The purpose of this activity is to receive an introduction to the teaching concepts addressed in TMM. Specifically, what are characteristics of struggling learners that make meaningful mathematics a challenge and what are strategies that are useful in making mathematics meaningful? We will be returning to this book in the future. It is a very good book.
- In reading your respective chapter you are to address the following:
- The major points (be judicious in what you choose) - provide enough detail so the others get a full sense of the point
- What are the major take-aways you have for each major point listed
- For the chapter on characteristics of struggling learners, address WHY kids are struggling and how this relates to the teacher's perspective (after all the point of this is to inform your teaching).
- For the strategies chapters, address WHY the strategies may work and how these strategies relate to your future teaching. How can you make use of these?
- Again, be judicious and be concise. You don't have to provide a full explanation of the whole chapter.
- In responding to the posts of others, identify a key point made and address how it can or will impact your teaching AND explain your reaction, e.g. are you surprised or is it common sense?
Your initial post is due by Sunday, June 2 at 10PM and your responses to the posts of others is due by Sunday, June 9 10PM.
Here are the chapter assignments:
- Sarah - Chapter 5: "Common Learning Characteristics that Make Mathematics Difficult for Struggling Learners"
- Tiffany - Chapter 8: "Making Instructional Decisions: Determining What and How to Teach
- Charles - Chapter 9: "Teaching for Initial Understanding: Using Effective Instructional Practices"
- Jim - Chapter 10: "Building Proficiency: Using Effective Student Practice Strategies"
- David - Chapter 11: "Planning Effective Mathematics Instruction in a Variety of Educational Environments"
- Neil - Chapter 12: "Using Technology to Promote Access to Mathematics"
From Charles: Chp. 9
ReplyDeleteThe main point covered in chapter 9, Teaching for Initial Understanding, is instruction and how the presentation or instructional material can then be broken down into four distinct stages or practices:
1: Teaching within authentic contexts (something familiar to students, i.e. middle school students can relate to bicycle tires or skateboard wheels)
2: Building meaningful student connections (connect and build on what they already know and what they are to learn. multiplication then to exponents)
3: Modeling and scaffolding instruction using a Concrete-Representational-Abstract (CRA) sequence (working with objects, then drawings, and lastly just mental math. Working with geometric figures helps students see and understand volume, then seeing it in a drawing they can relate to it and finally are able to see volume by a description)
4: Teaching problem-solving strategies (ability to break down problems into solvable steps. Finding angles of a polygon we break down the figures into squares and triangles which are easier to work with)
As educators, we know that struggling students will have greater success at learning new concepts if these concepts are presented in contexts that are meaningful to them. The addition of hands on material (shapes for geometry, items for counting etc.) will increase this understanding.
Students will: A) see value in learning the concept:
B) have a greater capacity to remember the concept and:
C) be more likely to remember the meaning of the concept.
The context must also be age appropriate, culturally responsive, of an INTEREST to the student, and the concept must be clearly identified.
In my substitute teaching I have utilized the techniques of: authentic contexts (relating to subjects that students can relate to), connections and problem solving but have not used the concept of working with objects to aide in developing the lesson/objective. The visual cues/benefits of hands on three dimensional figures are clearly evident and I will have to incorporate them into lesson plans. I feel that the difficult part, as a newer educator, will be to continue to build a variety of authentic contexts. I feel that connections are a natural progression from one lesson to the next, or at least they should be. Teaching problem-solving is the natural culmination of the lesson. Scaffolding is really the structure or steps of the lesson.
From Tiffany:
DeleteGreat overview! The point made about modeling and scaffolding is significant for being able to reach various levels of learners. I feel that this will greatly help the majority to be able to break down the pieces and succeed in learning. While it seems like common sense, it is easy to overlook every individual step and its meaning if you aren't planning to do it this way. If overlooked, that can be the difference in how many students really understand the objective and can repeat it later or not. I think this also helps students who cannot make the jump from seeing the problem and giving the answer to be able to really go step by step to get the answer.
