Its a well known fact amongst teachers that the burnout rate is at an all time high. Taking on the responsibility of forming tomorrow’s leaders is a daunting task. On a daily basis, teachers are asked to teach multiple grade levels and courses, follow several sets of requirements, teach subject standards, life skills, and values, coach/advise a team/club, be visible in the community, communicate frequently with parents, track student progress, give feedback, analyze formative and summative data and adjust curriculum accordingly, and the list goes on. Trying to accomplish all these tasks leads to high stress levels, feeling overwhelmed, isolation, and potentially leaving the profession.
By becoming a networked teacher, many of these stressors can be reduced/eliminated. Networked teachers understand that to be the best they can be and to create the best learning environment for their students, they must reach out to other educators both near and far. When teachers reach out and join networks they are basically creating a support system for themselves. They are able to make connections with other educators and resources that can provide support, inspiration, suggestions for improvement, and solutions. By joining a network, teachers are not longer the lone wolves of their classrooms. They can now communicate with others who are in or have been in a similar situation. Becoming a networked teacher could be as simple as joining and using Twitter, using help forums, and writing and reading blogs. The more networks teachers are able to make use of, the more resources and support they will be able to access.
Previously, I created a blog post about an inquiry based lesson plan that I use to teach students the Exterior Angle Theorem for Triangles. First I am going highlight aspects of this lesson where I used my network. Then I will make recommendations for additional ways they I could use my networks to enhance my or my students learning. Finally I will propose revisions for ways that my students could use networks to enhance their learning.
The first year I taught students about the this theorem, I used a direct instruction approach which wasn’t very successful. They students followed along in class but didn’t really retain the knowledge. I got the idea of making this an inquiry based lesson from a CCSS professional development hosted by KRESA. I made use of my colleagues in a face to face setting to design a lesson that could help students discover the Exterior Angle Theorem.
Another way I originally used my network in this lesson was by using digital and print resources. I found the assignment for this lesson by searching for Exterior Angle Theorem worksheet on the internet. The worksheet increases my students’ learning because it provides them with additional practice.
However there are other ways that I could make use of my networks to enhance my learning and the learning of my students. One way I could enhance the learning of my students is by using the internet to find a virtual manipulative for students to use to assist them in the measuring of angles. By using technology to measure the angles, the students don’t have to worry about measuring correctly. They can then focus their attention on finding a pattern between the angle measures. This will give them a better understanding of the Exterior Angle Theorem.
A way I could use the network to enhance my own learning is by posting my lesson on my blog or some other digital community. I could ask readers to give suggestions on how the lesson could be improved or an effective way they teach the same concept. This process would help me be more reflective on the effectiveness of my lesson.
As an extension to this lesson my students could use their network by teaching a sibling or parent about the Exterior Angle Theorem. This activity would get my students to think about the content outside of class which would increase their understanding of the theorem.
A final way my students could use their network is by posting the generalization they discovered on a class blog. If the students knew ahead of time that they would have to post their findings on the class blog, then they would be more likely to actively look for a pattern because they would want to make sure they had something to post. By making the students post their finding, I am holding them more accountable.
There are several networks that teachers can access to support them and their students. Using networks is not just another thing to add to teachers’ plates. It is a collection of resources that teachers should use to simplify all the other things that they are asked to do.
All students have the right to learn. Therefore when planning lessons teachers need to take into consideration the different abilities and learning needs of their students so that all students can achieve the same high expectations. Designing lessons and curriculum to give all students the same access to the same knowledge can be a daunting task but by following the Universal Design for Learning (UDL) the task becomes easier to accomplish. According to CAST, “UDL is a framework for designing curriculum that addresses the diverse needs, strengths, backgrounds, and interests of students in today’s classrooms” (2009). Using the UDL Guidelines –Educator Worksheet or Organizer teachers can assess how current lessons align with UDL and can even access links that suggest ways to make modifications to the lessons (CAST 2011). By following the UDL framework, teachers can ensure that they are designing and delivering worthwhile lessons where all students can achieve the intended goals and objectives.
UDL has three main focus areas to ensure that all students are able to learn the content being taught. The first area of focus is referred to as Multiple Means of Representation (CAST 2009). This section addresses how students recognize information and focuses on giving students access to multiple representations of information throughout their learning process. The second section of UDL is called Multiple Means of Action and Expression (CAST 2009). This section of UDL focuses on how students participate or demonstrate their knowledge and skills about the content they are learning. The third section of UDL is known as Multiple Means of Engagement (CAST 2009). The focus of this section is on how students are engaged throughout the learning process and how they are motivate by the learning or activity. The three different areas culminate in what students learn, how they learn it, and why they learn it (CAST 2011).
