Using Genius Hour Ideas in Math Class

 

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One of my goals last year was to incorporate more student content creation in my classroom. The journey was challenging but definitely worthwhile. Students created a variety of projects that helped showcase their math understanding. There were elements of choice in the projects and I felt like student engagement and curiosity bloomed.

This year I’m trying something different. I’ve always been impressed with the idea of using genius hour in the classroom. What intrigued me was the student choice and engagement piece. The idea of students owning their learning and being intrinsically motivated to participant in the learning process is important. Hearing stories from Paul and Joy inspired me to think of ways that I could apply a genius hour philosophy in an elementary math classroom.

I had a few discussions with colleague and kicked around a few ideas on how to get started. I started off with an informal wonder wall. Students started to generate questions that they would like to answer. I soon found out that this was a challenging task for the students. They weren’t used to this type of assignment. When asked to create a question for the wonder wall they had trouble. Many students asked what I wanted and were unsure of what questions to create.  I showed the students the Google and Siri test. If the question that they came up with could immediately be Googleable or Siriable (words?) then they should probably find another question. This actually worked as the class used some horrible and decent examples. After a while and some modeling, students started to compile a few different questions.

I then placed the different math strands on the whiteboard: geometry, measurement & data, number & operations and algebra. The class then started to sort their questions into the different math strands.

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Students decided on what math strand to emphasize and documented it on their recording sheet. The class then discussed the math genius project flow chart.

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I wanted to give students a bigger picture of what’s going to happen over the next month or so. Since my classes only have about an hour to work on this project a week, it’ll probably take at least a month of sessions to finish. I really have no idea though. It could take a couple of months, but it depends on how the students progress.

After we reviewed the flow chart the class will be moving into the research portion. Students will use a variety of tools/resources to research their topic to find some sort of conclusion. The students will be using the sheet below to document their research.

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So far so good. Next week the classes will continue to research their questions and think about what type of presentation tool they’d like to use. This is definitely a journey and I’ll be documenting our progress through this blog.

Additional files:  Source Sheet Check List

 

Estimating in the Elementary Classroom

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Using Estimation180

My school finished its ninth day of school yesterday. It’s been a journey as students are understanding class routines better.  At this point in the year, students and teachers are starting to become more solid in their processes.  Many of my students arrive to class at different times. Some students are at an elective or leave class a bit earlier/later than the rest of their peers. Regardless of the arrival time, when students enter the room they follow a flow chart. Students have their own folder and materials inside that are ready to go. I usually have some type of visual brainteaser for the week and a grade specific Scholastic math magazine. In the past I’ve used different types of math warm-up activities to start class.

This year I adapted my warm-up strategy. I wanted to individualize the type of responses within that warm-up time slot. After researching a few different tools, I decided to try Andrew Stadel’s Estimation180 this year. I think of Estimation180 as an opportunity for students to develop a stronger sense of numbers and practice estimation skills in the process. Initially, I thought that the site would be great for middle or high school students. I then found the below sheet and site that seemed helpful. This is one way in which student can document their thinking.  The template also includes lessons that could link to Fawn’s Visual Patterns site.

Click to download template

This template inspired me to adapt the sheet to fit an elementary classroom. I changed the template a bit to work with a third grade math class.  A few colleagues and I will be using this sheet early next week.

So now, students enter the classroom, pick up their folder and begin to work on their daily estimation challenge warm-up  sheet.  The estimation is displayed on the whiteboard. Students pick a high, low and exact estimate. I ask the students to prepare to tell me about the reasoning that they used to come to the concluding estimate. The class then completes the online portion of the site and submits a response. We then look at other responses and reasoning.

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After a brief discussion the result is revealed. Students write in the correct numbers and find the + / – . The entire activity takes about 5 – 10 minutes.

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I’m planning on using Estimation180 a few days a week and incorporate Visual Patterns for the rest of the days. The template also includes a few different reflection pieces.  I feel like these activities provide students opportunities to produce a product and reflect on the results. At some point I’d like to add a journaling component to encourage more reflection and possible goal setting.

