Day 3 8:30 – Review Comments 8:45 – PowerPoint on misconceptions. Slide 1: Math Misconceptions Slide 2: Three minutes total for slides 2 and 3. Read them to the participants. Slide 3: Ask for comments on the definition. Slide 4: 5 minutes. Read each question and ask for responses. Some misconceptions include: Counting to a million or a million zillion, Trying to apply the digits 0-­‐9 to a clock without understanding beyond 9, Measuring tool, money, saying things they hear adults say. Slide 5: 1 minute. Read and ask for comments. Slide 6: 20 minutes for slides 6 through 12. Why is it important for students to read numbers the correct way? Does it make a difference? Why? What problems could this cause later on? How do we fix this? Slide 7: Ask for comments. Have they seen that this can be a problem? Slide 8: Ideally students have enough exposure to these symbols that they memorize the meaning. Just as they see and write = when they hear or say “equal,” students should see and write < when they hear or say “less than.” To help students before they internalize the meaning, have them analyze the shape. Instead of the segments being parallel like in an equal symbol, which has marks that are the same distance apart on both sides, the bars have been tilted to make a smaller side and a larger side. The greater number is next to the wider end and the lesser number is next to the narrower end. Beware of language here: use “greater” rather than “bigger” because when integers are brought into play “bigger” creates trouble. Slide 9: Read and Discuss. Slide 10: Read and Discuss. Slide 11: Read and Discuss. Slide 12: What problems do you see on this shape poster? (They labeled a shape a diamond. It is actually a rhombus. Diamond is not a shape.) Ask if they have had experience with this issue. Slide 13: 1 minute. Read and ask for comments. Core Academy 2014 Day 3 Slide 14: 30 minutes. Pass out the packet. Explain that they are going to work in grade level groups and read each section carefully, stop after each section and have a discussion about the material. Show them there is a K, a 1st and a 2nd grade example. They have 20 minutes for this and 10 minutes for wrap-­‐up as a whole class. (If they finish their grade level misconception they can read one of the other ones.) After all groups have read their misconception have a spokesperson come to the front of the room and share what their group discussed for about 2 minutes each. Slide 15: 1 minute. Read and ask for comments. Slide 16: 25 minutes. Have participants discuss these questions in groups. Each group makes a chart describing what they talked about. Wrap-­‐up with the whole class. Slide17: Read quote and tell them how awesome they are and that we can use these misconceptions to drive our instruction for the better. We can be prepared for them. 10:15 – Break 10:30 Vocabulary task • 10 minutes -­‐ Have teachers look at the core and make a list of essential vocabulary. • 5 minutes.-­‐ Introduce teachers to the Frayer and the Marzano model for vocabulary development. (See attached pages.) Tell them these are only two ideas for vocabulary. •
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5 minutes -­‐ Group teachers in teams of two. Give each team a math term they got from the core. Have one team member use the Frayer model and the other one use the Marzano model for the vocabulary word. 10 minutes -­‐ Have teachers get with two other groups and share their word definitions. Preferable a K, a 1st and a 2nd grade team grouped together. 15 minutes -­‐ Have a class discussion about why teaching vocabulary with precision is important. How do they teach vocabulary? Share ideas. Why is it important for students to know the definitions of math words and terms? Teaching vocabulary explicitly with help eliminate misconceptions for our students. 11:15 – Lesson Organizer Show the lesson organizer and talk over the parts. • How do you see this helping you in lesson planning? 11:30-­‐ Progressions task Participants will play all the following games. With each version played participants will fill out the lesson organizer in their journals. Discuss the game as a class. Core Academy 2014 Day 3 Kindergarten version. Roll addition. Students roll two dice, add the dots and record the equation. • 1st grade version. 101 and out. Students get six rolls. They must use all six rolls. With the roll students can decide to have it count as ones or tens. For example if a 3 is rolled they can choose to add 3 or 30. The goal is to get as close to 100 as you can without going over. • 2nd grade version. 1001 and out. Play the same as first grade but add 100’s to the place value and have them try to get as close to 1000 as possible without going over. Questions: • How does the repetition in a game allow for practice without redundancy? • Notice the different ways in which the game requires students to compare quantities using place value. • How could teachers reinforce the idea that a digit has a different value depending on its position? 