I really enjoyed reading her geometry lesson on pages 96-117. What struck me was that in looking at the outline of her lessons, there were not many paper and pencil activities other than journaling until the latter part of her unit. In the past, this has made me a bit nervous because I like the seeing (in black and white) how they are progressing. I do think that in the long run, this method is better because the students are doing more work (exploring and testing their ideas) than the teacher (making copies/grading assignments). Isn't that the way it should be?
When Ms. Hargrave stated on p. 96, “I believe that if students are actively involved and engaged in learning tasks, especially ones that involve manipulatives, their learning will transfer to more traditional paper-and –pencil activities or test questions when needed,” reinforced something in my teaching style. Math should be very active and hands-on.An A-Ha moment was found on p.100 when I read about Ms. Hargrave using state and country flags in relation to geometry. What a unique idea! Another idea that was reinforced was using a “resident expert” to help teach the class. She called them group leaders. This frees up the teacher to troubleshoot or observe during the class. She describes this in the teacher commentary on p.105.Another idea that was reinforced throughout this unit, for example on p. 111 with the term “asymmetrical” and “polyhedron” on p. 115 is the importance of utilizing and reinforcing the correct vocabulary. I make this a regular practice.When reading Unit 5, Ms. Massey reinforced the concept of using authentic problems and critical analysis on p.128. These reinforced how important it is to make sure we include those things when planning math instruction.An A-Ha moment occurs starting on p. 132 about the students creating a chance chart and she had them use if for later activities. I would like to try this in my math class as it is personally developed by the student so would be motivating, but also a tool used for several things so then the students could refer back to it as well as see how the idea transfers to other activities.Another A-Ha moment is described on p. 135 when Ms. Massey describes the differentiated homework assignments. This is another idea I would like to try more with my students. I have done this somewhat in the past, but this tied in more with students’ interests as well as skill levels.Lastly, another A-Ha moment was involving “board games” on p. 136 as a connection to the concept of outcomes and the probability vocabulary was a unique one as well.
When Brandy B said, "the students are doing more work (exploring and testing their ideas)"I agree that that is what this unit shows.The more active the students are the more they are engaged. Also this makes the learning meaningful as they are exploring concepts andexperiencing the learning.
Looking at this reading through the perspective of a music teacher (trying to develop differentiation in a very limited time allotment) both challenging and enlightening “aha moments” come over me when perusing pre-assessment. (pgs. 101-2) I also see vast possibilities in implementing the charts found on pgs. 120-27. I use many of these techniques at a subconscious level, but in order to reach every student in my classroom, I’d like to adapt these charts to fit projects for my 2nd, 3rd, and 4th grade classes. I really like the idea of providing folders for every student for organizational purposes.
In response to Brandy B:We can also replace our old "pencil/paper" techniques with some of the technological 11 Tools!
My A-Ha moment came page after page as I kept writing ‘Interdisciplinary’ next to almost every strategy. The contributors who submitted these units of study continuously connect them to the many different content areas. On page 100, 112, and 113 the author connects the study of geometry and shapes to national flags. Also on page 106, 107 and 108 just to name a few, the author asks students to write about what they’ve learned and apply their knowledge in writing. The probability unit is full of opportunities to integrate real world problems, solve them and then write about the results of the research. All of these ideas are interdisciplinary-connecting and using all content areas to succeed. I also am impressed and intrigued with the idea of tiered assignments. So many times I have just done the ‘one size fits all’ assignment that worked great for some students-but I now know I wasn’t really meeting the needs of all my students. That’s definitely an idea I’m going to give more thought to and will see how it will works with my students.
