Math Learning and Assessment

At the beginning of this course I felt overwhelmed because I was learning how to apply several application on the internet. After learning how use those activities and I looking pass the number of task required for each week I learned more in 7 weeks that I did in a long time.

This course introduced me to blogging, jing and screencast, Diigo, Dan Myer, math forums, GeoGebra, live events on-line, google groups, wikis, and many more. I also got a chance to start developing my philosophy about what is important in math. The aforementioned became the foundation on which I designed lesson plans, commented on class members’ blogs, and created meaningful tasks that I could later use with students or as resources. From this course I am also moving forward with a new lens, as I prepare math tasks, I will be thinking about the level of math sophistication in the task and how to alleviate math anxiety in my students.

Unlike most online classes this course had the feel of a regular course because of the virtual classroom. Everyone was respected and their voices were heard during the online discussions.

The most difficult task for me was commenting of other class members blogs especially on their mini-units because I have a limited secondary math background and I was unfamiliar with some of the higher level math content.

A suggestion for future classes is students work as a group to continue developing a unit over the course weeks.

Excellent course and professor. Thanks for the opportunity to gain a new insights on teaching, learning and assessning math.

Live Event Reflection

#mathchat Thursday @ 7:30 – What maths should be in a curriculum that every adult should know or be able to do?

This live event gave the participants an opportunity to sound off about what maths should be in a math curriculum that every adult should know. This was a very interesting topic, most participants who weighed in stating that financial literacy should be in the curriculum. Most adults have the basic knowledge in mathematics but struggle with financial literacy as related to the real world. As I read comment being posted, I started to think about how our economy and how it has been affected by the poor decisions that people made with credit cards and borrowing money.

Some middle schools teach students about stocks but that’s not enough. Math curriculums should include simulations about using credit cards, how to invest, borrowing money, and how to build a stronger financial foundation.

Although several topics should be must haves in the curriculum, finanial literacy should be on the top of the list because several individuals are affected by the decisions they make because of the lack of knowledge about managing their finances.

As always another great discussion.

Math Anxiety

Math anxiety is defined as feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations Math anxiety can cause one to forget and lose one’s self-confidence (Tobias, S., 1993).

Math Anxiety Response to

Weeks 3 – 5 Lessons

Grace’s Week 3 Lesson – Linearity

Sam’s Week 4 Lesson – Symmetry

Kate’s Week 5 Lesson – Data Visualization

For more information about math anxiety take a look at the following links

Cause and Preventions of Math Anxiety

Coping with Math Anxiety

Overcoming Math Anxiety

Math Anxiety Quiz

Resources

Image: http://www.google.com/imgres?imgurl=http://mbaker.columbiastate.edu/cartoons_gifs/anxiety1.jpg&imgrefurl=http://mbaker.columbiastate.edu/Cartoons/cartoons2.htm&h=421&w=576&sz=31&tbnid=AL-OExkYRsnQfM:&tbnh=98&tbnw=134&prev=/images%3Fq%3Dmath%2Banxiety&zoom=1&hl=en&usg=__3n5Nz-6tMwzHHPTqZ4rcIPysBUc=&sa=X&ei=XQBzTJu_KsP48Aae18WbDg&ved=0CDwQ9QEwBg

Math Textbook Review

Until June of the past school year my school district used Math in Context, MiC. Most teachers did not like the program because they felt it did not address the basic skills that our students lacked. They were correct, however, MiC is content based. Instead of a large textbook, the program uses several small books (strands), each strand is designed to address a particular area of mathematics. The video below is a brief introduction a section in MiC – Insights Into Data.

Click to preview MiC

In relation to Bloom’s Taxonomy MiC uses questions that are application, analysis, synthesis, and evaluation levels. Students are presented with scenarios in which they required to study the information and make logical responses and also back up their responses with justification. The role of the teacher when using MiC is to ask the students questions that will eventually guide the students to an answer. The students arrive at their answers through discovery and group conversation. In my opinion the MiC textbooks were designed with the assumption that the students are on grade level. Since the book guides students, there are questions that seem redundant and this becomes frustrating to the students and the teacher. Overall, I believe that MiC addressed the higher levels of Bloom’s Taxonomy because students are asked to justify their answers based on the observations and problem-solving skills.

Creating Task – Triangles

1. Use the properties of triangles to create a game of Math-O, the games will be created as a review and  will be used to reinforce the concepts of triangles.

Assessment: Rubric

2. Create a classification poem about triangles. Creating Poems

Assessment: Rubric

3. Use your knowledge of congruence or similarity to create a podcast or screencast about triangles.

Assessment: Checklist

Live Event Reflection

#mathchat Thursday @ 7:30 – What types of tech should we use in lessons and when?