Creating Classroom Rules for Multiple Classes

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Every school year I give students an opportunity to help create our classroom expectations/rules.  Many teachers use this same strategy. I feel like having students as part of this process is important and often encourages additional ownership since their input is being valued.  The expectations that are created are referenced through the school year.

This year I went with a different strategy for creating our classroom expectations.   After exchanging a few Tweets with William, I was inspired to create one set of expectations for all of my classes.  Keep in mind I teach multiple classes with different students.

To start, I gave each student a Post-it note.  Students were then asked to create two or more rules/expectations that they felt were necessary.  Some students had a huge list while others barely came up with two.  I used this strategy for all of my classes on Tuesday.  All of the responses were collected and compiled.

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This is about 1/4 of the total amount

During that evening I put together all the suggestions in a Google Doc.  I had to combine some of the responses because they were so similar. (click image to enlarge)

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Student ideas

All of the classes voted and came to a consensus.  In the end I tallied up the votes and the class expectations were shown to the students the very next day.  I displayed a graph and the class discussed the importance of the top five expectations. This was also an opportunity to discuss why expectations are needed in schools.

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Reviewing student responses

After a classroom discussion, the top five expectations were chosen.  Students then placed their signatures around the expectations list.

Post-It NotesThe class then created anchor charts that gave clear examples of the different expectations.  I’m planning on keeping the charts up throughout the year and reference them as needed.

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This strategy seemed to work well.  I’m going to put it in my toolbox for future use.  How do you create expectations in the classroom?

First Few Days of School

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In less than a week my school year starts. The first week is so important in helping set the tone and stage for the school year. Usually I take out my lesson plan from last year to start planning out the present school year. Some of the activities are the same from year to year and others I tend to ditch. This post/plan is by no means set in stone, but it’ll be helpful in planning as school is just around the corner. Ideally, I’d like to get to everything noted in this post, but honestly I doubt that will happen.  Flexibility is key here and this is a rough outline.

Keep in mind that I usually see four different groups of students during the first day of school. Each group stays for their math block, which is about an hour.

Day One

For the past few years I’ve always had music on as students enter the classroom for the first time. This year will be no different. Students will enter the classroom and find their own seat. The seats aren’t marked. Once everyone arrives I’ll quickly introduce myself and ask the students about their summer. I ask the students to write down one activity that they participated in this summer that they’d like to share.  Students write this down on a Post-it note. I then take all the notes and read off the activities. Each student then claims their activity and tells the class a bit more about their experience.

The class then reviews the arrival / dismissal flow chart.   This is a time where I open up the floor for any questions. We then have a conversation about procedures within the classroom. This takes about 10 minutes. The class then participates in a hands-on geometry game. It’s similar to a Simon Says, but with geometry terms and movements. The students tend to enjoy this and it’s a time for them to get out of their seat and engage in a different activity related to math.

After a few rounds of the game we all find our seats again and I pass out the student consumable math journals. Students then take out their math supplies and start organizing their accordion file.  I model how the accordion file should look and place the tabs in the correct places. Students label their accordion file tabs and organize their materials. I give each student a class information sheet, curriculum guide and contact sheet. Students get all business-like and start organizing their files.

Then it’s picture time! We all line up in the front of the class and take a class picture. The picture is then usually used during Back to School Night.

Following the class picture students start filling out their hand. Students use a Sharpie and write their name on the hand and place it on the door. It remains there for the entire school year. In some sort of small way I feel like it also encourages ownership.

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Completed hand project

After all the hands have been tapped up on the door we move to the next activity, the puzzle piece community builder. This has been a staple activity for years. The puzzle starts like the picture below.

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I then cut out the pieces and each student creates their own according to the directions.  Students place their name, favorite place to visit, favorite math topic, an interesting drawing or whatever you’d like them to place on the piece.  All students in the class create a puzzle piece and then the puzzle is put together once everyone finishes. Once it’s finished it hangs in the room for the year.

