type of launch is to only make the problem stem available. The word problem should not have a predetermined question. It should only provide context and quantities. 
1. Read one: Teacher reads the problem stem to students. Discussion about what the story is about.
2. Read two: Choral or partner read. Students talk about the quantities in the problem.
3. Read three: Partner/choral read repeated. What is missing to make this a solvable problem?

The goal of this type of launch is to lead students to the key question: What mathematical questions can we ask about this situation?


Make a Conjecture
Students make a quick guess (without enough time to reason through the problem). This gives them something to either verify, disprove, or refine as they begin their work time to solve the problem. This strategy is particularly valuable for abstract tasks.



I hope these ideas give you a fresh way to launch your next mathematical task. Happy teaching!

Yours,

Ms. M

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Hello! I am so happy you are joining me for session one of A New Vision for Mathematics today. Today will be a general overview of what the math task cycle is, its effect on student learning, and the three types of tasks.


One one hand, we have our old way of mathematics: introducing a concept and its vocabulary, teaching strategies, students completing work and then (maybe...) applying to a contextual problem to extend their learning. Imagine the motivation, ownership, and learning if this process was flipped on its head.

First, students develop ideas through a real-world problem or task. Engagement is high and so is cognitive demand. The teacher provides contextual information and tools, but no clear and tried path. No math word or strategy. Students work on their own and with a partner or group--they develop ideas all around the problem. Some students show misconceptions they have about number, some draw models, some develop diagrams, some use mathematics concepts they already know to solve. Answers are both wrong and write. As a class, a rich discussion is held. What happened? Which strategies worked? Which one's didn't? The teacher provides vocabulary and draws out key concepts and mistakes to be learned from. This is known as the "developing" phase.

Next, where does the learning go? Students have many ideas about their new concept, but have not been afforded time to use all the strategies. Teachers will share a targeted concepts--i.e., today, remember what Suzy Q. explained to us yesterday about how she used place value? Let's use that concept to see if it will help us on our task today. Another launch of an engaging task, more work with more focus on a strategy and concept, another rich discussion. Students are solidifying ideas about mathematics--this is the "solidifying" phase.

Finally, students have developed and solidified all important ideas about their mathematics topic. They are ready to work on their accuracy and fluency. The teacher launches a problem string, mathematics game, or task that requires repeated reasoning. The students work and re-work the tasks, focusing on using strategies flexibly and attending to the correct answers in problems. This is the "practicing" stage, and marks the end of the mathematics task cycle.

Because students have built the knowledge themselves, they are likely to take ownership and retain it. Because they built the knowledge conceptually FIRST, they are likely to apply it and have a deep understanding. And all throughout the cycle they have been working on engaging problems and confronting their own misconceptions.

The math task cycle is powerful when teachers use it in the classroom, and can be used to ensure all students have access to deep conceptual understanding. No more "I'm not a math person..." All students can be successful in mathematics through the learning cycle.

Join me next time for a deeper dive into planning for learning in the three stages!

Yours,


Ms. M

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Over the past few weeks, I have been leading each grade levels planning meeting during their planning time. Each hour brings a new grade level and new challenges. This is my first time leading a PLC, and I wrote the proposal and presented it to my administrators. Although I had originally envisioned my trainings as a series of after-school meetings, my administrators offered me three professional days to take to train teachers instead. I spend all day, presenting to K-4. This has allowed me to individualize trainings based on the needs of the different grade levels. It has also allowed me to grow as a teacher and as a presenter.

This experience has been a great way for me to step out of the classroom without stepping out of the classroom. I won’t have enough teaching experience to enter coaching for another few years, but I am interested to see what coaching would look and feel like for me. If this is something I want to pursue, I would ideally have more experience across the grade levels. It is hard for me to reconcile this with my passionate love for kindergarten kids, curriculum, and difference-making. I am still wondering how I will bring these things I am passionate about together in my career. But I have a whole master’s to finish and several years to teach before I need to make any decisions!

The goal of the training was to expose teachers to the mathematics planning cycle in task-based learning, provide support in planning a task with assessing and advancing questions, and discuss formative assessment practices in the classroom.

Over the next few weeks on the blog, I will be elaborating on the training I provided the teachers at my school, and providing some key resources here. If you are interested in task-based learning for mathematics, I hope you will join me along the journey!