From Jim:
DeleteIn terms of what Charles wrote in '4' and in response to Tiffany, I agree. Breaking down a concept down into smaller and smaller individual pieces will go a long way in reaching as many learners a possible. However, one of my fears in teaching is that I won't necessarily know how to break it all down effectively. Presumably we are all pretty good at math. We already know how to do this stuff. When we do math we skip steps and gloss over some details because we simply already, 'get it'. Many, maybe most, students will need these specific extended details. I think it will take some effort to 'bring it back down to the basics' and present concepts at the level of detail most learners will require.
From Sarah:
DeleteAnother thing I have found that helps struggling students in instruction is to address common misconceptions before they have a chance to make them. For instance, the other day I was working with students learning how to find the volume of a cylinder (V=pi*r^2) and I made sure to make a note that when you square a number you multiply the number by itself twice, NOT multiply it by 2. I feel like addressing these mistakes initially reduces the chance of students making them later.
From: David
DeleteCharles,
I’m in agreement on using Real Life connection will help the student better understand subject matter. But we must also tie in to the CT Common Core Standards. I’m all for maximum flexibility (“Out of the Box”), but we need to consider CT CCS (Justify our position). Question: Do you fully understand CPR. I tried to put together an assessment for P. Vicinus homework assignment and it took me 2-3hrs and I’m still not sure I fully understand CPR scaffolding. Let’s talk. Thanks
From Tiffany:
ReplyDeleteChapter 8 – Making Instructional Decisions: Determining What and How to Teach
This chapter discusses ways to understand and assess your students in such a way that the teacher can then determine what needs to be taught and how it needs to be taught. From the information presented below, we have six takeaways: (1) student interests/experiences, (2) the level of structure/teacher support that is needed, (3) the level of understanding that students have (CRA) for the target concept, (4) whether students have receptive or expressive response abilities, (5) where (at what level) to begin instruction, and (6) what misconceptions students might have pertaining to the target concept.
We are giving the following guidelines –
Phase 1: Creating meaningful learning contexts using the Mathematics Student Interest Inventory (MSII) - This is a great way to get to know the kids and what your lessons should include when trying to connect to the real world! I had written this idea down after an observation where the connections were not reaching the kids because they were boring. I was so glad to see it here and get a better sense for how to effectively implement it! The kids write at the beginning of the year the things they like to do, individually, with friends, and with family as well as things they like to learn about, etc. The categories in which you want the students to respond are up to you. With the responses, the teacher should take a selection of them and align them with relevant math concepts/skills that will be taught and also jot down ideas for creating authentic contexts (aids in lesson planning when the time comes!)
...to be continued below...
From Tiffany:
Delete...continued from above...
Phase 2: Deciding what and how to teach via the Mathematics Instructional Decision-Making Inventory for Diverse Learners (MIDMIDL (1)) and the Mathematics Dynamic Assessment (MDA (2)) – (1)The MIDMIDL is used to determine the level of teacher support and structure that the students need. There are three forms used to do this…(a)Characteristic Inventory Form (be it whole-class or individual student) which rates the level of support needed based on number of students receiving special education services, Title I services, free/reduced lunch, history of behavior problems, and so on; (b) Math Curric/Content Inventory Form which rates the teacher support needed based on the degree of complexity of the content (single step or multi step), degree of accuracy required (estimation/classification or specific answer required), amount of instructional time available, and the foundational nature of the content (content based on old concepts or new concepts); (c) Instructional Planning Guide provides guidance for the teacher in how to teach a topic based on this information gathered previously determining the levels of support needed. (2) The MDA is used to assess the knowledge students have of a target concept, misconceptions that they have, and the level of understanding they are at (Concrete, Representational, Abstract and then receptive/expressive for each). The CRA Assessment allows students to demonstrate their knowledge on various levels. As teachers we need to be aware that students do not test the same and that does not translate into their not understanding the topic. The CRA form given in the text guides you in laying out the assessment to test for the various levels effectively. The Error Pattern Analysis is a sampling assessment to determine where mistakes are being made consistently so the teacher can address the misconceptions or gaps in understanding. This assessment can also be used to provide extra individual support. Another approach is called the flexible interview. This allows the teacher to ask the student how they solved a problem. The student is able to verbalize their response which gives insight into their mathematical thinking, which may be different from what is being taught, yet still be sound. Sometimes a student’s way of thinking can be insightful and a helpful method to let other students hear/see.