Previously I created a blog post about a lesson plan that I use to teach students the Exterior Angle Theorem for Triangles. I am going to break this lesson down using the UDL framework. I used the UDL Guielines – Educator Worksheet by CAST to breakdown my lesson (2011). First I will reflect on how the initial lesson plan design aligns with UDL. Then I will make revisions to my lesson based on UDL so that it will promote learning for all my students including students with ADHD (a special learning need I conducted reseach on).
After taking a look at my lesson plan using UDL as a focal lens, I found that I already have some UDL components built into my lesson plan. One UDL guideline that I include in my lesson is clarify vocabulary and symbols (CAST 2011). Before students begin investigating the relationship between the exterior angle of a triangle and the remote interior angles, I preview two vocabulary words with them; interior angle and exterior angle. This process involves me showing the students on a diagram where these type of angles are located on a triangle, discussing with students how the prefixes on the terms help indicate the location of the angles, labeling the angles on a diagram, and having the students identify where these types of angles are located in triangles. By helping my students break down the terms and show them where they are located in a triangle, I am giving them multiple means of representation and allowing them to connect with the content in more than one way.
Another UDL guideline that I include in my lesson is facilitate managing information and resources which includes “providing graphic organizers and templates for data collection and organizing information” (CAST 2011). While students are collecting their data about exterior angles and their remote interior angles I have provided them with a table to help them keep their information organized. The table is set up so each row is its own triangle. This way all the students can stay more organized and their information will more accessible and easier to read when they are looking for patterns later in the lesson.
A third UDL guideline that I incorporate falls in the provide multiple means for engagement category (CAST 2011). In my classroom, I have ACHIEVE posters that describe acceptable conversation, how to get help, what effort should look like, and the value of the activity for four distinct classroom activities; lecture, group work, assessments, and individual work. These expectations are reviewed frequently when students are asked to complete one of these types of activities. This way students know exactly what is expected of them for the type of activity they are going to do. By showing and referring to these posters I am fostering collaboration and community. Which according to UDL includes creating clear group expectations which I establish with my ACHIEVE posters (CAST 2011).
Even though I have some components of UDL already in my lesson plan, there are other guidelines that I could incorporate to make my lesson align more closely with UDL and specifically address the needs of students with ADHD. Just by introducing a virtual manipulative into my lesson, I am addressing several needs of students with ADHD and fulfilling more UDL guidelines. Students with ADHA can struggle to stay/be on task because they are easily distracted. However research has shown that students with ADHA spend a larger percent of their time on task when they are using a manipulative (Fowler, 2010, p. 49). This occurs because they are actually able to physically or virtually engage with content thus holding their attention for longer periods of time. Let’s take a closer look at at the effects of using a virtual manipulative.
My original lesson plan has students hand measure with a protractor the interior and exterior angles of predrawn triangles. The students do not have a choice about which angles to measure nor do they have a choice about how to measure the angles. In the end, all of the students will have the same angle measures recorded in their tables. For a student with ADHD this could be a very boring task that would not hold their attention. As a revision to the lesson, I would allow students to use the geoboard virtual manipulative created by Glencoe. Using this program, students could create their own triangles using virtual rubber bands. The program even has a virtual protractor that will assist students in measuring the interior and exterior angles. By giving students the choice to the virtual manipulative or traditional paper and pencil method, I am fulfilling the UDL guideline of use multiple tools for construction and composition (CAST 2011). Not only does having a choice about which materials to use help all students but it specifically helps students with ADHD. Research conducted has found that providing students with ADHD instructional choice will increase their academic engagement and deduce their behavior problems (Harlacher, Roberts, & Merrell, 2006, p. 10). This happens because students becoming invested in an activity when they get to decide the material they are going to use to complete a task.
Two other UDL guidelines I would address by using a virtual manipulative involve using materials that allow students to customize how the display looks. The geoboard allows students to customize their own triangles by allowing them to create the triangle anywhere on the board, and they can create any type of triangle (right, obtuse, or acute) that they want. Also students are able to use different colored rubber bands when they are creating their triangles. Being able to change the way the display looks goes along with the UDL guideline of offer ways to customizing the display information and the guideline of optimize individual choice and autonomy (CAST 2011).
