I’m sure you’ve never experienced this: things seemed to be going well until you assess, and then you find out you were in dream land! That happened to me after the last mini-quiz I gave my AP statistics students on confidence intervals. Although I gave them the sentence stems in their notes followed by whole class writing practice as well as individual practice, the assessment showed that they really didn’t know what they were talking about…no real surprise!
So I spent last night putting together a card sort on confidence interval statements around the Pink Sweetheart conversation heart activity. I created 16 statements, some written correctly but using different wording, some incorrect, some based on the statements the kids wrote on their assessments. They first had to read through the statements as a group. Then they sorted into correct and incorrect statments. Thats as far as we got today. More tomorrow…..
Today, during our 90 minute period, my precalculus students had a big, 50-minute quiz on rational functions along with solving equations and inequalities for any function combinations. So we had some extra time and I wanted to do a fun activity with them. In walked “Two Truths and a Lie.” Thank goodness I had this already set up. This was a wonderful way for students to practice close reading in preparation for their first quarter midterm which will be all multiple-choice. I have 15 cards ready to go.
My kiddos were so engaged and commented “This really helped me with my vocabulary” and “‘Cuz we had to be ready to defend our choices, I really made sure I could explain our group’s thinking.” Great use of 20 minutes!!
I love multiple choice and true/false questions as vehicles for authentic student argumentation as per the 3rd CCSS Mathematical Practice (highlights are mine):
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
Good MC questions are hard to come by, but even some of the questions from our book create that focal point for students to build an argument, present it to their peers, and critique the reasoning of others. On today’s worksheet, I inserted 8 MC and TF questions along with a GradeCam blank form for students to record their final choices. This gives students a chance to listen to their peers arguments, but have the ultimate decision to accept the choice or go with their own argument.
Once students decide on their choices, they come up to my computer and have their iPad scanned in student mode to see how they did. GradeCam in student mode identifies the problem number of incorrect choices, but does not tell them the correct answer…also keeps it anonymous from other students so the “fear” of public mistakes is alleviated. Students know which questions to go back to and are eager to “fix” their thinking.
One of the things I struggle with is how to give students enough time to be thoughtful while they complete activities but simultaneously not waste time on idle chatter or off-task behavior. In comes “Online Stopwatch,” a free service with a big display.
Today, my precalculus “mathletes” had a check-in on the last two sections. Usually I give about 10 minutes to complete 3 homework questions. Since there is no clock in the front of the room, this time I introduced “the clock” to help them realize they can complete the skill-based formative assessment in the allotted time…in fact, they were all able to finish in less than the required time.
Today I introduced the FRAPPY process to my new AP Statistics students. The term FRAPPY is an acronym for Free Response AP Problem – Yay! and was initially introduced to the AP community by Jason Molesky on his website StatMonkey.
Since this strategy has been a major part of my APS course, the writing and resilience of my students has massively improved. Check it out when you have a chance!
After yesterday’s Holiday Popper activity, I realized my chitlins needed some more practice in writing conclusions to significance tests in AP Stats. I wanted an energizing way to make writing a little more fun. With a quick Google search, I found this cool formative assessment activity on Mr. Orr is a Geek.com called Commit and Crumble. Jon Orr shares how he used the technique with his Algebra 1 class and his instructions are easy to follow.
Since students don’t put their name on the paper, this is an anonymous way to practice, to risk-take, and to get feed-back about their thinking around a problem or question. After my students wrote for 10 minutes, we then proceeded to the Commit and Crumble activity. Here are the directions I gave them:
After they did one round, I had the kids re-toss and re-select another paper. Then use a red pen to add additional comments. I also asked them to discuss the paper they had with their Clock Buddy (so they could see an additional paper). Using their iPad, I suggested that they take a pic of any write-ups that were especially good or helpful to them and attach to their Opener/Exit slips. This way they have a kid-friendly write-up that can be referred to in subsequent situations.