Determining what and how to teach is much easier for a teacher when the aforementioned information is known. Teachers have access to all of this information and it does not take much time to assemble. It needs to be done maybe twice a year (beginning and middle) to include for those who move into the district. It can be done more or less depending on what the teacher needs. This can be a critical fault on the teachers’ part if they just go ahead with teaching lessons that are not geared toward their specific audience.
Lastly, the chapter discusses teachers having an instructional hypothesis which comes as a result of the above plans put in place. There is no point to doing the MSII, MIDMIDL, and MDA if the teacher is not going to analyze the data. The instructional hypothesis is to include four conclusions: (1) the context, (2) what students are able to do, (3) what students are unable to do, (4) a rationale for the students’ understandings. The teacher is supposed to incorporate these findings into their next lesson to address misconceptions and gaps in understanding.
From Sarah:
DeleteI'm interested in the flexible interview technique that you described. In tutoring and intervention, I often use this technique. You're absolutely correct in saying that it's extremely insightful to hear a child explain their thinking. You can get their depiction of what they know and find any holes or discrepancies in their understandings of a concept. How do you think flexible interviewing would look in the classroom?
From Tiffany:
DeleteI think this could be seen as simple as the teacher walking around the room while students are doing work and asking them about a particular problem they are working on or it could be used as a more formal one-on-one where while the class is working on something, the teacher calls one kid to her desk at a time and discusses a problem that they either did on their homework or a test. It could be used as a learning tool to assess whether they understood a problem they got wrong or not. Sometimes the errors are just mistakes and students really know what it should be when they take another look. There are more ways but these are just some examples.
From Jim:
DeleteThat is truly a great idea: Find out what students' interests are and incorporate them in the math lessons. I think Nel Noddings alluded to some of this in our Philosophical Documents in Education Text. This could be done in the first 3 days of school as Scott Dunn described to us. Using assessments to find out where each student is can be tricky as Paul Vicinus discussed on Friday. Yet the assessments discuss seem to go a long way in evaluating where a student is and where they need to go educationally.
From: David
DeleteTiffany,
Again, Student interest connected to understand. See a trend? You also site the CRA model (p. 93-96). It's a little clearer in your chapter than Charles and my chapters. I strongly feel connecting to students interests for understanding is key, but what about considering the students FEELINGS? Yes, it’s key how students approach problem and relate them to issues in their life.
From Jim:
ReplyDeleteChapter 10 – Building Proficiency – Using Effective Student Practice Strategies
Math proficiency means more than just knowing how to do the math. It implies a greater understanding of the subject, an automatic reaction to arrive at a solution. This level of understanding is achieved through practice. Practice is more than just rote drills and worksheets. It should take into account the struggling learner and cater to these students’ needs. Several strategies are used in helping students achieve math proficiency.
The first, Structured Language Experiences, encourages students to use their own words, drawings or writings in explaining the topic. This would take place during a structured activity created by the teacher.
The second is Structured Cooperative Learning Groups/Peer Tutoring. This strategy needs to be highly structured as struggling students often are not included in the group due to their struggles. Pairing a student who struggles with one who does not has proven to be effective as long as they both are aware of the goals and expectations.
Strategy three is Mathematics instructional Games/Self-Correcting Materials. Games can be an effective and motivating way for the struggling learner to participate and learn. Board games, word problems and the like can be individualized or made to work with a whole class. Self-correcting materials are typically individualized only and provide immediate feedback for the learner. Flash cards are one example. The student looks at the problem on the front side then flips the card over to check their answer.