For my last revision, I would not have students work on this inquiry lesson individually. Instead I would assign all students a partner to work this. This will give students a sounding board to bounce their ideas off and another set of eyes to double check each others work. By putting students in a predetermined group I am creating a peer mentoring system were the students are able to hold each other accountable for their work and behavior. Using peer mentors fits the UDL guideline of build fluencies with graduated levels of support for practice and performance (CAST 2011). Students are building their math fluencies by talking about their measurements and the patterns they notice with their partner and the partners are giving each other support.
The Universal Design for learning is not rocket science and it can easily guide teachers when they are designing lesson and curriculum. However most teachers consider several of the guidelines in UDL without ever actually thinking about UDL. Just by designing lessons with student choice, group work, movement, and multiple representations of the same information teachers are already using many aspects of UDL which ensures that all students are able to be successful.
References
Harlacher, J. E., Roberts, N. E., & Merrell, K. W. (2006). Classwide Interventions for Students With ADHD: A Summary of Teacher Options Beneficial for the Whole Class. Teaching Exceptional Children, 39(2), 6-12.
Creating and designing quality teaching lessons doesn’t happen by accident. It can be a complex process when you break it down into its three core pieces content, pedagogy, and technology. According to Mishra and Koehler (2009) “expert teachers consciously and unconsciously find ways to orchestrate and coordinate technology, pedagogy, and content into every act of teaching” ( p. 17). These three pieces do not act in isolation. Instead they constantly interact with each other and when all three pieces come together they form Technology Content and Pedagogy Knowledge (TPACK) (Mishra & Koehler, 2009, p. 16).
Previously I created a blog post about a lesson plan that I use to teach students the Exterior Angle Theorem for Triangles. I am going to break this lesson down using TPACK.
First lets take a look at the three initial components: technology, content, and pedagogy. For this lesson, each student will be using a protractor and a paper with predrawn triangles on it for technology. The teacher is will use a document camera that is hooked up to a projector. The content taught in the lesson is the Exterior Angle Theorem for Triangles which states that an exterior angle of a triangle is equal to the sum of the two remote interior angles. As for the pedagogy, the majority of the lesson is inquiry based. There also a bit of direct instruction and whole class discussion.
We cannot fully assess this lesson without taking into account the context of the lesson. This lesson takes place toward the end of the school year in a geometry unit. In preceding lessons students have learned about supplementary angles, angle pairs formed when parallel lines are cut by a traversal, and the Triangle Sum Theorem. In a previous unit students learned how to solve linear equations. Students have also completed lessons where they collect data from a geometric structure, look for a pattern in the data, and make a generalization from the pattern.
To effectively integrate the technology into this lesson I must know how to use each piece of technology and the affordances (benefits) and constraints (limitations) of each piece of technology (Mishra & Koehler, 2009, p. 15). Let’s start with the protractor. It can accurately measure angles but students must know how to use it correctly or they will get incorrect information. Paper is another form of technology used in this lesson. Two benefits of measuring angles on paper are that the measurement has more concrete meaning to the measurer, and it is a visual representation. A draw back of measuring angles on paper is that the angle and triangle are static. They will not change. In order to look at an another example a whole new triangle must be created and remeasured. A document camera works well for showing an example or for modeling to the whole class. However, if one person does all the work then the students are not engaging in inquiry learning. Knowing the affordances and constraints of technology pieces can help a teacher decide which pieces of technology should be used in a lesson.
Now lets take a look at how some of the three initial components work together in lesson planning. The overlap between technology and content (technological content knowledge) explains how the pieces of technology are used in the lesson to present the content. Since the goal is for students to find a relationship between angles the most appropriate tool for them to use a protractor. The protractor is used to measure the exterior angle of a triangle and the two remote interior angles. This process is repeated using a different exterior angle on the same triangle and on different triangles. By measuring the angles the students is collecting data about exterior angles and their remote interior angles. The document camera is used at the beginning of class to introduce vocabulary words to the students and toward the end of the lesson so the students can see what generalization they need to have written on their paper. The document camera is also used so students can see the steps needed to complete the informal proof about the Exterior Angle Theorem. The interaction between technology and content cannot be over looked when planning a lesson.