Session one: What is the task cycle?

Session two: How do I plan a worthwhile mathematics task?

Session three: Where and how do I assess students?

Yours,


Ms. M

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Welcome back to the blog--I want to talk a little about our mornings today. In my class, there are about 15 minutes from 7:45 to 8:00 where students are in the classroom, but instructional time has not started yet. 

As teachers, we are doing 1 million different things in the morning. Greeting students, accepting notes, collecting forms and money, taking attendance, comforting students, finding breakfasts, and hearing tidbits students have been holding onto since the last time they saw you. Students need to be doing something that is engaging, high-yield, and independent. For me, I hate using paper and making traditional morning work copies, but I also didn't want to go the route of making morning tubs/boxes that would require changing out, upkeep, and planning. I wanted something paperless that would benefit ALL students.

Enter the paperless morning routines! All my students do is come in, grab their journals, and write a sight word sentence with a fill-in-the-blank. This helps students practice sight words, learn new vocabulary, and learn about sentence structure. 15 minutes is the perfect amount of time to fill in the sentence and draw a picture to match. There is also virtually 0 clean-up time required!

For accountability, I call over 1 table each day and give them a smelly sticker or a happy face on their paper for completed work. Students never know which table I will check, so they are motivated to get their work done. They also love the simple pictures and are excited about their topics each day.

For me, no copies, no materials, no prep. Just a PowerPoint slide!

I hope this very simply idea inspires you in your own classroom to simplify your mornings without sacrificing learning!

Yours,

Ms. M
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I love teaching comparing numbers and quantities every year in kindergarten! In kindergarten, these two standards address what kindergartners need to know and do to master number and comparisons:

CCSS.MATH.CONTENT.K.CC.C.6
Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.1
CCSS.MATH.CONTENT.K.CC.C.7
Compare two numbers between 1 and 10 presented as written numerals.
I developed some tasks that are designed to make sure your students go beyond "this one is bigger because 5 is bigger than 3." Ideally, I want my students to masters at least three strategies that they can defend to compare numbers: counting, matching one to one, and using a number path (number line or 100s chart). This is a great task to begin with. Students don't need any formal knowledge of comparing to be successful. Check in with their strategies as you walk around the room to see which strategies students are using. Pick students to present their ideas to the group. During presentations, you can provide the vocabulary (greater than, less than, and equal to). I also let students name the strategies they used--they called them "count," "matching," and "number line."

After completing the tasks and solidifying the strategies used in the tasks, your students might be ready for more of a fluency piece. You can have students partner up to roll dice and compare sets, have them roll and build a greater than, less than, and equal to set, or play "guess my number" while giving less than, equal to, and greater than hints (i.e. "My number is less than 18. My number is greater than 12. What is my number?"). I gave my students number lines to play this game so they could show me their guess.


Compare away! And download 3 comparing tasks below: 
Download Comparing Tasks

Love,

Ms. M

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I am so proud of the littles around this time of year. They are developing so well in their reading and writing skills, all at their own perfect paces.

Kids start to really pay attention to letters and sounds at this stage. They notice when one friend has a "long word" and they begin to venture out into spelling multi-syllabic words. I find this is the perfect time to begin introducing students to sound and spelling patterns that will serve them now that they have even MORE to say!

-ar is a good jumping off point for students because it is in a ton of words that are familiar to them that they might want to use--car, jar, star, start, cart. They will have a blast brainstorming other words that they can hear the sound in--and making up nonsense words with the sound as well.

I introducing the sound and spelling pattern using my district's sound cards which include a phrase "The big dog is barking /ar/ /ar/ /ar/" you can pair with a picture of a dog barking and a hand motion.

You can practice skills such as differentiating words that are spelled similarly, blending onset and rime, reading sentences, segmenting words, etc., throughout the week as you spend between 5-10 minutes reviewing the sound and spelling pattern. Even students who aren't quite ready to use it in their writing will benefit from the exposure and practice.

I love these PowerPoints to get this in to my daily phonics routine. I hope you find them helpful!

Love,

Ms. M

Get the -ar PowerPoint here!
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About Me

I am a third-year kindergarten ESL teacher in Nashville, TN. I have multi-lingual ESL students who come from 12 different countries and speak 10 different languages! I want to share the things I create to use with them, and have a space for other ESL teachers to come for resources and ideas.

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