Category: Better Practices

Assessment Retakes

Student assesment retakes have been a controversial topic among educators and parents alike. Some argue that giving students the opportunity to retake a test is necessary to ensure that they have mastered the material. This seems to be more prevalent around the circles that embrace standards-based practices. Others believe that it creates an atmosphere where students are not held accountable for their initial performance. I have seen first-hand how the idea of a retake plays a role in how students approach a test knowing they have a second attempt if the first goes awry.

There are several questions that must be addressed when considering implemeting as assessment retake policy. Where should students retake the test? Some schools may have designated retake days or a flex time, while others may allow students to retake the test during a designated study hall or after school. If it is after/before school, tranportation considerations need to be taken in to account. This can be an issue with invidividual teachers if no time exists for the retake. I know of some schools that build this “flex” time in to their master schedules while other schools leave it up to the teacher to decide if it happens.

Another important factor to consider is how much practice students should have before taking the retake. It is important to ensure that students have a thorough understanding of the material before retaking the test. This may involve additional practice materials or targeted review sessions with a teacher or someone else.

Additionally, it is important to determine how long the period should be between the initial assessment and the retake. Some schools may require a certain amount of time to pass before allowing students to retake the test, while others may allow students to retake the test immediately after receiving their initial grade. My thinking is that a certain amount of time is needed for error analysis and practice to occur before another attempt. Missing classtime for the retake can cause issues down the road.

Leaders should consider whether the retake policy should be implemented school-wide or on a classroom-by-classroom basis. Some schools may choose to have a consistent retake policy across all subjects and grades. Other districts or schools may leave it up to individual teachers to decide whether to allow retakes.

I believe the goal of any retake policy should be to promote student learning and achievement. I wrote about this same topic a few years back and am still refining my thiking on how to make retakes more effective.

Four Weeks Down

Students finished their fourth week of school yesterday.  Routines are fairly established although there have been interruptions with students quarantining during the past two weeks.  Flashes from last year have been making appearances in classrooms as teacher navigate working with Zooming and in-person students at the same time.  I’m hoping this is temporary but no one has the confidence to say that’s the case.  When students remote into a classroom it changes routines and impacts more that what I can write here.  I’m moving forward and attempting to find lemonade in the situation. Looking back at the last month I’ve found ways to engage students differently this year compared to last school year.  This post highlights two of those instances.

Fortunately, this year my students have been able to work in groups. Words can’t express how big of a game changer this is and what a loss it was last year. Breakout rooms were a poor substitution. I’ve been utilizing whiteboards and math stations throughout the classroom.  While students work on tasks I bounce from one group to another to ask questions and to gain an understand of students’ thinking.  During the last few weeks I’ve been reading through Building Thinking Classrooms have been using some of the strategies found within. Being able to give feedback through questioning at the stations and hearing the students’ responses impacts my next steps as a teacher. I’d like to expand the time at stations a bit more as the year progresses and as social distance policies evolve.

Another strategy that seems to be working this year relates to how students interact during brief math conversations. Students are often given a daily math task or question that’s designed to encourage dialogue. Students take turns discussing the strategy or steps involved in attempting to solve a problem.  While one student is talking the other student is giving non-verbal cues that they’re actively listening.  Students are then brought back to the class as a whole group.  I visibly randomly pick students to share what their partner said during that time.  The student that is picked doesn’t offer their opinion about what the partner stated although the strategy is discussed as a class. I’ve used this at least twice every week since school has started and have noticed that students are listening better in their groups. Another bonus is that students are using the strategies that they hear from their partner/class.

I’m hoping to carry both of these strategies forward as the year progresses.  

Considerations for the 21-22 school year

In about three weeks my school starts back up again. I have been told that this upcoming year will be different Last year many school started completely remote and then eased into hybrid as the year progressed. I am assuming there will still be some type of social distancing and masking involved for this year, but it depends on many factors. The next school board meeting along with ISBE guidance will most likely lay the groundwork for what will happen during 21-22.

