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Problem Solving Vs Mathematical Modelling

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Problem Solving Vs Mathematical Modelling

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Problem-solving's vocal point is centered around the idea of developing mathematical solutions whereas Mathematical Modelling relates to real-world scenarios and how the individuals subjective experiences influence the relationships between the information sourced from the scenario. It has more broader interpretations which promotes assumptions that can lead to varying solutions.

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Shayla Demark, Morgan Seach, Mikayla Bond, Tavarnia Gobel.

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Shayla Demark, Morgan Seach, Mikayla Bond, Tavarnia Gobel.

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In a sentence articulate how mathematical modelling is different to problem solving.

Mathematical Modelling uses real life problems and is open to interpretation where as Problem Solving is more of a mathematical approach.

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How is mathematical modelling different to problem solving?

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How is mathematical modelling different to problem solving?

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Isabel Andrews, Piper Cartwright, Madalyn Thomas and Beatrics Bonnici:

The difference between mathematical modelling and problem solving is that whilst problem solving components are apart of mathematical modelling, mathematical modelling is using maths concepts and structures to represent and analyse real world situations.

The concepts aren't explicitly mentioned and the situation is broader and requires more assumptions to solve the problem.

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Problem solving often gives all of the information and parameters needed to solve the problem within the question. You can then solve the problem from here with this information. On the other hand, mathematical modelling is much more broad and open to interpretation based on lesser amount of information given. Modelling can include different interpretations based on prior knowledge and abstract thinking from real world scenarios. Mathematical modelling often includes pictures as a stimulus to prompt thinking and parameters around the question.

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Problem Solving vs Mathematical Modelling

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Problem Solving vs Mathematical Modelling

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Problem solving is the application of mathematical reasoning to solve a given problem whereas mathematical modelling involves a real-world situation where mathematical concepts, structures and relationships can be drawn upon. This is why the two are closely related.

Ella Southall (I was on my 4th year placement week 6 and so was not in a group).

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Piper Cartwright, Mikayla Bond, Bobby Crozier

Mathematical modelling in primary classrooms helps students connect maths to real-life contexts, making learning more engaging and meaningful. English (2013) shows that working with complex data builds critical thinking and problem-solving, while Parish (2023) highlights how authentic contexts motivate students and show the usefulness of maths. Together, they suggest modelling fosters reasoning, collaboration, and creativity beyond routine procedures.

Mathematical modelling can be seen through examples, such as how much petrol is left in the tank, when writing a birthday card to know how much space to fill and when cooking and baking, specifically when making quantities different to what the recipe states.

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Insights about modelling in Primary School

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Insights about modelling in Primary School

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In mathematical modelling for primary school, it is important that students understand that modelling includes different approaches and perspectives, allowing all students to access the learning. Collaboration is crucial as it can evolve thinking skills, enriching their approaches as students work together to combine their perspectives. Relevant scenarios ensure students' engagement and allow them to apply their knowledge in different contexts, both inside and outside the classroom.

Lily, Samuel, Isabel

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Maelee, Morgan, Yanan and Alicia

There are many assumptions that mathematical modelling is a skill that should be introduced during high school, and that primary school students are not adept at learning (English, 2013). There has been a recent push to involve mathematical modelling into all year levels of both high school and primary school (Parish, 2023). However, mathematical modelling is a great concept to introduce into primary school because it encourages students to think more abstractly. It is extremely useful to connect the content that students are learning in other subjects to maths (English, 2013). For example, the gold-rush, the outside environment, natural disasters, or garden beds that they see in the school etc. (English, 2013). In the workshop, we discussed how students can find maths anywhere, and to encourage students to think about maths when they walk past a garden or when they go to the zoo.

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Insights on mathematical modelling

Parish's (2023) findings, that mathematical modelling can be relevant in a primary school context, were evidenced in today's workshop. This can be seen through the Mountain Dew example as it was simple and relevant to primary school students.

We also engaged with 3-Act tasks where we posed mathematical questions such as “I wonder how tall the Moon Man’s head is..”. We then explored mathematics in a meaningful way and translated the solution back into the real-world example.

As discussed by English (2013), students in a primary school setting will display variation in the models they create. There was a wide variety of approaches evident in the swimming task, similarly throughout the seminar, groups were demonstrating differentiated ways of thinking to come to a conclusion.