12:00 – Lunch 12:45 – Progressions PowerPoint Slide 1: In this module we cover the place value understanding portions of the progression document for the Number and Operations in Base Ten domain. Our objective is that teachers will understand the way students develop place value understanding and how that understanding supports arithmetic in all four operations. Slide 2: Read and discuss. How does the base ten place value system do what Van de Walle claims? Slide 3: Note that in the core there is a progression of ideas and operations that leads from place value understanding to using strategies for operations to using algorithms for those operations. Thus, place value understanding becomes extremely important. Have participants look at the clusters under each arrow and discuss in small groups how that cluster helps students to move to the next point in the progression. Note that these are just examples. There are many other standards in the core that illustrate the same progression. Slide 4: Ask the teachers to turn to their neighbor and talk about cardinality, one to one correspondence and subitizing. Share what they know with each other. Then hand out the Counting and Cardinality progression sheets from the CC and OA Progression document. Have them read and discuss the various points. Summarize the main points on poster paper. Slide 5: Hand out the Goody Bag Task and the Counting Mat Task . Ask the teachers to read them over and discuss them briefly in their groups. Ask, “How do these tasks help prepare students for place value study?” •
Core Academy 2014 Day 3 Slide 6: Have teachers read the kindergarten section in the NBT progression and discuss it in small groups. What does this standard require of students? Slide 7: Facilitate conversation and collect/chart answers Slide 8: Small Group Discussions – How can tools such as these representations be used to reinforce conceptual understanding of place value? Slide 9: Discuss at your table how to help children deal with the teen numbers in counting and in place value. Then click to the layered place value card idea. Slide 10: Introduce the 5 big ideas of place value on the next slides. Don’t turn to the progression document until you are told to in the instructions. Make certain that teachers have ample opportunities to comment and ask questions as you go through the big ideas. Pause often and ask “Why is this so?” and “Does this really matter?” and the like. Slide 11: Have teachers read the first grade section in the NBT progression and discuss it in small groups. What does this standard require of students? Slide 12: In Kindergarten we refer to ten ones and some other ones. In first grade we talk about 1 ten and some ones. The idea of ten as a unit is introduced. Slide 13: Read and discuss Slide 14: Drawings and place value cards can be used to connect number words and numerals to their base-­‐ten meanings. Eighty-­‐six is shown as “eight tens and six ones” and written as 86 and not as 806, a common Grade 1 error of writing what is heard. Slide 15: Read and discuss Slide 16: Use the hungry caterpillar task in the folder. Be sure to have a copy of the book available! Slide17: Have teachers read the second grade section in the NBT progression and discuss it in small groups. What does this standard require of students? Slide 18: Read and discuss Slide 19: Here is an example of a place value worksheet that you get when you search for “place value worksheets” online. It is also a non-­‐example of work that would elicit conceptual understanding. As you can see, it would not be possible to assess whether your students had a conceptual understanding of place value by them completing this worksheet. It would be fairly obvious to a student who does not understand place value that the first number goes with hundreds, the 2nd number with tens and so on. Even on problem letter h, where it could have asked for deeper understanding, the worksheet places a 0 for tens to eliminate any need for thinking Core Academy 2014 Day 3 Slide 20: Why is this a better way to show conceptual understanding? Discuss. Be sure the following ideas come out.Here is a snapshot of a worksheet practicing place value understanding. You can see how a teacher would be able to assess a student’s conceptual understanding of place value more clearly with the results of this worksheet. In problems 6-­‐8, the base ten units in 106 are bundled in different ways. This is helpful when learning how to subtract in a problem like 106-­‐37. In #9, we see that if the order is always given “correctly,” then all we do is teach students rote strategies without thinking about the size of the units or how to encode them in positional notation. Slide 21: Read and discuss Slide 22: Using base ten riddles like this one from Van de Walle’s book “Elementary and Middle School Mathematics: Teaching Developmentally” helps students think conceptually and flexibly in terms of place value. Exercises like this one can be used as warm-­‐ups, time fillers, or instructionally. Slide 23: Have teachers read the third grade section in the NBT progression and discuss it in small groups. What does this standard require of students? Slide 24: Read and discuss Slide 25: Read and discuss Slide 26: Ask the participants to think about how they could use pictures like this to help students visualize large numbers. Ask the participants to estimate how many people are in this crowd at the Rose Bowl in Pasadena, California. Have them discuss an answer and write it down. Share strategies, tell them Its capacity is 95,542, and, as it is full, the crowd is probably right around that number. Slide 27: Have participants discuss questions. Wrap it up. 1:45-­‐ Find Resources Give participants time to find resources online to focus on getting rid of misconceptions including how to teach vocabulary. 2:00 – Break 2:15 – Continue looking for resources. 2:30 Share Participants share resources they found with the class. 3:00 Videos https://www.teachingchannel.org/videos/math-­‐for-­‐everyday-­‐life https://www.teachingchannel.org/videos/passion-­‐for-­‐math?fd=1 Core Academy 2014 Day 3 Talk about how teachers make math reflect everyday life in their classrooms and why it makes a difference for student learning. How can we help students develop a passion for learning math? 3:15 – Wrap-­‐up, overview of tomorrow, poster comments 3:30 – Dismiss Core Academy 2014 Day 3