As I think about August I am tempted to plan out the school year as if it everything is heading back to normal. We are still in a pandemic and our schools should keep that in mind when planning. There are a lot of vocal opinions about masking, vaccines and social distancing that may impact what happens. Instruction last year shifted towards a mostly digital model and my hope is that we do not give up on using instructional components for the new year. Some students experienced success with that model, while others did not. Other students struggled with remote learning and could not wait to get back into the classroom. I would like to believe that schools can and should blend what worked with elearning with the benefits of being back in the classroom. It is not a simple transition and requires additional thinking, but something to consider for August.

Math Breakout Rooms

I was introduced to Zoom breakout rooms last March when my district went remote. Breakout rooms were novel and many teachers started to use them during the last couple months of school. It was one way to get students into smaller groups where they felt more comfortable sharing. They were awkward at first for students and staff but most were able to get their breakout room sea legs by May.

Fast forward to the 20-21 school year. Like many around the nation, my school started the year off completely remote. Having a head start in March helped most teachers get into a routine quickly. Most teachers started to use breakout rooms immediately and were able to see the benefits. The social interaction that usually occurs in-person can’t be exactly replicated, but a form of it can in a breakout room. I’ve been part of some amazing student math discussions in breakout rooms this year. I’ve also been in other rooms that were full radio silence. Some this year have had detailed agendas that students follow while others are more student-directed.

Most of my elementary math breakout rooms consist of 2-5 students. Since we are using a hybrid model I try to match students in-person with those at home. I found early on that partnering up kids in the classroom over Zoom causes major audio issues. Less students participate in the breakout room when there are more than five participants. Generally, students in the breakout room have a specific task or activity. Sometimes the assignment comes from their consumable journal and other times it might be a prompt. Students are usually in the their breakout rooms for 5-15 minutes. We have a 45 minutes block for math. While students are working I pop in and out of the rooms with my camera and sound off. I observe the conversation and ask questions if needed. Most of the time, I visit a room and listen to what’s happening, add something in the chat for that room and then move to the next room. After the breakout rooms close the class has a debrief sessions and I try to have each team discuss their solutions. This strategy has worked out well this year, but I’ve had inconsistent success.

I still have questions.

  • What makes a good breakout room?
  • What’s the ideal room size and time?
  • Does camera on/off matter?
  • How do you manage breakout rooms while teaching in-person and elearners at the same time?
  • Should students share their iPad screen?
  • Do you find annotation through Zoom helpful?

I don’t believe there’s a perfect formula for a breakout room, but there are better practices. Feel free to let me know what has worked in your classroom.

Math Exposure Isn’t Enough

A few months ago I remember sitting in a meeting where teachers were discussing students and their math placements.  The conversation revolved around the topic of whether students should change math placements for the next school year.  For example, should a student stay in a homeroom math class or be part of an accelerated class?  How will we provide additional math support for particular students?  These types of questions tend to occur throughout the school year, but action for the next year often takes place near the end of the school year.

The decision to change placements is based on a variety of factors, but many schools/districts narrow down their criteria using standardized assessment data.  That data is often in the form of achievement, cognitive, and/or even aptitude tests.  Each district that I’ve been in has had a different process to determine subject placements.  This placement process becomes even more apparent as students travel from elementary to middle or middle to high school. Students’ birthdates, norm-referenced test scores, and percentages often take center stage during these decisions.  Sometimes the conversation evolves into whether students would be able to transfer the skills to a more rigorous math program than the one that they’re currently attending.  The conversations are usually productive and emphasize how to best meet the needs of students.

The topic of exposure is often brought up when making these types of math placement decisions.  A quick Google search will bring up one of the definitions – “introduce someone to a subject or area of knowledge.” I have heard on more than one occasion the following paraphrased statements/ideas:

  • If students haven’t been exposed to the content then they won’t be prepared
  • Those students weren’t exposed to above grade level work so they won’t be ready for that class
  •  The reason the student scored at the ___%ile was because he/she was exposed to that skill before the test
  • If they’re not exposed to this class then they won’t take higher-level classes in high school

I feel like these types of phrases are thrown around lightly and in a way that doesn’t hit at a bigger issue  Being exposed to content doesn’t necessarily equate to applying it in different situations.  Showing a students how to complete a specific skill/process doesn’t mean that they fully understand a particular concept.  Students might understand a process, but are limited during the application stage.  Also, educators need to keep in mind whether an above grade level curriculum is developmentally appropriate for students.

