Association of Teachers of Mathematics in Maine

Chapters 2 & 3

05 Jul 2018 7:04 PM | Anonymous member (Administrator)

How often do you incorporate pre-assessments as you begin a new unit?


Think about an important topic that you teach and the tasks you use to engage students with the topic. Place the tasks on the Difficulty/Complexity graph on p. 77. What do you notice?

Comments

  • 10 Jul 2018 11:42 AM | Anonymous member
    I pre-assess 75% of my units.

    Looking at the graph on page 77 and thinking about my fraction unit, 50% of the tasks are in the fluency and stamina quadrants. Another 35% is in the strategic quadrant leaving 15% at the expertise level.

    There are some students (20% of students) who master the fluency/stamina levels and to meet their needs, 75% of tasks are at strategic thinking and 25% expertise levels. These students have difficulty struggling through problems, are afraid to fail, and sometimes don't want to take the risk to attempt expertise leveled problems.
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  • 13 Jul 2018 10:39 PM | Anonymous member
    I pre-assess my units more often at the beginning of the year more than at the end so maybe 45%. At the beginning of the year I don't know my students and their abilities so the information gained is very helpful. As the year goes on and the material is less review I don't pre-assess as often.

    Thinking about a solving equations unit that I have at the beginning of the year, students spend 15% of their time in the expertise section. They spend 30% of their time in the Fluency section. The rest of the time is spent on the other two sections about evenly. I think the numbers might be different depending on the particular unit we are studying. I tend to have students work in groups more when they are in the expertise and stamina sections so they can support each other.
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  • 16 Jul 2018 9:18 AM | Anonymous member
    I also do more pre-assessing at the beginning of the school year. It helps to know where students are coming into the new class and what they have retained from the previous year. This helps to plan review for the material that will be needed to proceed with the new topics. As we move into brand new material, I don't pre-assess as often but can quickly regroup or accelerate students into appropriate tasks.

    Expertise level work is often terrifying for some students so by incorporating the difficult parts into other steps along the way in smaller pieces and then having the students work together to see how it all fits together is a little more comforting. Then attempting the difficult parts all at once, first in a group and then also on their own, students can see that even the really difficult pieces are achievable. They don't always want to go on for that difficult accomplishment and about 20% of them will choose not to do the additional individual work. However, I am always thrilled when one of those students finally decides to take on the challenge and then comes to me after and says, "I don't know what I was worried about. I really can do this! Why would anyone not give it a try?" So much of what we do, I believe, is giving students the opportunities to discover their strengths and their own persistent selves. We can tell them every day that they can do it, and we do! But until they make that discovery for themselves it is hard to really believe.
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  • 16 Jul 2018 12:13 PM | Anonymous member
    In our math classroom all units are built into Empower. At the beginning of each unit, learners take a pre-assessment, which is broken up into the individual learning targets. Learning targets build from what should be background knowledge to DOK (depth of knowledge) levels 3 and 4 of the performance indicator (standard). The pre-assessment lets us know where learners are on their learning path to reach proficiency. If learners are proficient in certain areas, they are exempted from those learning targets. This allows for learners to move at their own pace and focus on what they need to learn, not to waste time on skills they already know.

