Coding and Positive Changes

Our school is in the midst of the Hour of Code.  This year more than ever, I feel like there’s more of presence of how technology, coding and the curriculum are connected. This is due to a number of factors.  A new superintendent, technology coaches and additional teachers are all playing a positive role with this connection.

This year I intentionally looked for ways to incorporate coding into my math classes.  In the past, the coding was fun and beneficial, but it felt as though it was disconnected from the actual scope and sequence of the curriculum.  It was great during the Hour of Code, but then the whole idea faded once school hit winter break.   While searching for curriculum connections, I came across Brian’s fantastic blog.  I started to find direct curriculum connections that I could use for the Hour of Code.  The two different videos that I used are below. Both were used for a fourth and fifth grade classroom.

Both were great in connecting basic coding and measurement skills.  It was interesting to have kids use their schema, as well as trial-and-error to find out how to calculate the area and circumference.  I gave students an overview of the Scratch blocks and let them figure out the solution.

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I feel like this was useful as Scratch helped reinforce skills that we’re exploring in class.  I look forward to incorporating it a bit more as this week progresses.

Side note:  Earlier in the day one of our technology coaches sent the elementary teachers a Google Doc of different coding QR codes (first and third) that can easily be used with an iPad.  This information is available for all teachers to use as needed.  Some teachers need a starting point and this may provide just that. This is one of the positive changes that I noted above.

What’s your strategy?

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My fourth grade crew has been exploring fractions for the past two weeks.  Students have been making some amazing connections between what they’ve learned before and what they’re currently experiencing.  Last year the same group of students added and subtracted fractions with unlike denominators. The process to find the sum and difference was highlighted and that’s what students prioritized.  That was last year.    Although the process was and still is important, this year’s focus in on application.  How do students apply their fraction computation skills in different situations?  That takes a different skill set.  Being able complete a simple algorithm doesn’t necessarily help students read a problem, identify what’s needed and find the best solution.  More so, I feel like the application and strategy piece trumps the actual algorithm process at this stage.

So, I brought out a fraction recipe problem from last year.

screen-shot-2016-02-26-at-5-26-13-pm Similar to last year, students had to change the recipe based on the amount of muffins needed.  Unlike last year, I didn’t introduce the fraction multiplication or division algorithm.  I had students work in groups and document their strategy to find a solution.

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Students had to indicate whether the number of muffins increased or decreased, by how much and how to change each ingredient.  The group conversations were fantastic.  Groups had a brief conference with me to discuss their strategy once they arrived at a solution.

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The conversations that occurred during my 1:1 meetings with student groups were beneficial.  Students took what they wrote as a strategy and elaborated with different examples.  I’m thinking that students will write in their math journals about their experience tomorrow.  I’m assuming that this will also help transition students towards understanding why the fraction algorithms work.

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Can you tell that I like my new stamps?

Estimating as Part of the Process

 

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My fourth and fifth grade classes explored fraction models this week.  I enjoy teaching about the concept at both of these levels concurrently.   I can see the linear progression of skills associated with fractions and the different perceptions of fractions.  My fourth grade crew is finding equivalent fractions while my fifth graders are multiplying/dividing fractions.   Both groups are finding success, but I’m also seeing similar struggles.  Students are fairly consistent with being able to convert mixed numbers to fractions and combine fractions. Issues still exist in being able to estimate fraction computation problems and determining which operation to use while completing word problems

This year I’ve been focusing in on making sure students are using estimation strategies.  This is especially important when dealing with fractions and eventually decimals.  Unfortunately, I tend to find that time spent on the process (algorithm) trumps the reasonableness (estimate) from time to time.  Part of this is due to past math experiences and time management.  After the last assessment on fractions, I started to look for additional ways to incorporate estimation within my fraction unit.  I came across Open Middle last year and I’m finding their fraction resources to be a great addition.  Both, my fourth and fifth graders completed a few different Open Middle fraction problems this week.

I’m finding that students are estimating a lot more when they are involved in these types of activities.  The tasks I use from OpenMiddle emphasize the need to estimate first and calculate second.  These types of puzzles are interesting for students.  They are low-risk, but yet have a high ceiling.  I also found this to be evident with an activity that I found out of this book. I can’t say enough good things about the ideas and resources found within that resource.

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Students had to find the missing numerator, denominator or variable.  In both, the Open Middle and Make it True activity, student worked in groups of 2-3.   I gave them about 10-15 minutes to collaborate.  The sheet below was adapted from the book above.