I believe the bigger issue here is equity.

  • Are all students receiving high-quality math instruction?
  •  Do the tasks and math routines allow students opportunities to explore mathematics and build solid understandings?  
  • Do students need enrichment opportunities instead of acceleration?
  • Will being exposed to a new curriculum/topic/grade-level be the panacea to move students to a higher math placement?  Is that even a goal?  

So many questions are above and I’ll admit that I don’t have a solid solution for them.  I think we have to go back to what a school/district values. I do know that I want students to be curious about math and dive into its complexities.  Classrooms should develop a culture where taking mathematical risks is the norm.   High-quality math instruction takes investment from a school and district.  Ensuring that this instruction is occurring and support is provided is also important.  Mathematical tasks that encourage students to observe, create, and apply their understanding beats limited exposure any day. Exposure is the first step and it doesn’t end there.

Coordinate Grids and Houses

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My fourth graders just ended a unit on decimals and coordinate grids.  The unit lasted about a month and a test is scheduled for next week.  This unit was packed with quite a bit of review, decimal computation and coordinate grids.  Students were able to play Hidden Treasures, use a 1,000 base-ten block (first time they’ve seen this), and create polygons using points.  One of the tasks that stands out to me for this unit involved a coordinate grid problem.  The problem caused the majority of my class to struggle. It was a great learning experience.  Many students thought they knew the answer initially, but then had to retrace their steps.  I modified the questions a bit from the resource that I used in the classroom. Here are the directions:

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So, many students read this and thought twice as wide meaning they’d have to multiple the width by two.  Even without looking at the diagram they assumed that this was going to be a multiplication problem involving two numbers.  Below the directions came the house and grid

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Even after seeing the diagram, students were fairly sure that they just needed to multiply the width (4) by two.  When digging a bit deeper into what they were thinking I found that students were looking at the height where the roof started (0,4).  Many were absolutely certain that 8 was the correct answer.  I had the students think about the direction and discuss in their table groups what strategy and solution makes sense.  Students had about 3-5 minutes to discuss their idea.  Students reread the directions and then started to gravitate their attention to “as it is” high and then started the problem over again.

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As I walked around the room I heard students say:

What is the actual height?

Does the original width matter?

You have to multiply it by three?

What do you have to multiply?

This is confusing.

I’m not sure about this.

Is this a trick question?

I’ve got it!

How do you know?

I thought the conversation that students had was worthwhile.  I probably could’ve spent a good 15-20 minutes on just the conversation. Fortunately, at least one person at each table starting to think that multiplying the x-coordinate by two wouldn’t work.  When I brought the class back together, I started to ask individual students how their thinking has changed.  Some students were still unsure of what to do.  I brought the class back to the directions and then more students started to make connections.  Eventually, one students mentioned that because the height is six, the width has to be double that, which is 12.  Another student mentioned that the x-coordinate needs to be multiplied by three to equal 12.  More students started to nod their heads in agreement.  The class then moved to the next part of the task.

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Students said that we should write down “multiply the width by three.”  I wanted students to be more specific with this, so I asked the students if that meant that you could multiply and part of the width by three.  The students disagreed.  A few students mentioned that you need to multiply four by three and that could be the rule.  Again, I went back to the directions, which asked students to create a rule.  After more discussion, the class decided that you needed to multiply the x-coordinate by 3.   Students were then asked to fill out a table to show what the new drawing would look like.

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Students were drawn to complete the third row above.  That made the most sense to them since the first two started with zero.  Multiplying the x-coordinate by three would create (12,0).  Most kids were on a roll then and were able to fill out the rest of the table.

On Monday the class has a test on this unit.  Even after the test I’m thinking of spending some time reviewing coordinates and having students actually re-create this house on a grid.  I believe it’ll be useful as later in the year students will start to look at transformations.  This may be a good entry point to that topic.