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Students usually have around 10 minutes or so to work on the puzzle piece before they leave to their next class. Near the end of class I remind students of the dismissal flow chart as they leave.

Day Two

While students enter the classroom I’m planning on having the arrival / dismissal flow chart clearly visible. Today students will help create expectations for the classroom. This takes up a good part of the class, but I feel like it’s worth the time commitment. Once the expectations are established, students sign their name and this document is posted on a bulletin board for the year.   I’m planning on having students practice logging into their online math accounts today. This is important because the math student reference book is only online.

Students will also continue to work on their puzzle piece. Today I’m planning on introducing Estimation 180 and the student recording sheet to the class.  I haven’t yet decided on what picture to use, but I’d like to incorporate this periodically throughout the school year.  By end of the class students should (emphasis on should) have finished their puzzle piece. Today I’m also taking pictures of students as they work. I’m looking forward to using our class Twitter handle and Instagram to document our learning journey.  Students will be asked to compile Tweets in their own words that I will send out throughout the year.  This is another way to document our shared math experiences.

Day Three 

Again, students will follow the flow chart that’s posted. I’ll remind students of the expectations that were created yesterday. Students will start to compile the community puzzle of the classes. Today I’ll introduce the math journal to the students. Students will write about their past experiences with math and maybe even write a short version of their math autobiography.   This is a good opportunity to talk about the learning process and how mistakes are valued in this class. I want students to be able to use the math journal as a reflection tool and a place to record their mathematical learning. While students are writing in their journal I generally play sometype type  of music in the background. Students find a comfy place in the classroom to setup their journal time. Once finished, the class will move to a math game/station discussion. Each grade level will play a math game related to their current goal. Some of the more regular games that we play are Angle Tangle, Factor Captor and Name that Number.

Day Four

Today is dedicated to the Marshmallow Challenge. Before completing the activity the class will have a discussion about the importance of being part of a community that’s supportive. We also discuss the math implications of building a tower out of food items. At the end of the time the class will measure all the towers. We then fill out a plus/delta chart indicating what worked and didn’t work. Students usually end this class by having a conversation about team work and building a classroom community of support/trust.

Day Five

Students will delve deeper into their mathematical understanding by completing different types of open-ended/response problems (similar to 1 or 2) in small groups. Students will be asked to explain their thinking and find a solution. Student groups will present their solutions to the class. Many of the open response problems have already been compiled and are found in the district-adopted curriculum. Afterwards, students will be asked to document their experience in their math journals. Students will also login into their Showbie account on their Ipads. Students will be using the iPads to turn in certain math projects throughout the year. Students will be asked to take a picture of their work, annotate their picture and turn it into their Showbie account.  This will also provide students with an avenue to share math work with others.

 

 

 

Thoughts on Questioning Techniques in the Classroom

photo credit: mag3737 via photopin cc

photo credit: mag3737  cc

Every year I find that pairing the right math activity while asking specific questions can yield some amazing student learning experiences. I would assume that most math teachers would agree that only giving a specific solution to a student doesn’t necessarily help them understanding concepts. Offering solutions without feedback or questions can encourage students to care only about finding the answer. The act of “answer finding” limits understanding and diminishes curiosity.

When I started teaching I spoke constantly. I would give examples and statements that I thought would help all my students. Looking back, I spoke more than I should. As I progressed in my career I found that constructing a mathematical understanding doesn’t always ignite from just listening to the speaker.  There’s a time and place for listening, but being engaged in the learning process is vital.  I soon found that a balanced instructional approach was needed so I decreased the amount of talking and started to ask math related questions instead.

Although statements are beneficial, effective questioning techniques can provoke a response from the student. Offering guiding questions, or questions that encourage students to delve deeper in their explanation benefits the student. I feel like part of my job is to create an environment where students are able construct mathematical understanding. When students struggle with that understanding, questioning techniques can be another tool that teachers utilize. Questioning also helps students think more independently and explain their mathematical reasoning in a verbal or written form. Students need to be able to explain why and how they find solutions.  This type of communication is an important skill to develop.  Before planning on using questioning techniques in the classroom there are some important points to consider.