The fourth strategy is Continuously Monitoring and Charting Students’ Mathematical Understandings. This strategy serves three purposes: 1) immediate student feedback, 2) feedback for teachers so they can quickly make changes to their instruction on an as needed basis, 3) a tool teachers can use to show the student what level of understanding they have about a topic. Students who struggle in math can become lost in their lack of understanding. They can easily become confused and consequently lack motivation. Keeping these students constantly aware of their of their progress helps them realize how far they have come. It also keeps the teacher constantly aware of the effectiveness of their teaching. By evaluating students’ understanding, teachers are also made aware of what was effective and what wasn’t in their teaching.
Strategy five is Maintenance of Mastered Concepts and Skills. It is important to go over concepts the struggling learner has mastered so they are not forgotten.
From Jim:
DeleteContinued...
All these strategies will no doubt be effective in helping learners maintaining proficiency in math. It seems like strategies one through four will be naturally a part of the modern classroom. Strategy 5, however, seems like it will require extra effort and thought to incorporate into a daily lesson. It would, therefore, be a good idea to include test and homework problems from material previously covered in effort to keep them sharp.
From Sarah:
DeleteIn one Algebra 1 textbook I was looking at there were "spiral" exercises which looped back to previously covered concepts. In most cases, the spiral exercises were relevant to the success in the current section. I think it's important for previous concepts to be revisited due to the cumulative nature of math. It provides struggling learners an extra chance to practice and an opportunity to more concretely understand something they may have struggled with previously.
From Tiffany:
DeleteI agree that strategies one through four seem like they would be naturally occur within the classroom. But I also think that strategy five would too...it just isn't as obvious. As Sarah mentioned the spiral exercises would be one way that you could maintain a mastered concept/skill. As we have been learning in our core sessions, another way to maintain a mastered concept/skill is to make it part of your schema. It doesn't have to be everyday but incorporate as many prior mastered concepts and skills into the initiation that can be somewhat tied into the new lesson. For easier concepts, they can be reiterated in the beginning of the instructional activity.
From Charles:
DeleteThe spiral concept should be a natural progression from one lesson to the next. I usually try to review the previous lesson and show students how this applies to the new lesson and also this shows them what they already know about the new lesson. Again, it goes back to scaffolding and breaking down the new lesson into small, incremental steps and then combining steps as you get further into the lesson/concept.
From: David
DeleteJim,
Interesting, an automatic reaction, such as “of habit”. Practice, practice and practice works their way consistent automatic response. Peering the struggling student with high levels great idea. Let me take it up one notch, peer the struggling student with the higher level student that is the best teacher within the class. The student that can and likes to teach other students. As far as caring, you got it Nel Noddling’s caring model. As the English say, “SPOT ON”. It’s the change (Delta) improvement that counts. The Struggling student can be the most difficult, but provides the most intrinsically rewarding to me as a teacher.
From Sarah:
ReplyDeleteChapter 5 (Eight Common Characteristic of students who struggle with learning mathematics)
This chapter describes common areas of difficulty for students who have trouble learning math. Under each characteristic I briefly mention ways to help students struggling in that area. These strategies were further discussed in chapter 9 and 10 (Jim and Charles’ chapters).
1. Learned helplessness-After continually experiencing failure in math, students come to expect it. These kids say they can’t do it before they’ve even tried or have their hand raised before you’re even done explaining. Their self-concept is such that they attribute their failure to internal forces (I suck at math, I can’t do math), and their success to external forces (got lucky, had teacher’s help). These students will resist new problem solving techniques, as learning new ones has never helped in the past.
Ways to help:
-Break down problems into smaller, more manageable pieces
-Provide visual organizers to point out key ideas
-Closely monitor progress, change instruction method quickly if not successful
2. Passive Learning-Passive learners do not actively attempt to make connections when learning new information. When solving problems, they do not try to draw upon their knowledge to attack the problem at hand. They are afraid to engage as it may lead to more failure. To them, math is very disjointed.