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Math Intuition

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Over the past two days I’ve been reading and rereading chapter 8-9 in my summer book study. Chapter eight discusses how mathematicians connect ideas.  From what I see in classrooms, this connection of ideas is often directed by the teacher and involves some type of classroom discussion that helps students construct understanding.  Intentionally setting aside time to have math discussions and connect ideas from students is worthwhile.  The prime example of Debbie (the teacher) allowing time for Gunther (student) to put the calendar in the shape of a clock was especially a memorable portion of this chapter.  That opportunity wouldn’t have occurred if the teacher didn’t take the initiative to intentionally plan to use manipulatives to have students construct their own understanding through a math discussion.  Having these student math discussions gives educators feedback in whether students are attempting to make/create connections and whether their overgeneralizing. Creating opportunities for student to make these connections is important.

Chapter nine emphasizes the need for mathematicians to use intuition. I appreciate how the chapter indicates that math is often perceived as a very logical content area.  It’s truly not, but the perception still exists.  Tracy states in the chapter that she’s come to see “mathematics as a creative art that operatives within a logical structure.”  I had to reread this a couple times to let it sink in. I’ve heard it over and over again that someone is “not a math person.”  What I find interesting about this is that mathematical intuition is developed.  Since it’s developed over time it can change.  I tend to tackle this issue quite a bit and address it at the beginning of the school year during Open House. Providing students with opportunities to develop this personal intuition can be a game changer.  It’s up to the teacher and school to create memorable experiences for students to develop math intuition. That’s a responsibility that each teacher takes up when they open their classroom doors. By increasing their math intuition, students may also increase their math confidence. Educators need to carefully think about the different math experiences that we provide for our students.  Those meaningful experiences aren’t always found in general textbooks.

After reading these two chapters, I started to think of what perceived/real barriers stop teachers from intentionally creating these opportunities.

I think sometimes teachers feel as though they’re required to follow word-for-word the scope-and-sequence that’s provided by a district.  This can be the case when a newly adopted text is revealed and teachers are highly encouraged to follow it to a tee.  Some texts even tell teachers what to exactly say, what questions to ask, and predicted student responses.  I’ve been though many different math text rollouts and this occasionally happens.  I see it more at the elementary level though. Having common assessments with a specific timeline that everyone needs to follow can also provide pressure for teachers to fall in line with a particular lesson sequence.  Deviating from that sequence may cause issues. I find that there’s a balance between what a district curriculum office deems “non-negotiable” and room for academic freedom within a sequence.  I’ve been told in the past that a district text is a resource, but for new teachers it may be more than that.  There can be a lot of anxiety, especially if certain parts of your instruction model have to follow a pre-determined sequence and is used for evaluation purposes.

Teachers need to feel comfortable in giving themselves permission to use their own intuition.  That may be easier said than done and it depends on your circumstance.  Despite good intentions, a published text won’t meet the needs of all of your students. I believe that’s why open source resources are frequently shared within the online teacher community. Supplementing or modifying lessons/questions with resources that match the learning needs of your students happens on a daily basis.  Dan’s Ted talk hits on that point.

I believe educators have permission to do this while still meeting a strict scope-and-sequence.  Teacher confidence also plays a role with how willing someone is to try resources outside of the textbook.  Elementary math teachers need to feel empowered to be able to use resources accordingly without feeling as though it’s going to be detrimental in their evaluation.  I think that sometimes teachers don’t exercise their academic freedom to the highest potential because it’s perceived as going against a district’s plan.  Having math coaches available and supportive administration is also important in changing this perception

The work that we do is important.  Creating mathematical intuition happens through repeated experiences.

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Sometimes those experiences are beyond the textbook/worksheet and educators have the ability to make them meaningful.  I’ll be keeping this in mind as I prepare for the new school year.