One “a-ha” moment occurred when I read the Unit Concepts and Generalizations for the geometry unit on page 96. I like the focus given to structure. I have taught numerous geometry units and it never occurred to me to give them that emphasis. I can see how that focus can make way for more real-life connections.The Geometry Rating Scale described on page 101 reminded me of a similar method I’ve seen demonstrated. The teacher had four posters ranging from stormy skies to a bright, sunny day. Similarly, the students placed their post-its along the continuum according to what they felt their understanding was. The students also can move their post-its as their understanding grows.In the “It’s All a Matter of Chance” Unit, I liked the idea of the chance chart continuums described on page 137. I also liked how the teacher had the teacher place events along the continuum, and then later on page 139 place fractions and percentages. I think it’s a good way for students to really grasp what terms such as “likely” and “unlikely” mean.
In response to cynthiamer...The comment “I believe that if students are actively involved and engaged in learning tasks, especially ones that involve manipulatives, their learning will transfer to more traditional paper-and –pencil activities or test questions when needed,” also grabbed my attention. I agree with the focus on hands-on activities. Nevertheless, I think there is a danger in assuming this transfer will automatically happen, especially with our lower-performing students. Not everyone, even adults, can easily see three-dimensional figures when expressed two-dimensionally. While it should not be the center of our instruction, students should be exposed to the sorts of figures and questions they will be exposed to on written tests.
In response to D.Pico's post on July 9th-which is in response to cynthiamer's post on July 8th:I have to agree with Cynthia-kids must be taught Math concepts concretely before they go to the paper and pencil algorithm. Too often we jump to the paper and pencil task because we think the students have the concept concretely, and all too often they do not. The geometry unit greatly supports the idea of using the concrete, hands on, touchable manipulative to teach a concept. Bravo to the teacher for setting it up in this way!
In response to Miss Roth - I do agree with Cynthia and the authors of "Differentiation in Practice" that math concepts must be taught concretely. What I question is that thinking that transfer to paper and pencil representation will happen automatically for all students. I have found that many of my fourth graders do well with the 3-dimensional shapes, but when they have to identify them from a 2-D drawing, such as are on the TAKS test, they have difficulties. Identifying transformations as expressed in the test formats are also difficult. If we recognize that students have different intelligences, we need to accept that not every one is as strong in visually-spatially. As I stated above, it should not be the center of instruction, but I do believe there should be some exposure to paper and pencil tasks, (or at least as long as the state will be evaluating them with a paper and pencil test).
On Page 102 the teacher gives the children a colored dot and asks them to rate their level of knowledge. There are no names on the dots and it is done during a break time, so the children are able to answer honestly and without worry that others will judge them. I really like how the children are able to assess their own knowledge. I love the journal prompts on pages 107. The teacher gives the students one of two prompts; one for struggling students and one for on-target students. The struggling students are asked to make real life connections, while the on-target students are asked to think hypothetically. These questions are great and will really challenge the students to think in both groups. It is something that could be used across grade levels and the answers would be so different at each grade level. I agree with the teacher’s comment about varying “starting points” on pg 119. Students love to be challenged and working in different groups at different times will definitely do that. I imagine this avoids a lot of lost looks and students racing to be finished, but instead has everyone working to their potential.
I suppose my "A-ha" moment involved the integration of various subjects into her geometry lesson. I loved how she tied mathematics to literature in Lesson 6 on page 110. It's something I have tried, but as the school year progresses, sometimes I forget to link literature with math. I also thought it was a good idea to use countries' flags to integrate social studies with mathematics, as she did for lesson 8 on pages 112 and 113. I think most of us think of integrating science with math and social studies with language arts. It's wonderful for students to see how all subjects are related.
In response to what Miss Roth said on July 9 at 9:08AM, "So many times I have just done the ‘one size fits all’ assignment that worked great for some students-but I now know I wasn’t really meeting the needs of all my students," that is honestly the reason why I started teaching small group math. In doing it in a small group format, I can adjust the content or pace of the lessons I am presenting to each group. That way, the kids who are struggling more get their needs met and the children who need a challenge get it. Before, when I taught whole group math, I saw that I was really only teaching to the middle.