Ways to help:
-Using relevant contexts in instruction and problem solving, encourage multiple strategies to solve problems
-Provide a way to monitor their progress in developing strategies for problem solving (like a journal)
3. Memory Difficulties-Students with memory difficulties have trouble retaining and remembering information. These students may have trouble with math facts and/or remembering steps necessary in problem solving. There are two reasons students may have trouble remembering: 1. Because they have trouble understanding the topic to begin with or 2. Because they have trouble remembering the information despite understanding it.
Ways to help:
-Provide meaningful ways (visual, mnemonic, etc.) for students to remember concepts
4. Attention Difficulties-Students with attention difficulties have trouble focusing their attention. They may miss a part of a lesson, leaving them to miss important details. They also may get distracted in multi-step problems leading to mistakes in the process. These students will also struggle to pick up on subtle details that differentiate different concepts. Students with attention issues don’t have a problem with attending, they have trouble filtering out all the sensory stimulation that catches their attention.
Ways to help:
-Using a range of sensory cues (including self-cues) to highlight the relevant features of a concept
5. Cognitive/Metacognitive Thinking Deficits-Students with metacognitive deficits have trouble keeping track of their thought process. They have trouble using and evaluating their problem solving strategies effectively. These students struggle with communication because they have trouble tracking their thoughts.
Ways to help:
-Explicitly explain how to be metacognitive
-Provide opportunities to learn strategies through teacher modeling
6. Processing Deficits-Students with processing deficits have trouble accurately perceiving their senses. Though these senses are intact, their brain processes them differently then they’re taken in. This causes students to misperceive information and thus learn things incorrectly. Processing deficits are also input/output oriented. Despite receiving and understanding the information properly, a deficit may cause information to be communicated improperly. (i.e. a child with a motor deficit may have trouble verbalizing a concept properly).
Ways to help:
-Using a range of sensory input/output to increase students’ likelihood of success
-Using “Making Every Minute Counts” questioning strategies to check for understanding
Continued:
Delete7. Low Level of Academic Achievement-Whatever the reason is for a student having difficulty in math, it often leads to holes in their knowledge base since they may not have the chance to fully master a skill. This leads to problems later on in their learning when they need to utilize those unlearned skills. Additionally, they may have deficiencies in other subject areas, like reading, which cause them to have difficulties in math.
Ways to help:
-Help students build meaningful connections in math
-Providing multiple opportunities to develop understandings
-Planning periodic reviews/practice of previously learned material
8. Math Anxiety
With all these difficulties in math, students who struggle develop anxiety surrounding math and often shut down when confronted with math.
Ways to help:
-Provide risk-free opportunities to learn and practice math
-Ultimately, helping the student to have success in math!
From Tiffany:
DeleteNice break-down and providing the ways to help for each type of struggling learner. This is a part of core that I am anxious to get to and learn techniques, so these math specific ones are great! I feel like a lot of these come out of number eight, math anxiety. If we could overcome a students math anxiety then they will be less likely to struggle in some of the other areas (helplessness, passive learning, and so on). When students feel confident in their abilities to understand the content, at least somewhat, they become more open to taking risks in the classroom.
From Jim:
DeleteIn America today it is perfectly acceptable to say, "I'm not a math person." Or, "I'm bad at math". I read somewhere years ago this is an American phenomenon. OK. So it's there and we as math educators have to deal with it. What leaves me cold is so many of our fellow non-math ARC students saying the same thing. And worse yet, some of the people presenting saying it too. These are practicing teachers and administrators with advanced degrees coming right out and saying they don't like or can't do math. Even if they never come out and specifically say it to students, some of this attitude must shine through. What message does that send to students?