We debriefed the question at the end, highlighting common errors while also discussing the importance of reading the prompt and doing what it says, not what you think it says. The question about significant evidence asked them to write a conclusion statement. However, many proceeded to do the 4-step process. They even calculated the t-value and the p-value when they were already in the given computer printout. We learned some valuable tips for exam taking today! Students said the writing and looking at other papers was helpful to them. We’ll see tomorrow as I will ask them to write a conclusion to submit to me.
PS. Added 3/6
Here is evidence of some students’ choice of a good answer! And they are different papers. Yay!!
I have a stack of crumpled papers and am thinking of having students find their paper (if they want) to see the peer feedback. Here is another resource for the Commit_and_Toss strategy with additional variations. What are some energizing formative assessment ideas you’ve used with success?
It’s hard to believe that I’ve stuck with this challenge for 100 days! Amazing and gratifying!
Today I had one of my formal observations today in AP Statistics. And it is FRAPPY day. The evaluating administrator is a former LA teacher and so the fact that a math class is actually doing technical writing (as per the Common Core English Standards) was well-met. Prior to today’s activity, I shared the Frappy process, the intent of each part and that my students were “well-trained” in the process.
And my students were exemplary! Everything I shared would happen did happen. The students were focused during the writing phase. They collaborated about their answers and adjusted with green pen ONLY after they discussed changes. They thoughtfully discussed the two student answers and wrote suggestions or questions along side the responses. They used the rubric to assess and score their own writing in red while asking clarifying questions about the rubric and the statistical processes and communication. They wrote thoughtful reflections about their level of understanding while also including suggestions to improve their understanding and communication. Here are some examples of their reflections:
During block today, we have started writing inference analysis using the 4-step process in AP Statistics today. I guided the kiddos through a problem, talking through the requirements in each step and what I would consider a complete analysis. Yes, I truly believe guided instruction is necessary at times. I then shared the Inference Procedure Response rubric (I’ve been working on this periodically for my professional evaluation), showing how the 4-step process matches to the required AP curriculum. When students didn’t have any more questions, I asked if they were ready to tackle a problem on their own and they enthusiastically said “YES!” So I had them write up the problem:
In her first grade social studies class, Jordan learned that 70% of Earth’s surface was covered in water. She wondered if this was really true and asked her dad for help. To investigate, he tossed an inflatable globe to her 50 times, being careful to spin the globe each time. When she caught it, he recorded where her right index finger was pointing. In 50 tosses, her finger was pointing at the water 33 times. Should Jordan believe her teacher? Construct and interpret a 95% confidence interval to support your answer.
My students had 15 minutes to work individually. For some. this was a little uncomfortable since I encourage so much collaboration in class. Once they were finished, they exchanged their paper with their 12 o’clock Clock Buddy. I handed out the rubric and had them go through their partner’s paper and assessing each part. I then collected and looked the papers over to check how student-friendly the rubric was, to see if there were any adjustments to the rubric based on its use, and to look at each paper individually.
The process was similar to the FRAPPY process shared by Jason Molesky, a process I use all year to develop good communication and familiarity with the demands of the AP exam. Unlike the FRAPPY process, the rubric process today gave students immediate feedback from peers on their own writing. I wanted my statisticians to see other students’ write-ups to encourage organized presentation of their ideas, which I think happened. I also wanted them to assess a peer’s write-up using the rubric in hopes of re-enforcing the components of a well-written response. It was a wonderful process and I know I’ll use it again.
I used the Navigator today in precalculus to assess their ability to use logarithm properties and techniques. Once the problem was completed, it was submitted through Navigator. Then we looked at the results as a class, deciding if an answer was correct, even if the form of the answer was different. The green indicates correct and grey is not. I then save the results to the Portfolio and use it as a formative assessment score for participation.
This question below was interesting because we talked about the difference between “undefined” and “no solution” which leads back to the leveraging difference between an expression and equation. After the discussion, I agreed to accept both since “they didn’t know” but from now on I wouldn’t accept no solution.
Some kids are so creative in their final answer form, trying to outdo others with the most complicated yet correct answer. After a couple, I had to put a halt to their creativity….but it was fun. They asked for more, too.