Tonight’s math chat provided several examples of technologies that teachers use to enhance their lessons and make them more engaging for students. Podcasts, SmartGoards, GeoGebra, Google Docs, Cameras, 3D Virtual Aids, Virtual Manipulatives, and Online Games and Simulations are some of the technologies participants mentioned. Most of these technologies are newer technologies and often when we refer to technology most people today think of things that can be done with a computer. Some items that are considered technologies of not to long ago are calculators, rulers and protractors. Not many participants referred to those items but they are still excellent tools that students use.

When should technology not be used?,  was another discussion which participants weighed in. Most participants commented that technology should be used as needed and as a means of engaging students. Most were concerned that students become dependent on the calculators and would prefer use the calculator instead of a paper and pencil. This is a discussion that has been going on for ages. Do calculators slow down a student’s ability to complete math problems with paper and pencil? In my opinion, once students understand and grasp a concept and can master how complete problems with paper and pencil they should be able to use a calculator so that they could complete their math assignments faster and more efficiently. Students should also be taught that a calculator is not a crutch and anything they can do on a calculator can be done with paper and pencil. Also most standardized state assessments (PSSA) require students to complete a section of the assessment without the calculator.

The discussion above led to the question about how participants feel about no Interactive White Boards (IWB) or online activities in the classroom. Not many participants responded to this question but in my personal opinion the idea of not having an IWB or online activities in the classroom seems far-fetched in most classrooms of today but before IWB’s teachers found ways to engage students in math lessons. I also believe that good math teachers will reach and engage students whether they have IWB’s and other technologies in their classrooms or not. Math classrooms continue to change as more technologies become available to teachers. With these technologies educators can make math come  alive in the classroom.

The discussion ended with the question about what technologies will participants use in their classrooms in the up coming school year. Podcasting was a popular response because several participants were interested in how to do a podcast. I will definitely introduce the teachers I will be supporting to GeoGebra, screencast, and provide professional development on using calculators more efficiently.

As always it was another informative discussion.

Bloom’s -Task – Assessment

Isosceles Triangles

Knowledge

1. Draw an isosceles triangle.

2. Circle the isosceles triangles in the picture below.

Comprehension

1. Multiple Choice – Chose the correct answer

Which statement is true about an isosceles triangle?

a)    All side have the same measure

b)   Two sides have the same measure

c)    None of the sides have the same measure

2. True or False – Write T (True) or F (False)

Isosceles triangles have two angles with the same measure. ______

Application

1. Maria is planting flowers around an isosceles triangular garden. The perimeter of the garden is 62 feet and the shortest side is 12 feet, what are the measures of the other sides of the garden?

Show your work.

2. One of the angles in an isosceles triangle is 48°, write the steps to finding the measures of the other angles in the triangle.

Analysis

1. Construct an isosceles triangle. What are the characteristics of an isosceles triangle? What properties of geometric figures do you know that might be of help to you to construct an isosceles triangle and guarantee that it is isosceles without using any measurement tool?

2. Use GeoSketch Pad to manipulate an isosceles triangle

Synthesis

1. Create a word problem about isosceles triangles.

2. Using the properties of an isosceles triangle, design a review game about isosceles    triangles.

Evaluation

1. Given triangle ABC, with D on BC and AD bisecting angle A.  The center of the circle circumscribing ABC is the same point as the center of the circle inscribed in ADC.  Prove that ABC is an isosceles triangle.

2.Use the 2-column approach to justify the statement above.

Scatter Plot Lesson Plan

Purpose: This lesson is designed for 8th grade students to explore scatter plots.

Prior to the lesson have students work in groups 4 to collect data on 20 people on one of the following topics: number of hours people work and their salaries, amount of hours high students study and their GPA, student’s arm span and their heights.

Give students a worksheet of a scatter plot about the population growth from 2000-2004,  have the students answer the following questions.

What was Washington’s percentage growth from 2000 to 2004? _________

What other information can be given for point labeled Washington? _________

Which state had the largest population growth by July of 2004? _________

What information can be given from a data point? _____________________________________

______________________________________________________________________________________________________________________________________________________________

___________________________________________________________________________________________

Write a statement about North Dakota? ____________________________________________

_________________________________________________________________________

Discuss the responses with the students. Discuss and explain the following term using the scatter plot above: data point, scatter plot, cluster, outlier.

Explain to the students that they will be creating scatter plots using the information they collected from the survey they completed with their group. Have the students use the Excel application on their computers to enter the information they collected from their survey. Guide students through creating a scatter plot in Excel.

Discuss with students how a scatter plot shows a relationship between two sets of data. Have students identify the outliers, and the clusters with the scatter plot. Next have the students write a brief statement about the data based on the scatter plot.

Assessments

A Look At Assessments

Assessment is an on-going process aimed at providing insight and improving student learning. It involves making expectations clear to students and setting outcomes for learning. It used as an indicator on how well student performance matches those outcomes. It uses the resulting information to improve student learning. The assessment process helps to support academic culture dedicated to assuring and improving student learning. Assessment of student learning occurs at various academic levels. http://www.oaklandcc.edu/assessment/Definition.htm

In the educational world data drives instruction, educators are constantly collecting data about their students in the form of assessments. Assessments provide educators with vital information that determine instructional strategies, interventions, student placements, IEP goal, and school wide plan.