From: David
DeleteSarah,
I live with these mental health issues every day. My wife is a psychiatric/mental health APRN. I discussed the mental health effects on learning and education with her and can provide the following:
There are many mental health problems that can complication a students’ educational process of math. There can be issues with depression and generalized anxiety, which will decrease their ability to stay focus and understand the classroom instruction. The student may have other mental health diagnoses such Pervasive Developmental Disorder, Communication Disorders, Learning Disorders, PTSD, or any combination of Disorders. The students’ may have behavioral problems such as Disruptive Behavioral Disorder or Oppositional-Defiant Disorder. These students can cause other students to be distracted from their work. There could be environmental problems at home or in their neighborhoods. A parent may have mental health and/or substance abuse problems. If a student had a death of a close family member, this may cause problems with focus, attention, mood and motivation. If could be violence at home or their neighborhoods. The student may use substances; which would have a major impact on their learning any subject. The student may be dealing other personal traumas that would cause a loss of focus and concentration. There are numerous other mental health, environmental and physical health problems that can cause a student to have trouble learning math besides ADHD.
From Neil
ReplyDeleteChapter 12: Using Technology to Promote Access to Mathematics
Main point: Math can and must be made meaningful for all students, regardless of grade and ability. Technology offers an efficient way for students both to self check and to augment their math understanding so that the core principles are relevant, current, sensible and fun. Also, technology is advancing in new ways to further enhance teaching and learning opportunities.
Technology is broadly defined as hardware (e.g., calculators, PDAs, computers and smartboards), software (e.g., spreadsheets, graphing algorithms and commercial CD/DVD products) and the internet (e.g., dedicated web pages and instructional videos). All of these products continue to expand and their availability is increasing geometrically.
The use of technology must be tied to teaching objectives, the needs of students, and should be seen as a tool for instruction and not an end itself. Technology should not just be viewed as a tool to increase efficiency, but rather as a way to enhance learning.
Technology can be used to enhance the 5 major idea content areas:
1. Numbers and Operations
2. Algebra
3. Probability and Statistics
4. Geometry
5. Measurement
The potential benefits of using technology include:
building proficiency (especially for struggling learners who may require multiple practice opportunities while maintaining interest),
creating authentic contexts in which students can learn and apply math concepts,
providing ways to test conjectures or hypotheses to concretize concepts
using graphing or spreadsheet capabilities to explore algebraic ideas or functions
facilitating higher order thinking by circumventing basic skill difficulties
The chapter discusses numerous critical aspects of technology:
-How to select appropriate software
-Expanding uses of wireless technology in the classroom
-On-line resources for students and teachers
-Special education-specific resources
Finally, the chapter discusses teaching strategies for incorporating the use of technology, such as guidelines (strategic and tactical) for deciding when and how to use technology, how to integrate into the curriculum, and how to address needs of struggling learners with technology.
From Tiffany:
DeleteI love the use of technology in the classroom but also at home. I think that technology has given us a new world to work with in the ways in which we can get information across to students with different learning abilities. I like the idea of flipping...using an internet resource to give the instructions(typically a video) as a homework assignment and then doing discovery and exploration of the content in class. I also like being able to give parents relevant resources (either at the beginning of the year, beginning of the lesson, or alongside a homework assignment). Being able to empower the parents to get involved at home could have a great impact on the child's success. We cannot expect that parents will have the knowledge to help with assignments, but we do have the opportunity to bridge this gap.
From Jim:
DeleteI was talking to a teacher in the Coventry School System today who said the kids can use technology against the teacher. Kids will find work arounds to the road blocks put up by software to prevent cheating on computer based projects and tests. They will find ways around you finding out how they have copied their homework from other sources and so on. This is a little off topic, but the person I talked to said some seniors in his school this year took various videos of a young attractive teacher's rear end as she walked in the hall way and posted it on youtube. They were told by the administration to take it down but refused claiming it was their right to free speech.
From Sarah:
DeleteTiffany, I have a friend who's son was in a classroom where the teacher often flipped the classroom; she LOVED it. Not only was she reminded of concepts her student was learning that she may have forgotten, but she also knew exactly what the teacher was expecting the student to know. This way, she could ensure that her student was completing the homework consistently with the teachers expectations. I love the idea of empowering the parents, because like Jim mentioned in another comment, lots of adults admit to their deficiency in math and hopefully this can help them model enthusiasm for math to their (our!) students.