    In our scientific notations unit, learners spend some time with fluency, especially in the beginning when working on the exponent laws, some time on the expertise tasks when working at the DOK 3 and 4 tasks, and the majority of the time working on tasks that are in the strategic and stamina quadrants. I notice that throughout the unit, depending on where they are at on their learning path, they encounter tasks from all four quadrants.
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  • 17 Jul 2018 10:57 AM | Anonymous member
    This summer I am focusing a lot in my intervention groups on strategies for addition and subtraction that have to do with place value, efficiency, and conceptualizing the meaning of addition and subtraction. Many of my students don't know what to do when I give them statements such as "10 more than 56." They don't see the connection between that statement and the equation 56 + 10 = ___. They also don't see how 17 - 3 and 17 - 15 would require different strategies for solving when counting back (17 - 3 would be better solved by "count back from," and 17 - 15 would be best solved by "count back to.")
    So, I start lessons with a number talk to get their strategies out, and then an objective statement. The number talks would fall in Strategic Thinking because they can utilize the strategies they know, but must work to process others' strategies in order to connect them to their own.
    Often I will use a problem solving scenario instead of a number talk and have them discuss the problem and how they would go about solving it, and how to think about the answers they come up with. This is in the same quadrant.
    When we have our active practice it is often an independent or cooperative challenge which either falls in the Stamina or Expertise quadrant depending on what they are ready for.
    The end of a group or class I teach is a time to practice skills that are supplemental to the work we did together. In other words, easier, but necessary to maintain. These fall in the Fluency quadrant.
    This is just an example of how one of my intervention lessons fits into these quadrants.
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  • 17 Jul 2018 10:59 AM | Anonymous member
    Oh, I forgot to mention that pre-assessment is a part of every unit I teach. I have a variety of methods of pre-assessment. Ongoing formative assessment and adjustment of instruction is an essential component of my practice as well.
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  • 18 Jul 2018 9:47 PM | Anonymous member
    It's been our practice to do a pre-assessment for every unit at our school. I know that the 6th grade teachers stick to this pretty consistently. In 7th and 8th grade, less so, teachers claiming they are sure the material is new for their students. It's been a goal to get everyone to use pre-assessments for every unit.

    Thinking about the 6th grade unit Introducing Ratios. The tasks start out very much in the fluency quadrant: low difficulty and low complexity as the students learn the language and recognize what ratios are.
    As the students gain some confidence and understanding, the tasks move to greater difficulty while still being on the low complexity range, Stamina.

    As the unit progresses and students apply previously learned concepts, the problems start to have higher complexity. They may still need some practice with problems in the Fluency an Stamina quadrants, but they can tackle the Strategic Thinking. Toward the end of the unit, they encounter problems that could be described as "Expertise", involving high difficulty and high complexity.
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    • 20 Jul 2018 9:58 AM | Anonymous member
      I wonder if the 7th and 8th grade would be willing to start using pre-assessments which are more diagnostic style or "Am I Ready?" type assessments to get them used to seeing the value in where students are in terms of what will be asked of them in the unit. Also, I was thinking -Sure the material MAY be new to them, but they may have been exceeding the standard in the previous grade level, and often the next step for some teachers to push the students forward is to introduce concepts from the grade up in the continuum. Not that that would be the best idea, but it happens. Also, some students have a natural affinity for algebraic concepts, and could show understanding without having been exposed!
      What I am saying is (and I am most likely preaching to the choir) the grade 7 and 8 teachers may not recognize the value in pre-assessments because they don't know the reasoning behind how the students could have any knowledge of the concepts in the unit, but perhaps if they were to give one, and have a grade level meeting to go over the data, they could discover that there are multiple entry points and levels within the class even having no prior exposure to the concepts in the unit. They might just need to be encouraged and guided through the process?
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    • 27 Jul 2018 12:43 PM | Anonymous member (Administrator)
      That’s awesome! I wish we had more opportunities at a higher complexity,
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  • 27 Jul 2018 12:39 PM | Anonymous member (Administrator)
    Some years I preassess more than others. Last year I found my students felt defeated, so I abandoned the practice. I have had other years where students have been motivated by pretests and have connected the learning back. I plan to do more again this year. I am thinking about just taking a complex problem from the end of the module test, and a couple of discreet skills.

    I would say our text generally provides opportunities in the Fluency and Stamina sections of the grid. In order to incorporate more strategic thinking, I alter the way it is presented in the text. I don’t think I give any tasks in the expertise section. This is definitely an area I could work.
    An example of stamina to me would be a multi step application problem using addition and subtraction for my grade 4 students. Specifically, “the population of Saco is 378,249. Biddeford has a population of 123,486 less than Saco. Portland has a population 597,368 more than Biddeford. What is the population of all three cities?
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