I was recently chatting with a teacher who is frustrated that every year her students seem to make tremendous progress with the grade-level content they are learning, only to later score Standard Not Met on the CAASPP in Spring. Particularly vexing, she said, is that her students learn the lessons, successfully complete the exit tickets, and even pass the chapter tests her grade-level team co-creates each year.
This is a frustration I hear frequently! How is it possible that we often students who do so well with the math they are learning in the textbook, pass the teacher-created chapter tests, and yet they do not do well on the CAASPP? Almost as s survival technique to live with such frustration, we demonize the CAASPP saying test scores don’t matter. Or maybe the students didn’t take the test seriously enough. Or perhaps the student was just having a bad day.
While some of those reasons might be true, the real reason there seems to be such a gap between the success of “textbook math” and the lack of success with “CAASPP math” is due to the famous Last Mile problem. Once we learn what the last mile problem is we can then identify solutions to it and thereby see the CAASPP results we have always been hoping to see.
What is the last mile?
In the contexts of telecommunications, transportation, and delivery, the last mile is the last leg of a journey. It is often the most complicated and challenging portion of the entire journey.
Shipping widgets thousands of miles across the ocean from the factory to the warehouse is remarkably simple with huge ocean liners. Trucks and a highly-effective highway system move those widgets to smaller warehouses closer to the folks in suburbs and cities who purchase those widgets. It is the final phase of the delivery process in which a delivery person navigates his cargo van through congested surface streets, hunts for homes with addresses long ago obscured by a bushes or trees, comes across locked gates, or has to avoid unleashed dogs…in order to finally deliver the widget.
The last mile of delivery is far more complicated than the first several thousand miles!
The Last Mile problem is so vexing that Amazon sponsored a challenge to encourage participants to create novel solutions to reduce the cost of the last mile of delivery. The winner received $175,000!
It turns out that education has its own Last Mile problem.
What does the last mile look like in education?
There is a rigor gap that exists between the rigor of the textbook and the expected rigor of the CAASPP. As a result, students who seem to be “on track” during the year with the textbook suddenly score below proficient on the CAASPP.
Teaching a new concept for the first few weeks seems simple enough. The last mile problem becomes very evident when the teacher notices a significant gap between the math knowledge the student learned from the textbook and the math knowledge the student is expected to know on the CAASPP exam. We call this gap the “rigor gap”.
How do we solve this last mile problem of closing the rigor gap?
How to solve the last mile problem
We have created a five-day protocol using the FIABs that are freely available on the CAASPP website. Use this protocol once you have finished your textbook chapter and before moving on to the next chapter.
Prior to using the Last Mile Protocol, you will first teach the math content in your math textbook. At the end of the chapter, prior to moving on to the next chapter, you will do the following 5-day protocol. It does not need to be Monday through Friday, but that is the most common approach we have seen teachers use.
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Select FIAB/IAB and create a testing session (select non-standardized administration). Students will work with a partner on the FIAB. Each student will have their own laptop and are expected to work together on each problem. It is recommended that students use scratch paper folded into BOX 6 to show partner thinking! Use CERS to view your data. Identify the most-missed questions that you will use on Tuesday and Wednesday. Video: How to create a test session and then view the results
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Students work on most missed questions (MMQ). Have the students work in groups of three to increase interaction and thought process. (Building Thinking Classroom model or some other student-centered inquiry is recommended.) |
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This is an optional step, you can extend your most missed questions (MMQ) and follow the same instructions from Tuesday or you can proceed to instructions for Thursday. |
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Cleanse the palette. Use Thursday to teach concepts that were most missed using materials other than the FIAB. This could be a Desmos activity or a Kahoot or any other non-FIAB resource. |
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Create a testing session with the same FIAB/IAB from Monday. This time you will have students complete the FIAB individually (select standardized administration). The FIAB scores from Monday and Friday will be available to you in CERS. |
Benefits of the Last Mile Protocol
The first four days of the Last Mile Protocol is an exciting mixture of instruction AND assessment…all at the same time. As students are working with their partner on Monday, the teacher observes the class, noting on a clipboard which students seem to understand the mathematics and which students need help. On Monday, the teacher is welcome to help students with any problems they are struggling with. Sure that means the student will get the answer correct, but the teacher will have ALREADY received the assessment data needed: the student did not know how to solve that problem.
Another benefit (especially for younger students) is they get to experience the user interface of the online CAASPP exam. It is during the Last Mile Protocol that students learn
- How to use the online calculator
- How to enter the answer (especially fractions) to the question. For example 2/7 would be marked wrong, but
is correct.
- The unique question formats that are common on CAASPP, but the textbook likely used more commonplace wording.
- …and so much more
What is the goal?
Once the data from Friday begins to show up in your CERS, what are you hoping to see in the data? Our goal is to have 20% or fewer students scoring in the red band.
Of course it is would be nice to have lots of students in the green band, but your real goal is to teach the ENTIRE class, but measure your success by the percentage of students in the red.
How to support the students in the red?
The six recommendations for supporting students who are struggling:
- Systematic Instruction: Provide systematic instruction during intervention to develop student understanding of mathematical ideas.
- Mathematical Language: Teach clear and concise mathematical language and support students’ use of the language to help students effectively communicate their understanding of mathematical concepts.
- Representations: Use a well-chosen set of concrete and semi-concrete representations to support students’ learning of mathematical concepts and procedures.
- Number Lines: Use the number line to facilitate the learning of mathematical concepts and procedures, build understanding of grade-level material, and prepare students for advanced mathematics.
- Word Problems: Provide deliberate instruction on word problems to deepen students’ mathematical understanding and support their capacity to apply mathematical ideas.
- Timed Activities: Regularly include timed activities as one way to build fluency in mathematics.
Tips for Monday and Friday
It turns out that how the problems are delivered to students has a great impact on whether students show their work or not. When the math problems are provided to the students on paper (like a traditional test from back in the day), students are much more likely to show their work compared to the same problem being delivered on a computer screen.
The MCOE Math Team has discovered that for FIABs, IABs, and the CAASPP itself, a significant number of students do NOT do the necessary mathematics in order to successfully answer the questions. Instead, students often read the question on the screen and simply guess at an answer.
We have done a fair amount of action research trying numerous approaches to increase the likelihood of students showing their work on paper. The most effective (and easiest) way to increase students showing their work in the BOX 6 format. Consider requiring students to show their work in the BOX 6 format.
Students fold a paper into sixths. This creates space for students to show their work on 12 questions. Give students points (or some other reward) for showing their work on the BOX 6 paper. (This is for participation only…not accuracy.)
The BOX 6 approach greatly increases students who are willing to show their work because each of the six little spaces is a discrete area for each problem. The BOX 6 is even more effective than simply giving students a blank piece of paper. There is something magical that happens once students have folded the paper.
In summary
It is essential that teachers incorporate regular use of the FIABs into their pacing and sequencing of their lessons/standards. Waiting until the last couple of weeks prior to CAASPP testing to do “test prep” with the FIABs is simply educational malpractice. There is no other name for it.
Bake an extra week at the end of each chapter to to the Last Mile Protocol before moving on to the next chapter. In doing so, you will have finally solved the Last Mile problem.
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