Geometry in Architecture

Misconception/Preconception Check technique can be used in in the beginning of our our six week architecture/geometry to elicit any misconceptions and to appropriately remedy to them. questions on volumes, surfaces, different types of angles, Pythagorean theorem, triangles, spheres, and circles will be asked on the pre-assessment. Such questions will be of low level of difficulty, and will be on the basics on the above concepts. Such test will give me an idea as to what students really need and opens the door for me to explore and use different remedies to correct those misconceptions. A post-assessment will be used after the six-week project to make sure that students eliminated those misconceptions, and learned what they were supposed to learn during the six week project. The post-assessment will be of a slightly higher degree of difficulty than the post assessment.

Memory Matrix: I believe we could use the memory matrix throughout our lessons. It would be particularly helpful in recalling definitions of angles and triangle congruencies, as well as when you can use them. Columns could be the definition and the rows the words, and they have to put an x in the square where the word and its definition meet. It could also be used to line up certain angle types with where they are used in the student's projects, so they remember where those things are seen.

Few days after the post-assessment, I will use the empty outlines assessment technique to make students think about the concepts they learned during the six-week. Such technique will give the students an opportunity to connect all the concepts they learned. It is important for students to not only connect different mathematics concepts, but also to get the big picture, which will solidify their understanding.

Minute Paper: We could use this as a daily assessment at various points in our project. After we do a Benchmark lesson or an Investigation into something new we could have them write a minute-paper on “Write a minute-paper on what new things you learned today.” Or during weeks where there are multiply “lab days” in a row, we could have them turn in minute papers on “what did you accomplish today?” This type of assessment would be great for keeping track of participation without putting a stressful grade on the students. It also helps the teacher see what the students feel is the most important parts of their lessons.

The analytic memo assessment can be used for our geometry in architecture project. The students will be researching different types of architecture around the world. Each group will write a memo about the architecture of their region. This would help the students to have concrete information about other groups’ activities.

I think that the students could gain assess their understanding of the geometry in architecture project by writing a one sentence summary. This will help the students truly comprehend the important topics which were covered during the project.

I will use the concept map technique to be able to assess relationships and connections that students make related to the focal concept of similar triangles. I will be looking for notions, such as angles, triangles, congruence, similarities such as SSS, SAS, ASA. If students are able to come up with a concept map that include all of the above notions, then students would have shown that they understood the big picture of what was being taught. if not, I will have to come up with different explanations, until they are able to connect and conceptualize the above notions. As students are making different connections between concepts, they will be significantly developing their meta-cognitive skills, which is crucial for their overall understanding of math concepts.

Approximate Analogies: This would be good to use in our project when we do definitions of new words. WE have two benchmarks where we cover lots of new vocabulary and definitions, as we could use the approximate analogies to make sure they don't confuse words that are commonly confused. Ex: Complimentary is to ___ as Supplementary is to 180. This is a unique vocab quiz in a way that helps students see relationships between certain math topics.

I will use the documented problem solutions' technique to first assess how students solve problems, and second to assess how well students understand and describe their problem solving methods. I will use geometry problems that involve proofs of theorems, such as the Pythagorean Theorem, which will be a good indicator of the step-by step mathematical reasoning students utilize in solving such problems. As a result, I will be able to point out wrong mathematical reasoning that students use, and be able to remedy to those mistakes by appropriate educational means.

The Annotated Portfolio: This is perfect for any long term project, but I would like to use it in this project as a way to keep track of student work. There are so many steps to our project that making the students create an annotated portfolio would be very productive. This makes the students think about why they are going through each step of the project, and talk about what they learned at each point along the way. Each student will compile have a copy of each thing their group produces, will put it in their portfolio, and write a paragraph about why they did it and what they learned from doing it. This is also a good thing for the teachers to look over at the end of the project to see what the students thought were the most important things to get from it, and where they had the most fun, so they know how to change it, if at all, for the following year.

Application Cards: This can be very useful in our project because the entire thing is based around real-life connections. Every time we introduce a new idea, students can fill out a card with at least on example of where it can be used in their building. This way when design time comes they have a collection of ideas on how to integrate the concepts into their building design.

I would implement the project prospectus for our unit geometry in architecture. This will help the students to understand what they will be designing and help the instructor to know when students are off in the wrong direction.

Student-Generated Test Questions: Since during our project we don't have a formal test, we hoped to give out small quizzes or exercises throughout the project. If once a week, students submit one sample test question based on their experiences, I could compile them into short quizzes or worksheets, so that the students get to explore what other groups are learning about, as well as get good exercise with the concepts.

I could use the classroom opinion polls assessment technique to elicit misconceptions that students may have before every benchmark lesson. That would allow me to correct those misconceptions that students may have, so they can build new knowledge on correct conceptions. If not addressed, those misconceptions can dramatically impede on student's ability to learn new knowledge. This type of assessment can be used as a pre-test assessment before benchmark lessons.

Goal Ranking and Matching: Since our project does not start on the first day of class, I think that this technique would be good prior to starting the project. Give students an idea about what the project is about and ask them to write a list of things they would like to learn out of the project, and the order of importance. This would be a good way to gauge what parts of the project to focus more on, but of course, you must still focus on the math even if all the students are only interested in say blueprints, but at least as a teacher you will know there is a genuine interest in learning that topic when you get there, and can pay special attention on it. This will help students become more interested and willing to participate if they know you are trying to work with their interests.

Self-Assessment of ways of learning: Since we know that many students don't learn well in a lecture style class, we have decided it is important to develop a PBI style of teaching and learning because students may do better in this manner, but there are many other ways that students learn, and not all learn best in the way our project is designed. This is another good assessment to do prior to staring our lesson. If students can think about how they learn best, and in what setting, then the teacher can take that into account when setting up groups, or laying out the plan for each day. Students who work in the same way would be benefited by working together, and knowing how each child learns best will help the teacher set up the project to accommodate to those methods.

I will use the diagnostic learning logs assessment technique, which would provide me with important insights into students’ awareness of and skill at recognizing their strength and weaknesses in their learning styles. Such type of assessments will improve student's meta-cognitive skills. They will have the opportunity to identify, document, and propose solutions for their own learning difficulties.