Since all the previous comments are on the Geometry Lesson I, even though I loathe geometry re-read that section also. It's easier to comment if you discuss what everyone else is discussing. Sometimes marching to a different drummer isn't the best course.Anyway, the writing prompt on page 107 ""Imagine a world without any circles" is tailor made for a GT student. Talk about tapping into their different view of the world! It would really be fun reading their responses. They could use Tikatok http://www.tikatok.com/ and create an on line book. I always try to incorporate as much technology as possible with my GT kids
cynthiamer, I too like the flag lesson on page 100. Back when the district still had Facts on File on line I used their country information sheets to teach "point and click" to the kindergarten and first grade students (our students do not arrive at school with mouse skills). The students loved looking at the flags and got so excited when they spotted similarities.
Brandy B, I like the fact that aren't many "there were not many paper and pencil activities" in this unit. I only see my PGP students 2x a week for 45 - 60 min. so it's difficult to incorporate much paper & pencil. I much more prefer to do active hands on activities. It also suits my teaching style.
In response to On Life, Education, E-bay....I also loved the writing prompt on page 107..."Imagine a world without circles." I can only imagine the responses I would get from my students!
Geometry - should I stay or should I go? I'm finding this section of our reading very intriguing but honestly had to MAKE myself go further. I am almost 100% positivity that my brain cannot compute mathematics like the rest. So, when this subject came about, I panicked! Resuscitating my urgent desire to get my 6 hours of completion!!Sigh! Here is I go!On Page 96, I loved how the author quoted Conwell, "The Study of geometry is especially fitted to the youthful mind. It encourages the development of intelligence, imagination and diligence." Had my teachers been more excited to teach Geometry, I probably would not had to bring in pictures of Tigers for extra credit!I learned this concept using paper, pencils and maybe a protractor or two... We were never taken out to discover faces, angles, edges, vertices,3-D objects in our environment. I can even remember asking myself, "When will I ever need to use this information again in my life?" (I like the activity on page pg. 103!) Not knowing that each concept builds on another... I wish, that my education was more like the ones we provide today. I think it is imperative to explain to children the value of what they are learning and how it will be used years to come. By giving them hands - on exploration, it helps make learning more meaningful and gives ownership on what the concepts are to be learned!I love the way this author also brings the imagination out! As I looked on page 107, I thought of the book: The Greedy Triangle... When teaching this to kids, I have them manipulate a pipe cleaner... I think a great way to close for the day and add reflection, would be to piggyback off of: Level 1 & Level 2 (Perfect for differentiation). I am going to add some of these pages to parts of our roadmap. I think that this is the ONLY way I will remember the wonderful activities!!!
My “A-Ha” moment came early in chapter 4, pages 95-96. Recently, I attended a Model School Conference in Nashville where a great deal of discussion took place about “Rigor, Relevance and Relationship”. Throughout the whole conference we learned about Quadrant D teaching. This means teaching children skills that can be transferred to other areas that are predictable or unpredictable. In addition to this, I have been reading a book on the most current brain research and its connection to the elementary classroom. So reading the first page where the author talks about encouraging students to think of geometry as an integral part of the world and to see geometry terms as communication that extends about the classroom, was like throwing open the door. While I have always felt that I tried to connect my students work to the “real world”, I see now that there is so much more that I can do and always this needs to be in the forefront of my thinking. It needs to be relevant to their lives. And my Quadrant D teaching is very much staying away from the “worksheet approach” as stated on page 96 and trusting that the learning will transfer to the more traditional test questions when needed. I also loved the author’s Pre-assessment chart with the circles. This is my weakest area and I have learned quite a few strategies that can now be used in my classroom. This chart of students rating their own level of knowledge is something I think my second graders could easily do.
I love Theresa's idea about the Greedy Triangle and the pipe cleaners. What a great way to bring in literature and connect math, literature and use manipulatives.