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Fifth graders worked on this for 10-15 minutes.  Class discussion followed

They shared ideas, estimated and came to a consensus on what the solution should be. I had the student groups write their answers on the board and the class discussed all the different solutions afterwards.  The class conversation incorporated a decent amount of review and also gave an opportunity for students to ask for clarification.  I’m looking forward to having more classes like this. The class conversation component that occurs after a collaborative effort is starting to become an even more valuable piece of my math instruction.

Self-Reported Grades

The first trimester grading period ended about a week ago.  Soon, students will receive their report card grades and teacher comments.  The majority of teachers in my school have been carefully crafting the right words to be placed on the report card.  These comments often communicate how the students are learning compared to the standard, possible struggles, and next steps to improve their learning journey.  The report cards are usually sent home via backpack and most students gravitate towards the letter grade that is at the top of the report card.  My school isn’t standards-based so that letter grade is often a place of emphasis. The rest of the report cards components come secondary.  I’ve noticed this trend for years.  This year I’m changing up this process to help students understand and reflect on their own learning before they receive their actual report cards.  I decided to create an activity based on Hattie’s self-reported grades influencer.

In preparation for this activity I filled out each report card with comments that I thought were appropriate.  These comments mentioned the scope and sequence of math skills explored during the trimester.  They also communicated what students could bolster during the second trimester. I left the actual grade portion of the report card blank.  I also left the MS, LS, AC and NI blank.  These were for students to fill out.

I gave each student their partially filled out report card and student file.  The student file contains all of the unit assessments for the first trimester.  Students were also asked to use their math reflection journal during this activity.  This tended to help empower the students as they were given all the tools needed to fill out their own report card.  Before students started to assess themselves I decided to review what the MS, LS, AC and NI meant.

screen-shot-2016-11-13-at-7-21-40-amThis took the most time, but I feel like it was worthwhile as students were connecting how particular math skills fit within certain learning goals. They started to analyze their unit assessments, journal and reflection sheets to determine whether they mastered the skill or not.

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After students filled out their report card I met with them 1:1 for about five minutes.  We had a productive conversation regarding where the student assessed themselves.  Sometimes the students were right on point, while other times they were very critical of their own performance.  The process of reviewing their own performance brought a new meaning to the actual report card.  Some students also asked questions about the comments and asked that certain items to be taken out or added.

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When the report cards come out I find the students have a few different reactions.  Some students shove the report card into their backpack while others critically analyze their results in preparation to answer questions from their parents. In an instant, the amount of effort and time spent in crafting the right words can easily be ignored or highlighted.  I’m thinking that this activity will help students to start to see their report in a different light.  Self-assessing takes time, but this is an activity that I plan on using during the second and third trimesters.

Decimals and Number Lines

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My third grade class is learning about decimals. Students have been identifying place value positions up the hundredths place. So far students have been successful in decomposing numbers into expanded form and using base-ten blocks to compare decimals.

Comparing decimals between the tenths, hundredths and thousandths proved challenging.  I was finding that some student were perceiving that a larger number indicates a greater value (0.1 compared to 0.09). I asked students to place decimals on an actual number line. This was where we ran into a few problems. There was a disconnect between comparing decimals with symbols and comparing them on an actual number line. Students understood how to use the greater, less than and equal sign but became confused once hundredths were introduced. After running into this issue multiple times, I was starting to find that some students could compare decimals, but didn’t understand where to place them on a number line.  Then maybe they didn’t understand the value in relation to a number line?

The next morning I ate my breakfast and paged through Teaching Student-Centered Mathematics, a book that I’ve been using this year.  This resource is a gem and I highly recommend any middle school or even upper elementary teachers to add it to their inventory. After reviewing a few a few different options I came across an activity from NCTM (page 151) that was placed in the book. I thought this might be a worthwhile activity for my third graders. The project asked students to place decimals on a number line between 0 – 1. The project also asked students to explain why they placed each number in a specific location.  I thought this might be a good way to assess whether students can translate their value of a decimal to a number line.   That morning I asked students to use dice, create a number line and explain why they picked each point on the line.

I collected the projects and had to reevaluate whether to proceed with the next lesson. Some students knocked it out of the park with some fabulous answers, while others needed some work. Regardless, it was the high-quality feedback that I was looking for and I was able to quickly address misconceptions.  That was an #eduwin situation.

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Next week students will be adding and subtracting decimals.  That should be interesting as my students use the partial-sums and traditional algorithms.