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Insights about Mathematical Modelling in Primary School:

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Insights about Mathematical Modelling in Primary School:

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Mathematical modelling supports students to engage with authentic contexts, making math explorations meaningful and purposeful (Parish, 2023). Furthermore, such 'problems allow for a diversity of solution approaches and enable children of all achievement levels to participate in, and benefit from these experiences' (English, 2013). These problems promote collaboration between students with a diverse range of mathematical experiences of knowledge, which overall supports their learning development. In the workshop, we saw examples of this when the Moon Man problem was posed, showing how everyone had similar ideas, but the strategies in which they undertook to get the outcomes were vastly different. Moreover, showing how maths is interwoven through mundane objects and contexts and how we as learners can apply mathematical reasoning to produce sound solutions from assumptions made about the situation.

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Today, we began with Real  World Situations and broke them down from messy ones into mathematical situations (B&C).

We did this through using real-life experiences such as the amount of toothpaste used and how many times a day we brushed our teeth to provide context to the problem (C&D).

There was different solutions found as some of us attacked the problem different from others, based on what made sense. This helped us revise our solutions as we had to identify what we wanted to know, the amount of toothpast needed or the how many days one tube would get us (E&F).

A report has not be started yet as some people did different tasks but additionally, there is still variables to be investigated such as people travelling.

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Majority of our group reached the Mathematical solution. Morgan and Mila explored the toothpaste problem whereas Bobby explored the Cats problem. Bobby used the statistics to mathemetise and form a model to produce a more realistic claim finding about 100 cats if the orignal cat is 3 years old. So he recognised he found himself in the second stage of the modelling cycle before transitioning into working mathematically to solve for the solution (stage 3). As for Morgan and Mila, both found that you need a pea sized amount of toothpaste (stage 1). Both did further research but Morgan went to solve for the solution (stage 3) whereas Mila was still formulating assumptions about the problem and getting a better idea of the posed problem considering how many people are on the trip, size of the container and so on (stage 2).

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Ella Southall, Piper Cartwright, Arlee Bennett

1. Real world solution

1.  looking into the amount of toothpaste in grams that people use when brushing their teeth.

2.  how many times a day do people brush their teeth on average

3.  cost of toothpaste

2. Mathematical Solution

1. How many grams per brush x number of brushes per day x number of days

3. Real world meaning

1. China has minimal health and safety laws for toothpaste, hence the traveller wanting to bring their own

4. revise model

1. unhappy with the amount of toothpaste suggested

5. revise model

1. still unhappy with the amount of toothpaste suggested

6. accept solution

1.  came to an agreement that it is likely that we use 1 gram of toothpaste per brush (2 grams a day)

Now we are ready to begin our final report.

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When working through our tasks today (Yanan and Alicia - Toothpaste Task, Maelee - Cat Problem), all members of the group began in stage A: messy real world situation. To move to stage B of the modelling cycle: real world situation, assumptions were made according to the context of the task. This was particularly relevant to the toothpaste task where there are many factors to consider and interpret. An example of this is considering that there is a 100ml limit for taking liquids overseas. Regarding the cat problem, once assumptions were made, it was possible to structure the task and begin mathematising to move towards stage C: Mathematical model. An example of this was creating a calendar to demonstrate the timeline of pregnancies and mathematising this in a table.

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Problem solving involves finding a solution to a mathematical problem set in the real world, comparatively mathematical modelling differs as it is based in messy, real-world situations and mathematics is then used to better understand and analyse the situation.

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Benefits and Challenges of Mathematical Modelling:

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Benefits and Challenges of Mathematical Modelling:

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Benefits:

-It is accessible to all students as the mathematics involved works off of pre-existing knowledge

-Helps support student productive disposition and motivates students to see that mathematics is meaningful and applies to everyday contexts

-It helps equip students with the power to exercise the fundamental duty as a citizen to appreciate, critique and use models and modelling that permeate our modern world

Challenges:

-Students may not have the knowledge necessary to apply the modelling process. This can also contribute to increased maths anxiety.

-The process of implementing the steps necessary to make the mathematical modelling process meaningful can take considerable amount of time and planning that teachers may not be able to do. They may also lack the knowledge and skills to implement it.

-Initial presentation of mathematical modelling structure can manifest student confusion and reduce self efficacy due to the subjective nature of the problems posed

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Benefits of MM in primary school mathematics

1. Connects students to mathematics in a real-world context

2. Students engage a range of critical thinking skills to complete modelling tasks

3. Mathematical modelling tasks can address a range of curriculum areas

Challenges in implemented MM in primary school mathematics

1. Pushback regarding 'lack of explicit teaching'

2. Tasks often run over an extended period of time and can take up multiple lessons

3. Lack of confidence from teachers about how to tach MM as a process

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Benefits

- Connecting to real world problems and situations,

- Collaboration and communications,

- More involvement and understanding if it’s related to real world scenarios,

Challenges:

- Time pressure,

- Issues/lack of with student foundational skills,

- Balancing task design to students capabilities

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Benefits:

Students are able to think critically and creatively in class. They can think outside the box and have to make considerations to their models.