From: David
DeleteNeil,
We have seen in several ARC presentations the value to effectively use technology. Effective Use of Technology can enhance almost everything. It’s important the teacher be current with technology in order to be most effective.
From David:
ReplyDeleteChapter 11 – Planning Effective Mathematics Instruction in a Variety of Educational Environments
In order to establish the lesson framework, we understand ten basic principles:
1) Target math concept
2) What was learned in my math assessment
3) Instructional hypothesis
4) Various student ideas and apply them to the instruction
5) Authentic context
6) Differentiating between student needs
7) Introduction to the class
8) Scaffolding
9) Practice
10) Evaluation of my teaching and students understand.
When building an instruction plan, we need to consider all these elements.
First revisit the students understanding of pervious material and what issues you would expect.
What were the problems that the students had? Then identify the teacher object of the plan along with student level of understand and observation assessment. The plan needs to include several aspects of the individual and whole class knowledge. A Pyramid of percentage of students that understood the material is effect. Break it down into all, most or some understood, and also was it concrete, representational or abstract. The teacher needs to use tools to determine the level of support the whole class and the individual. This can also be broke down by grouping students. This way the teacher can determine how to address difference between the students. The teacher may need to develop a plan for the whole class or various plans for others groups. The plan needs to consider the connection with pervious plans and the expectations of the students. A good approach is to look at alternative ways to solve math problems. You may to address special education students. The four key objectives are: lesson objective, procedures, student feedback and the evaluation process. Collaboration between teachers can be beneficial. The chapter presents several examples and tools to fine tune instruction strategies, techniques, and key ways to evaluate student knowledge. With a detail plan that considers past knowledge of the students, identifies objectives and degree of satisfaction they are method, the teacher better prepare future plans.
From Tiffany:
DeleteThis was just discussed in great depth today during core so I really understand what you are saying! I feel having the checklist of what an effective lesson plan entails is invaluable. Prior to this I was still unsure of exactly how much of what to put into my lesson plan. As we begin to teach and build our personal pedagogies, I think that some of these 10 elements will become more second-nature and natural to us. (Until then, I won't mind if they keep showing up in our readings and giving us varied senses for what each could look like!)
From David
DeleteYeah, wasn't it ironic that lesson plans were covered right after this exercise. There is a lot of great information in this chapter on lesson plans. I just touched the surface in my blog. I'm still trying to fully understand the Concrete Representational Abstract (CRA) concept (p. 172-173). I like the way Differentiated Instructional lesson plans are presented. Not just by one special individual, but in groups (p. 175-178). Keeps this to one lesson plan.
From Jim:
DeleteThe assessment portion of this material was discussed by Paul V in further detail on Friday. ".. percentage of students that understood the material..The teacher may need to develop a plan for the whole class or various plans for others groups" If students aren't getting the concept, we can't just repeat the same thing over again. If they didn't understand it the first time in the way it was presented why would they understand it the second time? It's about as effective as shouting something that wasn't understood. New approaches and ideas need to be considered.
From Sarah:
DeleteJim, I totally agree. That's why I love the turn and talk that Paul V. uses in his presentations. Used in a classroom setting I think it can be really effective in getting students to share their understandings of a topic and the peer-talk can help struggling students to better understand a concept. I think this process would need to be carefully monitored, however, because you wouldn't want students sharing incorrect information with one another.
From Charles:
DeleteWhen I have substitute taught, I have observed that in small groups when students discuss new lessons or procedures, even if they say exactly the same thing that I just said, because it is coming from one student to another sometimes the listening students understand it. Weaker students also are more comfortable asking questions amongst their peers to get an explanation than to ask in front of the entire class. Lastly, students can more readily relate the lesson to concepts or ideas that are more relevant to them, i.e. party favors instead of our famous widgets!