Today begins the process of implementing a formative assessment lesson (classroom challenge) from the Mathematics Assessment Project. These classroom challenges involve three parts, a pre-assessment, a collaborative activity, and a post assessment. The goal of pre-assessment is to uncover student misconceptions. The questions are non-routine so students must think critically to answer and thus incorrect ideas surface immediately. You should expect wrong answers as a means of learning more about your students. When you click on the lesson link you will see a page of information about the lesson and I highly recommend you read this material if you are unfamiliar with classroom challenges. The lesson PDF is linked at the bottom of the page. Click on the PDF and scroll down to page S-1. Page S-1 is the student pre-assessment. Copy this pre-assessment for every student as your learning check today.
Each student is given his/her own copy and should work alone. You can clarify the directions of the assessment but do not help students with the questions even though they are sometimes difficult. Tell students before you pass out the papers that this is a pre-assessment for an activity that they will be completing in a few days and some questions may be difficult but do their best to answer every one. This is not a grade but will give you valuable information about what students know and what they still need to figure out before the unit exam. Say whatever you need to so students are not panicked but also so they work diligently and do no give you papers full of IDK. Allow about 10-15 minutes to complete.
The activity today was designed for students to work within collaborative groups. I did not design any example problems that should be demonstrated whole group before the rest is assigned in groups – all problems are assigned to students in their cooperative groups. If your students are struggling to begin these challenging questions you can use a variety of strategies to help them begin.
Strategy One: Mission Impossible – If you have some groups who are successfully working through the problems then you have experts in the room who can act as resources for the struggling groups. I would suggest a Mission Impossible spying session to help struggling groups gather ideas for beginning work. After the spying session, allow groups time to debrief and begin working again as you are moving about the room assessing student progress.
Stragey Two: You could also use Scripting to create a map of ideas to help struggling students. Ask student groups for suggestions of useful ideas to begin working the first problem. Clarify for everyone that you are not looking for a full description of how to work the problem. You simply want to script a variety of ideas for getting started on the problem. Then allow groups time to choose an idea and begin working again. After a time, pull students back together. If one group chose a certain method for beginning then script how they used that idea to work further on the problem. You can stop here and then allow more time to complete the problem before scripting final answers on the board. Always circulate to assess students and provide feedback as students work.
Stragey 3: If students are working through the questions and only a few groups are struggling, much less than 50% of the room, then allow groups to work as you focus your time and attention on providing feedback to groups who need additional support to move forward and be productive.
You could allow this entire class period as a work day and then present answers to the problems on the follow day, but I only recommend this option if almost all your groups are really understanding and you know they are working correctly. Your second option is to again chunk the problems into smaller groups of work so students are working and then coming together for a mini-wrap up of the work they have completed so far. Changing activities gives students something new to focus on and prolongs their attention span. If you spend the entire class period on the second day reviewing answers, it needs to be interactive or else you will lose many to short attention spans.
I would not spend a long time closing the lesson today. You need all the time you can get for students to work and present their thinking. As just a short close to the day you could spend just about five minutes discussing the history of computers and technology. I always like to share my stories of computer class in high school in the 1990's when I need a DOS disk to "start up" my computer. I talked about the internet and how no one I knew in high school had internet. We didn't get a personal computer until my sophmore year and it was huge and used only for typing papers and other processing programs. If you have any old computer parts or old cell phones (a bag phone would be great!) then bring them in and share.
If you have never used a formative assessment lesson (classroom challenge) from the Mathematics Assessment Project then you really need to begin some extensive planning now. These lessons are wonderful and I try to use at least one in every unit because they are so effective at uncovering student misconceptions and then helping me to modify instruction to address those misconceptions. I put a time of five minutes on this section but that is misleading. The time spent on this section will be outside of class and could add up to two or three hours of preparation.
When you click on the lesson link you will see a page full of very valuable information on how to use these lessons. These lessons are very effective when you are very prepared and they are very ineffective when you are trying to "wing-it." You need to read all the materials (the PDF is a packet of teacher instructions and student resources.) This lesson requires cards for the collaborative activity, which you will begin in roughly two days. This means you need to be copying and cutting cards before you begin the activity. I use parent volunteers, aids, office staff, and when desperate students to help cut cards and manage the prep time required. The card sets to be copied (one set for every group) are located on pages S-2 through S-4. I usually paper clip each sheet of cards together and place all clipped sets into a large manila envelop. You want to keep each "type" of card set separate because you give students cards at different times. So for example, the cards on page S-2 would be cut as one sheet for each group. I would cut one sheet apart and clip that one sheet with a paper clip (blank cards and all) and then put them in a large enveloped labeled set A. The cards sets on page S-3 would be copied and cut separately and clipped and placed inside a different envelop labeled as set B. All this cutting and labeling needs to be completed prior to the day you begin the activity.
Also completed prior to the activity is the pre-assessment. When you gather the pre-assessments from today, you have about two days in which to review student answers before beginning the activity. In those two days, you will review the work looking for two things: common student misconceptions in order to generate some guiding questions and to group students homogeneously. When misconceptions surface, and they will, your plan is to find the common group level misconceptions and write some guiding questions that will help students to think about their understanding. This may sound like a difficult task but if you look at page T-3 of the lesson plan PDF you will common student misconceptions that research has proven often occur with this lesson and then some suggested guiding questions. You can use this page to help you get started.
You want to create about four to five class level guiding questions that will be used throughout the activity. You also want to begin grouping students for the card match activity. I recommend grouping students homogeneously. When looking through the pre-assessments (Do not grade these and begin to mark questions wrong or right!!!!! Only assess them for misconceptions - ink pens down!) Pair students together who seem to struggle with the same concepts. You want students to work productively and at the same pace through the card activity. You do not want one student to carry the other but instead for them to work to learn together. If I have students who struggled to complete any questions correctly then I might choose to make these students into a group of three instead of a pair so there will be more support during the activity and these groups are where I focus the majority of my time and feedback. Begin tonight to look over pre-assessments and group students for the activity ahead.