Another overlap occurs between content and pedagogy (pedagogical content knowledge). This overlap explains how to teach the content. The first part of the lesson uses direct lecture to introduce students to the vocabulary words exterior angle and remote interior angles. The intention is not for the students to become proficient in using the words. The intention is to bring the students attention to these two types of angles since they will be looking for a relationship between them. Direct lecture is the best pedagogy to get students the basic information about the vocabulary. The main part of the lesson is inquiry based. This is the best pedagogy to provide students access to the content because the students will construct knowledge about the relationship between interior and exterior angles which will give them a better understanding of the concept. The students will collect data about several exterior angles and their remote interior angles. Using this data they will look for a pattern between the angles, and then make a generalization about the measurement of an exterior angle and sum of the remote interior angles. In this lesson the students will discover the Exterior Angle Theorem. The process of discovering the theorem will help the students attach more meaning to the theorem, increase their understanding of the theorem, and allow them to apply the theorem in the future. After the students have finished their investigation, the teacher will lead a discussion about what generalizations the students found. This will solidify each student’s confidence in the pattern he/she noticed and make sure all students have the most precise generalization at the end of the inquiry. They the teacher will use guided modeling to walk the students through an informal proof using supplementary angles to write an algebraic equation. The teacher is leading this activity because it is only the second informal proof that students have seen. However the teacher will prompt the whole class with questions so they students are helping to build the informal proof. At the end of the lesson, the students will work individually on an assignment to show that they can use, apply, and understand the the Exterior Angle Theorem. The strong relationship between content and pedagogy is critical to consider when lesson planning.
Another overlapping section of TPACK occurs between pedagogy and technology (technological pedagogical knowledge). In this section the teacher must think about how each technology tool aligns with the pedagogical approach of the lesson. During the direct instruction at the beginning of the lesson the teacher is delivering vocabulary knowledge to the students by using the document camera. This gives the students one focal point to get their knowledge from. However during the inquiry part of the lesson, students are working on their own with their own protractor and sheet of paper with triangles on it. Allowing each students to use a protractor is the most appropriate for this situation because it ensures that each student is discovering the theorem on his/her own. Also students are looking at multiple examples when completing this inquiry. They are looking at the relationship between exterior angle A and remote interior angles B and C in Triangle 1. Then they do the same process with Triangle 2, 3, and 4. Then then look at exterior angle B and remote interior angles A and C for all four triangles and the same for remote exterior angle C. So essentially they are noticing a pattern by using 12 different examples. This will help the students to see that the relationship between the exterior angle and its remote interior angles can be applied to several triangles so they can make a generalization about all triangles. After the inquiry the teacher pulls the class back together as one unit by making the image on the document camera the focal point. The interaction between technology and pedagogy plays an important role when lesson planning.
When all three components of TPACK come together during lesson planning a lesson has been created that uses the best available technology combined with the strongest pedagogical methods to teach specific content. By no means is this lesson perfect . It could be improved if the intended learning outcome does not occur at a high enough percent. If one of the components of this lesson were to change then the other two components would have to adjust. (Mishra & Koehler, 2009, p. 17) According to the lesson from class today, teaching with technology has the best outcome when the lesson is functioning in the sweet spot (the middle) of TPACK.
Let us not forget about the context or overlying environment of this lesson. Students will struggle to be successful with this lesson if they are not able to accurately measure angles with a protractor. The relationship between the measure of the exterior angle and the two remote interior angles will not be as prominent if some or all of the measurements are incorrect. To compensate for the inability to correctly use a protractor, the pedagogy could change and students could work with partners. Or the technology could change and the students could use a dynamic geometry software on the computer. If students have not previously engaged in inquiry based activities they could be slow at getting started because they are waiting for guidance/directions from the teacher. First time inquiry students might struggle to see the pattern between angles because they are not used to looking for relationships. Also students may have difficulty verbalizing the pattern they see because the names of the angles change from example to example. However most of these potential hangups can be over come by adjusting different pieces in TPACK. After all, it is a dynamic framework of knowledge with multiple ways to emphasis the different pieces.
Have you every tried to make a sandwich (peanut butter and jelly or ham and cheese) using a fresh loaf of sourdough bread? Most likely you have. Was it challenging? No probably not, because you had a knife with a serrated edge to easily slice the bread and possibly a straight edged knife to cut the block of cheese and/or spread the peanut butter and jelly. Now imagine trying to create that same sandwich with only the use of a metal olive spoon, metal spatula, and cookie cutter. Seems a little bit more challenging, doesn’t it? However the task is not impossible and surprisingly still tasty.