Students are able to work as a team and collaborate to create a solution to the model. It also gives students more control over their learning and they can lead their investigation.

Since the models reflect everyday life situations, students are able to understand more of the meaning behind their learning. Students are likely to be more engaged in the learning because they can relate to it more.

Challenges:

Students might not know all of the content that is needed for students to complete a mathematical model. It might require knowledge of different maths, so students might struggle to engage in the model.

Not all students are going to be working at the same level in maths. Especially in composite classes where there are 2 different year levels. Therefore it can be difficult for students to be on the same page.

Mathematical models often cover multiple curriculum areas, to which students will likely need to know prior to engaging in the modelling. This can be extremely time consuming, and the modelling process can often span over multiple lessons. Therefore, it can consume a lot of time in a small amount of school space.

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FINAL REFLECTION;

Personally, I believe I have created a deeper understanding of mathematical modelling and how it can be used in a classroom. It's more about letting the students explore the answers/ solutions rather than the teacher just talking at them. There shouldn't be a time limit on projects like these, as sometimes they can extend for multiple weeks; however, there is STILL learning going on. Similarly, I believe more teachers should understand mathematical modelling more so they feel comfortable teaching it and exploring it. Mathematical Modelling also correlates with multiple other subjects and curriculum.

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Throughout this unit, I have developed an understanding of the importance of mathematical modelling, particularly in a primary school context. This reflection discusses two key ideas: the development of critical thinking skills and connecting mathematics to real-world contexts.

Through participating in mathematical modelling tasks, students use a range of skills to move from one stage of the cycle to the next,  some of these include: making assumptions, mathematising, analysing and justifying. Not only are these skills key for the development of students mathematical understanding and skills, but these skills can also be applied across a range of subject areas, as seen in the sea of mud activity which expanded across multiple areas of the curriculum.

Additionally, mathematical modelling outlines to students the real-world implications of mathematics. It is important for teachers to demonstrate to students the importance of what they are learning to their everyday lives so that they are able to understand the purpose which will enable them to develop a productive disposition towards mathematics. Mathematical modelling draws on these real-world scenarios and students connect these situations to mathematical concepts to better understand the situation and produce a solution or representation.

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A key idea I developed in the mathematical modelling unit is that mathematics is more about assumptions, testing, and refining models for real-world problems that are often messy, rather than just seeking exact answers. I also realised that collaboration enhances modelling, as diverse perspectives help identify errors and improve solutions. These insights altered my approach to problem-solving, prompting me to focus more on flexibility, justification, and reflection, rather than simply seeking a single correct answer.

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Engaging with the unit has given me a lot of clarity surrounding the mathematical modelling cycle. A key element that stood out often was the ability to critique and alter your work, showing the process is not linear, and rather we jump between it is different stages to best solve the posed problem. It showed me how constantly evaluating the mathematics, assumptions, and other influences can contribute greatly to the outcomes we get. Another key idea that was evident throughout the unit was how much it interconnects with problem-solving, particularly having the problem relates to real-world scenarios. As a teacher, we must show students how relational mathematics is to our world and how mathematics is meaningful and supports everyday living. In doing so, I started to note how the modelling cycle not only strengthens students' metacognitive abilities but their problem-solving skills as well, in turn, reinforcing their productive disposition. This to me was particularly emphasised in the Sea of Mud problem, as it was evident that students felt motivated to help that community by using mathematics to justify environmental relief efforts. It also showed how their collaboration not only strengthened ideas but supported the development of mathematical expression and language as well.

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One of my main takeaways from learning about mathematical modelling in this unit is the importance of connecting maths to real-world contexts. Modelling helps turn complex, practical problems into mathematical terms, making the subject more relevant. It shows that maths is not just about abstract numbers but a tool for problem-solving and decision-making in everyday life. This means students can have the freedom to try and solve real world problems that observe in their lives using the problem solving strategies.

Another key takeaway is that modelling is not always about finding a perfect answer but about making reasonable assumptions and testing possible solutions. The process often involves refining models, adjusting variables, and interpreting results in context of the problem. This helped me realise that mathematics is an iterative process, where flexibility and critical thinking are important. This is a good reminder to students that even if you don't have all the information we can still come to appropriate conclusions.