The environment

Students have to be open to answering the questions that are posed. In order for questioning techniques to work, students need to feel comfortable enough in the classroom to offer their ideas and explain their mathematical thinking. This environment is often intentionally built by creating a positive classroom learning community early in the school year.  Students will often participate less if they feel as though their input isn’t valued.

The timing 

Teachers can spend extensive time planning, but I find the best times to use effective questioning techniques are in the moment. Learning can be messy and teachers need to be able to have questions available depending on where students are in their mathematical understanding.   I’ve seen great question techniques used in whole class and small group settings.

 The questions 

The questions that are posed truly matter. When I started teaching my questioning techniques were less than stellar. Through time I’ve learned to expect more from my students. When given a chance, students are fully capable of expressing their thinking. Teachers need to allow students opportunities to do just that. The questions should prompt a response from the student beyond yes or no.  I want to get the students talking about their math process and learning.

 

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Other classroom questioning resources are below.

Effective Questioning Techiques
Asking Questions
Using Questioning to Stimulate Mathematical Thinking
Leveled Math Questions

 

 

 

 

 

 

 

 

 

 

 

Teaching and Scuba Diving

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Last week I took some personal time to disconnect and spend time with my family before school starts up again. While away I decided to swim and snorkel. I’ve always enjoyed snorkeling and watching the life under the ocean. We stayed at a particular facility that had a scuba diving class. My wife and I decided to take the class and learn about the scuba diving experience. The class was great and the instructor gave a basic overview of the equipment and we practiced different skills in a pool before heading out into the ocean. The ocean experience went so well that we decided to pursue a scuba certificate.

The instructor communicated that a certificate would require us to read an instructional book, take a test, practice skills in a pool and then show mastery of the skills in the ocean. That evening I read through the book. The book began with a section on performance-based mastery.  The section explained that students will be instructed using student-centered learning strategies.  Meeting the objectives are what’s important – not how long it takes.  As I read this I felt a bit of weight come off of my shoulders.

Each section had questions that required an answer and then you checked your own answers on the following page. At the end of each section there was a review of the content. After a few hours the book was complete.  The next morning I reviewed the book and my responses with the instructor. Time was given to ask questions. I was then given a 30 question open-book test. In all honesty, I have to admit that I used the book to find some of the answers. The test wasn’t timed and I didn’t feel anxiety during this process. After the test was complete the instructor quickly reviewed the answers and then we jumped in the pool.

The instructor went through specific skills that he showed me in advance. We learned how to clear a mask, check air gauges, and establish buoyancy.  There were many other skills, I just can’t remember them all as I write this post. I’d like to say that I perfectly practiced each skill on the first try, but I didn’t. In fact I commend the instructor for his patience with me. After each failed attempt the instructor gave feedback and we tried again. After about 3 hours we were finished and ready to show the skills in the ocean. My wife and I then went down to the bottom of the ocean to demonstrate the skills needed for a certificate.

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After the ocean dive, I reflected on this learning experience and came up with a few takeaways:

  • I never received a grade or even an official percentage during this process
  • The feedback I received during this journey was clear and could immediately be used
  • I practiced the skill until I was able to independently complete it on my own
  • I was given time to reflect on my performance and ask clarifying questions
  • My documented proficiency was based on my last dive

I also thought of how much more pressure I would have felt if I was graded on each section of the certificate process. I would most likely fixate on each individual grade and not necessarily the skill. Instead, this process had me focus on the skill and the proficiency of that particular skill. I was able to fail, reflect, ask question and retry until I became proficient.  I found the low-risk opportunities to practice were beneficial during this learning experience.  This led me to ask …

How often do educators utilize these strategies in the classroom?  