The task of creating a sandwich using nontraditional tools is similar to the teaching that occurs in most American classrooms. Everyday teachers have an end goal in mind of what needs to be accomplished in class by the students (make a sandwich). This is called the content. Then the teachers have to consider all the different ways that the students can learn the material or the material can be taught (how to make a sandwich). This is called pedagogy. And finally the teachers need to consider what technology or tools are available (spatula, olive spoon, and cookie cutter). This will be referred to as technology. The true art of teaching comes in when teachers use the best available technology and pedagogical knowledge to teach the content to the students (How to use a spatula, olive spoon, and cookie cutter to create a sandwich). The framework of designing and building lessons can be guided by Technology, Pedagogy, and Technology Knowledge also referred to as TPACK (Mishra and Koehler, 2009, p. 15-16).
Since I am a math teacher I have a vast array of content knowledge about math. I know the math topics my students need to understand when they walk away from my class. I also have a wide selection of techniques that I can use to deliver the content to my students such as direct lecture, inquiry based, discussion, partner work, hands on modeling etc. However, I have limited accessibility to high tech technology devices, but I do have access to graphing calculators, scientific calculators, protractors, compasses, algebra tiles, sticky notes, and a variety of other normal classroom supplies. I might not always have the technology that is best to help my students understand a concept. But when designing my lessons I need to make sure that I am using the best available technology that I have and that I am using the technology in a way that will maximize my students understanding and learning of the mathematical content being taught. Sometimes this might involve using my available technology in a new way or re purposing the technology (Mishra and Koehler, 2009, p. 16). Designing lessons and teaching should be a continual process of reflection. For example, while designing activities I need to continuously ask myself what is the value in doing this activity a specific way and do I have another technology that will work better?
An example of how TPACK can be applied in a math classroom is with adding and subtracting positive and negative integers. I could simply use direct lecture to teach the students a step by step procedure on how to add and subtract with integers, but pedagogically I know that most students will not retain this knowledge and will not be able to apply it down the road when they are just given the steps. I also know that if the students are able to discover the steps, then they will attach ownership to the steps and be more likely to apply them down the road. Then I have to assess my available technologies that can assist students in adding and subtracting. If would be nice to use an internet program, but the computer lab isn’t available. The students could use calculators. They could use the calculator to compute, and then try to make a generalization from a pattern they notice. But this lesson is normally done at the beginning of the year and students are not developmentally ready to see the pattern. My best form of available technology is probably algebra tiles. Using the tiles, students can model the math problems and physically see the mathematics as it occurs. They will be able to manipulate the tiles to come up with the correct answer. After manipulating several problems they should be able to start making generalizations from the patterns they keep performing. Eventually the students would be able to make their own step by step procedure for adding and subtracting with positive and negative integers. Using algebra tiles will take a significant amount of time longer than giving the students the steps. However, the end product will be better.
By following the TPACK framework teachers are able to make solid decisions about what to teach, how to teach it, and what technology would best assist in making sure students get the most learning from the activity.
This is an 8th grade math lesson that is aligned to 8.G.5. of the Common Core State Standards. In this lesson, students investigate the relationship between an exterior angle of a triangle and the remote interior angles. After looking at several examples, the students are asked to make a generalization about the measure of the exterior angle in terms of the remote interior angles. The students will then apply this generalization to complete their worksheet assignment. Further assessment is completed through quizzes and a test.
This lesson is used toward the end of the year in a geometry unit. Before completing this lesson students have completed lessons about supplementary angles, angle relationships formed by parallel lines cut by a traversal, and Triangle Sum Theorem. Also they are introduced to vocabulary terms such as exterior angle and remote interior angle before they begin their investigation. Throughout the unit, students have completed other lessons where they have to make a generalization based on the pattern(s) they notice.
Do you ever ask yourself, “Why are my students struggling to retain knowledge about how to simplify expressions?” I have seen students struggle with retaining and applying this very concept on multiple occasions. The students tend to just add all the terms together or add all the terms with variables together and all the terms without variables together. By doing the aforementioned processes, the students fail to follow the basic principles of simplifying expressions. Normally these principles are taught using direct instruction. The students are given vocabulary terms and are even asked to identify the different terms in an expression to demonstrate that they understand what each term means. They are then instructed or shown how to combine like terms to simplify an expression. The students are even able to complete a worksheet or textbook assignment with a high degree of accuracy. However when the assessment (taken at a latter time) is taken by the students, they do not show that they have actually learned how to simplify an expression. The major problem with direct teaching is the teacher is doing the majority of the work and the students are just reacting. As Spiro and DeSchryver (2009) mentioned “direct instructional guidance…makes students’ cognitive tasks easier” (p. 111). The students have done minimal thinking for themselves and are just following a procedure that was given to them. Because little cognitive ability was asked of them, they are not able to transfer the learned material into their long term memory.