My "A-Ha" moment was when I was reading in chapt 5, page 144 lesson 6 when the sampling of probability was explained- I could see the different assignments based on the levels at which students would be at. I love the way the author added the teacher commentary- gained a lot of insight into do's and don'ts. I think all the tasks were engaging and all the students would enjoy the lesson- you might even have students wanting to try higher level tasks because it was fun. I think the use of the jigsaw method of sharing at end of lesson is something that I can easily apply so that all kids can feel accountable.
I agree that Theresa's idea about using literature to intergrate and connect math, reading and manipulatives is an awesome idea. Would love to hear of more books that people know of that kindof "kill two birds with one stone" - (multi-tasking)- Time seems to always be short!- Sharon G.
My aha moment came in Chapter 5 on page 138-139 about the Penny Flip lesson. I really like the differentiated homework practice and can see myself using this lesson when I teach elementary.
In response to Sharon: I had the same "aha" moment that you did. I think the lessons on probability would really encourage the students to expand themselves.
My biggest “A-ha” moment was very small and probably insignificant to most people. I loved the idea of using geoboards in connection with geometry and have mostly avoided them in my career because of rubber bands. I can honestly say I had never thought to use yarn as stated on page 108. I also like the ideas on page 113 to integrate symmetry with the study of state and country flags. I am self-contained and I’m looking for as much integration as possible.
In response to Miss Roth on July 9th- I agree that the integration is wonderful. As 4th grade teachers we see any writing integration and push forward with it. We need that differentiation and integration at all grade levels! Writing the the backbone of differentiation- there is no "one" way to meet all students needs! They're all at different places at different times!
In response to Cynthiamer on July 8th, reinforcing the correct vocabulary is essential at our level. Connecting the terms throughout math will benefit them so much as they get older. I feel it’s just another way we can differentiate by letting students who need challenging research the origins of the roots, prefixes, and suffixes. It makes the vocabulary so much deeper.
@ Carrie - I agree about the rubber bands. I have found that when I buy hair ties (you can get 100 for a $1), kids are less likely to shoot them across the room. However, I remember that group that you just had, and I too would be scared to death giving ANY of my friends things that could fly in the room! :)
@ tif - I agree whole heartily about using literature as much as possible with math. In fact, at one time, our school had such a cool collection of "math books" for each grade-level. I used them SO much that I own many of the titles. I'm not sure what ever happened to them. It was nice and convenient to go into the hallway and grab them whenever I needed... I have a feeling that they are now in our literacy library (out of sight - out of mind since I don't see them...) or people have taken them and have become hoarders. At any rate - they are nice to have and the kids LOVE them!
I really liked the fact that in chapter 4 she changed the paper color for tiered assignments. I feel like my students often know who the high students are, and who the low students are, but by changing the color and changing grouping as much as possible, it helps keep students from identifying themselves as being one color or stuck at one level.
I agree with Of Life, Education, Ebay and Books's cooment on July 11 that there weren't too many paper and pencil activities in these chapters. I too would rather see my students doing hands-on assignments and exploratory learning. I myself don't like to sit for long and would rather be doing a hands-on task than filling out a worksheet, and I know my 3rd graders would prefer that!
The Geometry lesson was my favorite of the 2 that we explored this time around. I loved how it was broken up and so simply organized. It is easy to see myself taking this lesson and re-designing it for multiple grade levels to work with classes in the library. I love the fact that it's math-related, b/c I don't get to do a great deal of math-oriented teaching in the library, but I think this set of lessons beginning on page 95 would be great to break down and use in library lessons. In particular, on p. 95 where the author talks about the teacher reflection when designing the unit, my a-ha was being reminded that when it's geometry, students bring a WEALTH of knowledge and experience at MANY varied levels.
In response to Ms. E's comment... I'm fascinated with the conference you went to related to Quadrant D teaching... I love how this is conceptualized, and I agree that this area of "teaching" is something I would do well to work on in a more focused manner. The word "rigor" keeps coming up in many of my education discussions, and I think it's time that I made sure that everything I plan is focusing on making sure that my students are presented with appropriately rigorous activities that they can apply to multiple areas of their life. The library is a perfect place to teach lessons like this!