This is just something I’m considering before school starts in a few weeks.

By the way, we passed the final dive and are looking forward to diving at some point in the future.


photo credit: CaptPiper via photopin cc

 

 

 

Math Acceleration or Enrichment

Acceleration v Enrichment

Acceleration vs Enrichment


A while back I was asked a question about student acceleration and differentiation.  The question related to different types of acceleration opportunities for students that master math content before others. This question is often at the heart of differentiation for high achieving students.  I thought awhile about the question and started to brainstorm what opportunities truly exist or if acceleration is needed in those circumstances.   In an education setting acceleration is often associated with a curriculum that is moving faster or happening at a quicker pace than the norm.

In math at the elementary level, concepts are usually built upon one another and acceleration seems to be valued. Similar to a lattice fence, once one concept has been mastered, teachers often move the student to the next row/concept.  The goal is to continually move students in an upwards trajectory towards the next concept on the ladder.

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Upward trajectory

When acceleration is the focus, students are asked to master and then move to the next numerical concept. For example, If student A has mastered 2.0A.A.1 they automatically move to the next concept, 2.0A.B.2.  Keep in mind that mastery is often defined by the author of the assessment.  Mastery could be correctly answering a few abstract problems in a row or answering 90% of the answers correctly.  In the author’s mind, the faster this process occurs over time the more the student learns.  This isn’t always the case and the perceived notion of learning might not actually be occurring. This is especially prevalent with online adaptive software programs. This type of philosophy often facilitates minimal understanding and can lead to problems down the road.  Also, students that are accelerated are often asked to answer questions more on an abstract level rather then explore mathematics constructively.  Creating a personal level of mathematical understanding is valuable.  Focusing in on only the abstract doesn’t always lead to a learning experience or a better understanding of math.

I believe acceleration has a place in the elementary classroom, but I don’t think that it should be the default.  Honestly, I feel like accelerating is easier than providing opportunities for enrichment. Instead of acceleration why not emphasize enrichment for students that have already demonstrated mastery? I think the word enrichment gets caught up in buzzword land, so here’s a formal definition:

Miram-Webster defines enrichment as the process that improves the usefulness or quality of (something) by adding something to it.

Enriching math instruction doesn’t necessarily mean that students quickly move from one concept to another, but instead it may focus on practical application and problem solving.  Developing strong problem solving skills enhances the usefulness of mathematics.  I find that students benefit when given opportunities to enrich their understanding of mathematics.  In addition, enrichment provides opportunities for students to practice relevant skills that become immediately useful.  Logical thinking, abstract reasoning, and problem solving can all be part of the enrichment process.  All of the skills that are practiced through enrichment activities can be used cumulatively throughout a math curriculum sequence.  The picture below is just one example.

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Enrichment

Students often need to have a foundational understanding of mathematics to be successful at the middle and high school levels. Logical thinking and abstract reasoning skills tend to contribute to the background knowledge for algebra and geometry concepts.  Problem solving is a skill that’s used throughout school and life.  Enrichment opportunities encourage students to use the math learned and apply it to practical situations.  It also enables students to solve problems using trial and error and find multiple solutions.  Perseverance skills are also practiced during math enrichment opportunities.  Instead of completely emphasizing the upward trajectory of concepts, students that experience enrichment opportunities develop skills laterally and may cement a more solid mathematical foundation in the process.  It may also enable students to see mathematics in a new light, not just a lattice of concepts placed in chronological order.  Feel free to review MathwireNRichMaths and Andrew Stadel’s Math Acts,  for a few different examples of how to incorporate math enrichment opportunities.

There isn’t really one right answer to the question found at the beginning of this post.  The solution includes a possible combination of acceleration and enrichment, but immediately leaping to acceleration might not be the best option.

How do you use math enrichment in the classroom?

 

 

 

 


National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors

Enrichment. 2014. In Merriam-Webster.com.Retrieved July 21, 2014, from http://www.merriam-webster.com/dictionary/enrichment

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