Inservice Days

Many district are is in the midst of planning their 2016-17 inservice/institute days.  These days, sometimes called PD days, often include communicating initiatives aligned to district goals.  Sometimes school goals are included in this process.  As far as I can remember inservice days have always been part of my school year.  The content is sometimes applicable to what’s happening in a particular school, other times it’s more aligned with a district goal. Most teachers have experienced successful and unsuccessful sessions.

Last night I came across this Tweet:

David asked an important question.  I’m not an expert in the field of PD, but I’ve experienced some amazing and not-so-amazing sessions in the past.  I’ve also put together plans for PD and other sessions.  Through this experience I’ve been able to evaluate PD sessions a bit better.  Below are four questions to consider before putting together a PD session:

 

 

Are there clear expectations?

Being intentional in communicating expectations is key.  I’m not necessarily talking about listing the objectives of the session. I’m more concerned in what participants should be able to do with the information after it’s been delivered.  How will this impact teaching and learning?  Having a clear understanding of what’s expected and a timeline can help avoid confusion.

Is there an explanation of why?

I think this is sometimes missing from PD sessions.  Why are we learning about guided math, reading workshop models, grading practices, etc.?  Giving the why can help people understand the reason for a particular session.  If it’s not explained than staff may feel as though the reason is directly associated with someone not in the school, which may or may not be a good thing.

Will there be opportunities to revisit this initiative?

Educators aren’t generally fans of participating in a PD session that communicates that what’s being discussed will be fully implemented but it doesn’t happen. If the expectations is that all classrooms need to do x, y z than that should actually happen.  Starting an initiative and abandoning it halfway through the year doesn’t help with rapport or climate.  A successful PD session allow opportunities for additional help and follow up as needed.

Is there a reflection opportunity?

This may be more of a matter of personal opinion.  I tend to learn best by reflecting on what I’m learning and finding ways to practically put it into practice.  That reflection can happen after the session but embedding it in the session can be a valuable.  Sometimes a reflection opportunity can reveal itself through follow up conversations.  It also keeps the conversation going to ensure that consistently is occurring in a school/district.

When creating a PD session I tend to consider the questions above.  The questions aren’t always applicable, but it’s a place to start.  Would you add any other questions?

 

 

 

Multi-digit Multiplication Strategies

 

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This past week my third grade class investigated different ways to multiply numbers.  Before diving into this concept I asked the students their thoughts on multiplication.  A few students explained to the class their view on the topic of multiplication.

  • repeated addition
  • double or triple “hopping”
  • using arrays
  • “timesing”
  • Increase the number by “a lot”

Most students were able to showcase examples of the above.  Even though their vocabulary wasn’t exactly spot-on, students were able to come to the whiteboard and show their thinking.

I received different responses from the students when asking them about multi-digit multiplication.  Actually, it was more of a lack of response.  I feel like some of this is due to exposure.  A few students raised their hands and asked to show their process to multiply multi-digit numbers. These students showcased their ability to use the traditional algorithm. The class reviewed this method with a few examples.  Although students were finding the correct product they had trouble explaining the process. Students weren’t able to communicate why it worked or another method to find a solution.

On Tuesday my class started to explore the partial-products algorithm.  Students were able to decompose individual products and find the sum.  This made sense to students.  Students were able to connect an area model with the partial-products method.  They started to write number models right next to each partial-product.

Later in the week students were introduced to the lattice method.  This method seemed “fun” for the students, but didn’t make as much sense as the partial-products method.  Students were able draw the boxes and create diagonals to find the product.  Some students had trouble with laying the boxes out before multiplying.

During the last day of the week students were asked to explain in written form how to multiply multi-digit numbers.  Even though all of the students could use the traditional, partial-products and lattice methods, they were stuck for a bit.  Soon, most students started to lean towards using the partial-products method to explain how and why this method works.  I asked one student in particular why it made sense and she said “I can see it visually and in number form.”  Although most students were able to use the other methods effectively they didn’t seem confident enough to explain why the strategies worked.

Students will be expected to multiply multi-digit numbers on the next unit assessment.  The method to multiply these numbers will be determined by the student, but I’m wondering how many will gravitate towards the strategy (not just the process) that they understand.

 

 

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