In response to Miss Roth on July 9... I, too, am guilty of the 'one size fits all' model, particularly when we are pressed for time during library lessons. However, the more I differentiate, I know my students gain more from every moment they spend with me. I also agree that most of these concepts are very inter-disciplinary... they fit and meld with so many of the ideas we're to be working on with students these days.
As a Language Arts teacher, I loved seeing the development of writing and reading skills in this Geometry unit. For example, p. 107 has different writing prompts based on the students' level and p. 108 incorporates prefix and suffix vocabulary instruction.
In response to cynthiamer, I also liked the idea of having group leaders who can teach the other students. I think this is something that really free me up to do some small group instruction. This would require some planning and training of the kids, though. I have so much to think about before the beginning of the year.
To support Miss Roth's comments, I agree that these units showed that interdisciplinary curriculum can work. I know the district is moving in that direction, so I'm very eager to read about successful interdisciplinary units. Even though I don't teach math, I feel like there are many good ideas offered in these chapters.
I agree with what D. Pico said on July 9 about the focus given to structure. I too believe that it will give a more real world perspective to the kids, which is ultimately the main goal of what we are doing.
I have actually had many "Aha" moments through out this book and many points that reinforce my teaching beliefs. Some of the most recent connections I have made with this book is on page 96. The author reinforces the need for hands-on activities. I think being an early childhood teacher, it is second nature to always teach using manipulatives, especially in math. However, I think sometimes in upper grades, there is so much pressure to prepare the students for test that its difficult to always provide students with the time to "handle and explore objects in their environment." Another connection, I had was the differentiated homework assignments discussed on page 135. When I taught a second grade class that consisted of many GT students, I provided choices for their homework on Wednesday. I would also try to vary with multiple intelligences. The students loved it! I had some students that would do both assignments and I also got a better idea of what each student knew.Though I have had many "aha" moments, the "List-Group-Label" activity on page 102, gave me an idea of how to informally track each students progress throughout the unit and for the student to also track their progress. If I gave each student a cut row of the little colored circles(the ones used for garage sales), then asked them to personalized their circles by drawing the same picture on each circle (like a star, heart, ball,etc.) then place their name on the back of the strip. I would keep the strip so I could tell which sticker belongs to which student. One color(say the orange) would be used to place on the chart to display the students beginning knowledge. Then in the middle of the unit I would bring the chart back out and the students would place the next sticker (green) on where they are know in their knowledge of the unit. Then at the end of the unit the students will place yet another color(yellow) to show where they ended up. *I would make sure to leave at least one sticker with the drawing on the slip of paper so I will always know which circle belongs to which student. This will allow me to provide extra help for students that are not progressing enough or may need to revisit the unit and also allow me to provide adavanced activities for those that are at the end of the chart.
In response to Brandy B... teaching/learning should totally be like that. As John O'Flahaven, believes, teachers shouldn't be doing all the work during the lesson...it should be students. The teacher is the facilitator. The student is the worker (learner) and if students are "actively involved and engaged in learning tasks" as the author state, then I think its possible. It just take careful planning on our part!
Ah's I love the interdiciplinary approach to the lessons. We have a high focus on getting the most bang for the buck and being able to stretch the curriculum in this way will help us to accomplish that. I love using literature in math(pg 110 Grandfather Tang's Story) , but find that harder to do as the concepts get more and more advanced. In the upper levels using the lit as part of the accessing prior knowledge can be a great way to intro lessons. Love the idea of using flags for geometry (pg 112). It's an interesting connection and encourages students to think outside the box.
As with many others, I agree with what Brandy B. said about wanting to see the paper pencil work of the students to make sure that they are "getting it". It is hard to let go of the accountability that is tangible and move to more observation and recording data.