Grading Practices

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School started about two months ago.  Since then so much has happened and the first trimester is closing upon the school.  Report cards are starting to creep up on teachers and the very busy month of November is knocking.  My school has parent/teacher conferences as well as a bunch of professional development sessions planned for the turkey month.

While thinking back about the last two months there’s a lot that comes to mind.  Specifically, I made a change in my grading policy.  I wrote about that here. I decided to move from a point-based system to something that better resembled a standards-based approach.  It’s definitely not 100% standards-based, but it’s moving towards that model.

Basically, students complete a quiz or project and receive it back with my feedback.   Students either get a M or NY.  If they receive a M they file away the papers.  A NY means that the students are required to redo/change the assignment so that they meet the expectations on the second attempt.  I keep the score on the second attempt.  It’s not a perfect system, but I believe this policy is making positive ground.  My reflections on the first two months of using this are below.

1.)  Students are much less anxious about the quizzes and projects.  Maybe knowing that they get another opportunity allows them to take a risk or try a new strategy that they otherwise wouldn’t have considered.

2.)  I’ve become more precise in what I expect students to complete.  Part of this is due to wanting to make sure that a boat load of students don’t have to redo the assignment because of unclear directions.  I’ve been using a “criteria for success” indicator on each project.  This eliminates the points aspect, but also gives students an opportunity to evaluate their own progress on the assignment before turning it in.

3.)  Students are a bit more assertive in looking at their own misconceptions/simple mistakes when they look at a NY that’s returned to them.  Some students ask for additional help or resources before completing the assignment a second time.  Students aren’t allowed to redo the assignment at home so some have used technology tools in the classroom to research the skill before making a second attempt.

4.)  When I first started using the M/NY criteria I found that time was an issue.  It still is although it’s managed a bit better with some clear expectations upfront.  Students that receive a NY have to redo the assignment before the end of that unit.  Some students finish it on the day I return the sheet, while others wait until close to the last minute. I don’t accept the assignment after the unit is over.

5.)  It’s not perfect.  I don’t think any grading policy is perfect.  It takes students more time to complete assignments, especially if they have to take it twice.  There’s also more feedback involved, which takes additional time.  Also, this policy is in place for assignments, but not necessarily tests.  What happens to students that take more than twice to achieve mastery?  Good question and I haven’t answered that yet.  The district still requires letter grades at the upper elementary level.  My district current doesn’t use standards-based grading, but at some point it may move towards that model.  I’m already seeing positive strides in my own classroom and a slight change in how students view assignments.  It’s more of a focus on moving towards the mastery of a concept vs. look at my points.  We’re making positive progress.

Angle Relationships

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My fourth graders are just about finished with their unit on geometry and measurement.  They classified angles earlier in the week and are now looking at angle relationships.  This is one of my favorite topics to teach as it involves logic and an understanding of basic geometry.  I’m finding that students are becoming better at measuring angles using a protractor.  Using Angle Tangle has helped in that process. They’re able to identify and measure acute and obtuse angles comfortably.  Reflex angles still give them issues, although this is improving as students are able to subtract an acute or obtuse angle from 360 to find the measurement.

Students then moved on to angle relationship skills. When asked to find the missing angle in a triangle they immediately started to look for their protractor.  Students wanted to find the actual measurement without looking at what types of relationships actually exist and if a protractor is needed.  So on Tuesday the class reviewed interior angles.  Students found through patterns that they could split a convex polygon into triangles and find the sum of angles.  This was eye-opening for some students and you could tell that they were relieved in seeing that they wouldn’t have to measure all of the interior angles.

One of the assignments called students to create  polygon and find the sum of angles without actually measuring each interior angle.  Some students were stumped while others students looked at how a triangle’s sum can aid in finding the sum of other polygons.  The student projects turned out well, although some had to redo them as the drawing actually started to get in the way of creating triangles.  This is one of the better projects.

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I could tell that students needed a bit more practice with using angle relationships to their advantage.  On Thursday I asked students to create a qudrilateral using a straightedge.  Students drew arcs to indicate the angles on each vertex.  The quadrilaterals were cut out and the sides of the shape were torn off.  Students lined up the sides and the class had a brief discussion on what they noticed.

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Right away, some students noticed that the arcs didn’t line up.  They also noticed that the four corners actually created a circle. Some even said that the total was 360 degrees. Students checked their work by using a compass to add all of the angles together.  Their prediction rang true.  This was a winning moment as I could tell that students were starting to grasp this concept better.  I gave each student some tape and they tapped together their circle to their folder.  I’m hoping it stays on their folder and in their memory banks.

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