It’s important that assessment occurs in order students to be provided with the instructional supports necessary for them to be successful. Through this assignment I realized that assessment examples overlap assessment categories. Educational Leadership indicates that formative and summative assessments are sometimes because of the intended purpose of the assessment. To learn more about the assessment see the chart below.

As a teacher who likes to use creative ways to assess students I find it difficult to say I like an assessment over another because I assess based on student’s abilities, needs, and IEP goals. Like most educators, my concern, I have to be very careful not to run into the trap of teaching to a test. No Child Left Behind and the push to make AYP sometimes limit the assessments used in schools. As a teacher in a district with a scripted curriculum and the types of assessments dictated it’s sometimes difficult to use meaningful assessments.

Type of Assessment	Examples
Formative Assessment- Occurs during the instructional process and provides information that teachers use to adjust learning and teaching in order too ensure students are making strides toward achievement for the targeted standard based learning goals. Helps teachers determine the next steps during the next steps during the learning process Students should be active participants as a means of promoting student involvement and student achievement.	Criteria and goal setting Observations Questioning Strategies Self Assessments and Peer Assessments Student Record Keeping
Summative Assessment– Given periodically to determine what students know. Serves as a tool to help evaluate the effectiveness of programs, school improvement goals in alignment to school curriculum or student placement in specific programs. Cannot be used at a classroom level to make immediate instructional adjustments or provide intervention because they occur well after instruction has been given. Data from summative assessments are also for school accountability AYP.	State assessments District Benchmarks or Interim Assessments End-of-Unit or Chapter Test End of Term or Semester Exams
Objective Assessment – Based on all the students learning the same things Have a true answer	Multiple Choice True False Short Answers
Subjective Assessment – Based on teacher’s judgment to determine the grade Takes longer to grade Consist of complexed questions	Essay type questions
Self-Assessment – Informs the learner Encourages independent learners Can increase student motivation Help students check if they mastered a topic, skill or concept	Peer Review Practice Quiz Games Interactive Activities
Peer Assessment – Students evaluate each other Critique each others work	Rubrics Checklists Feedback Diagrams
Authentic Assessment – Reflect real-world situations Consist of topics and issues that interest students Students produce a quality product or performance Students are aware of the evaluation criteria and standards Allows for self-evaluation and self-correction	Portfolios Constructed Responses Self Assessments Observations Projects Exhibitions Rubrics
Constructed Responses – Students apply knowledge, skills, and critical-thinking abilities to real-world, standards-driven performance task Students construct their own answers Teachers use the information to gauge students’ understanding of skills such as graphing, measuring, sorting etc..	Prompts Short Answers Showing Work Visual Depiction Activities
Selected Responses – Students are provided with response to choose from	Multiple Choice True/False Matching Fill in the Blanks
Standardized Assessments – Predetermined criteria Administration and scoring are in consistent manner	PSSA Assessment SAT’s
Performance Assessment – Students demonstrate something that meets a specific criteria	Research Papers Create Math Models Producing a Book Exhibits Culminating Activities
Ability Assessments – Designed to assess a student’s ability to complete certain task Results from the assessment determines placement into programs Provides teachers with information about deficits with skills to be addressed through intervention Assess student’s readiness	Woodcook-Johnson III Iowa Algebra Aptitude Test Cognitive Abilities Test

Resources

http://www.nmsa.org/Publications/WebExclusive/Assessment/tabid/1120/Default.aspx

http://vudat.msu.edu/subjective_assess/

http://www.rapidresources.com/res_const_response.asp

http://jonathan.mueller.faculty.noctrl.edu/toolbox/tasks.htm

http://www.rmcdenver.com/useguide/assessme/online.htm

http://www.riversidepublishing.com/products/wjIIIComplete/index.html

Live Event Reflection

#mathchat Thursday @ 7:30 – How do we assess whether or not mathematical concepts have been grasped and understood?

This topic aligned with Task 5-4 on assessment. The discussion started out with examples of assessment such as journals, sticky notes, observations, formative and summative assessments. To assess understanding during instruction red and green cups is an excellent idea or just have a conversation with the students. There was a consensus that assessment is a vital part of instruction and should occur often. We discussed how to assess whether students just understood a concept of if they  apply the concept. Suggestions for assessing student’s understanding included having students recall facts or use a formula, and for assessing student’s ability to apply a concept they could complete a project.

Toward the end of the chat a question about what do we do with the information gathered after an assessment. Suggestions included proving students with feedback and using the information to re-teach.

Assessment is indeed a vital part of the learning process and teachers should have a toolbox of assessment strategies and an idea of what to do with the information they receive after assessing students. I think teachers need more professional development on the steps to take after assessing students in math.

As usual it was an excellent and informative live chat.