Math Intervention for Enrichment

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This school year I’ve been given the opportunity to work with a select group of second grade math students.  Since early October I’ve been seeing two groups of around 20 students for approximately 30 minutes twice a week.  These 40 students were selected based on unit pre-assessment scores and teacher recommendations.  The second grade students that I see tend to be in need of enrichment of the math skills that they’re exploring in class.  This enrichment can take on many forms, but mainly I’ve been looking at have students develop a better understanding of numbers and patterns.  I’ve been asked to expand on the unit being taught in class and report back progress that students have been making.  The groups that I see are designed to be flexible and change depending on a particular math unit.


 

Here area  few things I’ve observed as the year has unfolded:

1.)  30 minutes twice a week is a short time period.  I’m all for packing in as much instruction as possible, but 30 minutes goes by very quickly.  I’ve had to redesign many of my lessons to overlap the two days in a week.  Retention can also be an issue with this.  I spend each session with a bit of review and that has seemed to help.

2.)  I’ve had to incorporate my own pre/post-assessment to show student growth.  At first I thought this was extremely time consuming as students only have a small amount of time in my class and I want to make sure that the class time is being used appropriately.  This year many of the classes in my school are using the same pre-test as the post-assessment.  I’m using that model right now but it may change as the year progresses.

3.)  I’m not able to meet with the second grade team every week so we decided to use Google Docs as a communication tool.  My students’ pre/post assessment scores are located in the shared doc and can be assessed by any of the second grade teachers.  I also attached a copy of the pre/post assessment to the document so teachers are aware of what topics I’m addressing.

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4.)  I’ve been using effect size to show student growth.  I learned about effect size in more detail after attending a Visible Learning conference over the summer.  I feel like this has been a useful tool and has shown some insight into student gains in my class.  This tool has also been important as it brings some finality to the units that I teach and can be used as one data point in transitioning students in/out of my class.

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5.)  Student reflection is key.  This year I’ve been giving students a copy of their pre-assessment stapled to their post-assessment.  Students are then able to review their growth and ask questions.  The focus is on student growth and not necessarily on point value or grade.  Thankfully at second grade students aren’t used to traditional grades yet.


 

I’m looking forward to seeing how this enrichment opportunity develops over time and the positive impact it has on students.

 

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.

 

 

Posting Daily Objectives

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I’ve been in schools that have highly encouraged teachers to post daily objectives. The topic of posting visible daily objectives has been controversial over the years. I’ve been in many teacher lounges and staff meetings where this topic has been at the forefront.  Social media has also taken aim at the issue.

Lately, the idea of students understanding the daily objective has been highly emphasized in my district.  It seems to also play a role in what administrators are looking for when they drop into the classrooms. This year administrators and teachers are walking through classrooms with a checklist to collect data. One of the items on the list relates to whether the classroom objectives are posted. If so, do students understand the objective and how it applies to their learning?  These are heavy, but quality questions for elementary students to answer.  The data collected will eventually be shared with administration and teachers in order to improve practices.

I believe that students need to have an understanding of the goal for the class. Having an understanding of the expectation is important and can give students a potential goal to keep in mind throughout the class. Also, students should have an idea of what’s expected (criteria for success) to show that they’ve personally met the objective. What I’m finding though, is that how the objective and criteria for success is communicated matters.  Moreover, how students internalize the objective can play an important role in how students perceive the instruction and make connections.

So how are teachers communicating the objectives to students? I’ve observed some classes where the objective is neatly written on the board next to the daily schedule. Students can recite it after quickly swiveling their head towards the board. But does that truly mean that they understand the objective? I would say not in all cases. Teachers are also using “I can” statements to communicate goals.

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Some schools require or highly recommend that teachers use the “students will be able to …” (SWBAT) method. After writing SWBAT on the board the teacher places the objective in the correct place. This standardized approach might be an easy way to ensure that the objectives are posted, but again, I go back to wondering if this impacts learning and is internalized by students. Other teachers are transforming their objectives into kid-friendly language. They’re using verbs that might invoke more student curiosity or interest. Students will “investigate” “wonder” “explore” _____ skill. In addition, teachers are giving students a picture of how the goal will be achieved. In other words, teachers are showing one way in which students will show how they’ll achieve the objective.

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It’s clear that communicating the objective is important. How that’s communicated matters, but it may look different depending the teacher, school, or students.  What are your thoughts?


Links to consider:

ASCD – Know where your students are going

Grant Wiggins and his take on posting objectives

Plans for a New School Year

School is just around the bend
School is just around the bend

As with most summers, this one has gone by quickly. Fortunately I was able to find some time to relax and attend a few different workshops/conferences this summer. One of the highlights was being able to attend a visible learning conference with colleagues from my own school. Being able to purposefully plan with colleagues has it’s advantages.  I also had opportunities to read for enjoyment over the summer and put together some ideas for the new school year. After reflecting on what I’ve been learning I decided to prioritize two personal initiatives for the new school year. The two ideas below are not new, and I feel like they’re obvious to some, but I’m finding deeper reasons for why they’re essential in the classroom. The ideas are general and I expound on them in a narrative first and how I plan on using them in my own practice second. By writing them down I’m hoping to review the ideas throughout the year to see what progress has been made. It’s also a way to keep me accountable.  Here are a few things I want to keep my eye on during this upcoming school year:

Relationships and culture matter

I don’t think educators can say and see this in practice enough. Building a relationship with students in a class matters. It matters to the students on a personal level and helps in the learning process. Although many educators feel pressured to jump right into curriculum, spending time building a community-centered learning space is important. Students learn better when they think their teacher cares about them. Building a classroom community from day one pays dividends throughout the year. Students need to feel like they can make mistakes in the classroom. That doesn’t happen unless students feel safe in the classroom.

I plan on taking the first few days of school to engage students in community building activities. The class will be completing a “get to know you” survey and set expectations for the class. We’ll also be completing the marshmallow challenge and have some rich conversations around math and mindset. I feel like instructional strategies make little impact if students have a fixed mindset. The same could be said for teachers. Before delving into content I want to ensure that the classroom community is moving in the right direction.

Learning is more important than the teaching

Learning happens in a variety of forms. In schools the learning is more important than the teaching. Students often learn when they’re empowered to do so. Teachers can create the right environment and give students strategies to learn, but the learning is ultimately their responsibility. I believe learning needs to be visible to the students and the teacher. Documenting the learning through paper, digital, audio, or video means can give both students and teachers artifacts that can be utilized to show growth.

I‘d like to make learning more visible in the classroom. I’m planning on having students use math journals to reflect and document their learning journey. I’m also planning on using effect size data to show student growth over time. To do this I’ll need to create additional pre-assessments to analyze pre/post data. I’m also planning on moving away from letter grades on unit assessments. Instead, I’m going to have students reflect more on the skills being learned in class.  This is a change from past practices so a lot of modeling may be needed.


School is soon approaching and I’m close to being ready. Most educators that I know are fixing up their classrooms or getting ready to start school very soon. With a new year comes a new group of students and another opportunity to make an impact. How will you make an impact?