From my teaching and learning experiences, I have noticed that students gain a deeper understanding about math concepts when they discover patterns and make generalizations about the patterns with very little direct guidance from the teacher. Students are capable of discovering and noticing patterns about how expressions are simplified without direct instruction. By using this inquiry based lesson and with the assistance of circuits students should be able to not only recognize the patterns used to simplify expressions but they can also make generalizations about the patterns and apply the generalizations to more challenging situations. The hyper linked lesson below is an introductory lesson that will help students become more proficient at simplifying expressions. Students should have prior knowledge on what a variable is, and what a variable expressions is. However they do not need and should not have had experience with combining like terms.
For this lesson, each partner pair will be given a circuit board. The left column of the board will have an unsimplified expressions and the right column will have five possible “simplified answers.” When a student connects the metal clip to the correct answer the bulb will light up. If a student connects the metal clip to an incorrect answer, then the bulb will not light up because the circuit has not been completed. Using the circuit will give students immediate feedback and allow them to start seeing differences between the correct answer and the wrong answers. Students will be given ample time to work through the different circuit boards which according to Martinez and Stager (2013) will allow the students to try different approaches and modify their thinking process.
After identifying the correct answers the partners will work together and discuss answers to questions about how they arrived at the correct answer. The questions are designed to help the students begin to notice patterns between the unsimplified and simplified expressions. This metacognitive process helps the students reflect on their work, makes their thinking more visual, makes patterns more apparent, and increases the likelihood of transfer (Donovan, Bransford, & Cocking, 2000, p. 67). After completing several boards and sets of reflective questions, students will make generalizations about how to simplify expressions, and they will begin to use their generalizations to complete more circuit boards.
The answers to the reflection questions will be recorded in a Google document that is shared with the teacher. This will allow the teacher to monitor all the work the students are completing and the students thought processes. By monitor the students thought processes, the teacher can easily have a discussion with individual partner groups about misconceptions they are forming. By addressing and helping students work through misconceptions early on, it will keep the students from building a misconception from a misconception. This will ensure that the students are more successful in the lesson but will not take the learning opportunities away from the students.
To keep the students motivated to complete the inquiry honestly and not randomly guess, points can be assigned every time a partner guesses incorrectly. The partner with the least points for the activity can be seen as the “winner.” After students have completed the inquiry part of the lesson with the circuit boards it is important to have a whole class discussion about the patterns they noticed and generalizations each partner pair created. This discussion will establish a procedure for simplifying expressions that the students can take ownership of. Once the students have taken ownership of the how to simplify expressions, then they will be able to recall the procedures in the near and far future. They will have actually learned and now understand how to simplify expressions and why the procedures work.
As a follow up activity (possibly the next day), students can make their own simplifying expressions circuit boards. I would have each student focus on making a board that contains an expression structure that they found challenging the previous day. This way the students would be reflecting on their own learning. After completing the boards, the students would get a chance to share their boards with each other. Having students share their work with each other will motive them to create a better product (Martinez & Stager, 2013). An added benefit of having the students share their work is that all students will get additional practice with simplifying expressions were troublesome or challenging to them or their classmates.
By making this lesson inquiry based instead of direct instruction students will gain a deeper understanding of the material, attach ownership to the final product, be more reflective about the processes they are using and patterns they are seeing, and be able to use the procedure they discovered when ever it is needed. Although the inquiry lesson will take more time, it will produce better results. Because the end goal is for the students to actually learn and understand how to simplify expressions by combining like terms.
Regurgitating information and knowing enough to pass the test will no longer prepare a person to be successful. Instead pattern recognition and being able to organize knowledge around a central topic are needed skills.
Everyday I try to help my students become more proficient problem solvers and deeper thinkers. The rubix cube is a problem that people of all ages can relate to. Many have tried to solve it but few actually have completed the task. However that doesn’t stop us from playing around with one when it is in front of us. Although the rubix cube isn’t a real life problem, the persistence and problem solving skills used to complete the task can be applied to real life situations.
stacyblemaster 