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I feel like I learnt a lot during this unit. There’s a lot to the mathematical modelling process and a lot to consider. I think one my biggest learning points was that maths doesn’t have to be one straight answer. It’s not necessarily about the answer you come to, but about the process to get there and then your ability to justify it. Modelling also includes exploration and discussion, which makes learning richer and more meaningful.

I started this topic with apprehension because I like having a simple answer, but grew to really enjoy modelling because the process was extremely fun and intriguing. I liked that it related to real life problems and inspired a lot of discussion. I can visualise this being really productive in classrooms and inspire more love for maths in students who might not typically enjoy maths.

The review process is also very valuable because it challenges students’ thinking and encourages them look back at their learning. It also finds areas of improvement or gaps in knowledge.

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I believe mathematical modelling is extremely important for both teachers and students. It is not just a way to learn mathematics, but more importantly, a tool that makes mathematics more practical and interesting.mathematical modelling improves teachers’ teaching methods. Traditional teaching is mostly teachers lecture and students listen. But with mathematical modelling, teachers can act as guides they design interesting tasks for instance, asking students to design a small garden and calculate the amount of soil or grass needed, offer help when students encounter difficulties, and encourage group cooperation and idea-sharing. This makes classes more lively, boosts students’ participation, and helps teachers focus more on developing students’ abilities rather than just imparting knowledge.

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After completing the past 4 weeks of the mathematical modelling unit, I have realised how important this process is for teaching and learning mathematics. Mathematical modelling involves the use of mathematical concepts, relationships and structures in which can assist in modelling real world situations. This ability to connect mathematics to the real world and use models to represent this thinking process will assist students in becoming educated citizens in the modern world. By following the mathematical modelling process, students are able to critically reason and make assumptions on given information to further apply it to a real world scenario, which is an important critical and creative skill. Mathematical modelling is also embedded within the curriculum for all students and can interconnect with other subjects such as geography and English, further reinforcing its everyday importance. Due to these findings, my biggest takeaway from this process is that students can apply their everyday and mathematical understandings to more complex real world situations which are important skills students need in the modern day world.

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After completing the four weeks of mathematical modelling, I have realised that there is a lot more to maths than just addition, multiplication etc, and that there isn't always just one correct answer. People see things differently and have different approaches that they may take, and thats okay, mathematical modelling is not linear and not one way is right or wrong. Mathematical modelling can be used in the classroom when trying to figure out a problem that is around school, for example the garden bed task we did, and this is beneficial as the students are collaborating with one another but also using maths skills they have previously learnt to answer a real world problem that they have.

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Throughout this unit, one of the biggest learning points I had was with the mathematical modelling cycle. This cycle demonstrates that learning with the use of mathematical modelling is not linear, and there are many steps within this process. Being able to communicate, and justify your findings to ensure they are satisfactory, whilst also being able to interpret the mathematical output is significant in understanding this cycle. This unit also helped to remind me that within mathematical modelling, collaborative learning and thinking can promote new ideas, help solidify your understanding, make you think about concepts differently, help develop new forms or patterns in thinking and helps to justify your methods overall.

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One big idea I have developed over the past 4 weeks of learning was how important mathematical modelling is. When I first started this unit, I had never heard of mathematical modelling therefore I did not think it could be that important. But by participating in lecture and seminar material I was able to realise what it is and how important it is for children to learn. By not having one linear answer for the equation, it allows children to learn and develop mathematical skills in different real life scenarios. It differs from traditional learning where the students sit and listen, but by relating it back to real life situations. This alllow's children have some sort of relationship with the question and may make it easier to complete.

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Problem Solving vs Mathematical Modelling

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Problem Solving vs Mathematical Modelling

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Problem solving is mostly mathematical it uses mathematical reasoning and understanding to find a solution or multiple solutions to a problem. Problem solving typically asks a question or poses a problem and using reasoning and understanding we can determine a solution. Whereas mathematical modelling typically depicts real world situations and applies that to maths concepts. It usually involves problem solving techniques to model and understand real world issues.

Harry Fleming

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Final reflection

In this unit I found mathematical modelling really interesting. I liked that it wasn’t just about getting the “right” answer but more about exploring different variables and seeing how the problem could change. It made me realise how maths can actually connect to real-life things and why it matters.

I also noticed the modelling cycle isn’t just one straight line, you often go back and rethink what you’ve done, which made sense to me. The very first week of activities showed how maths can link to other subjects and also get students working together and thinking in different ways. Overall, I learnt that modelling can make maths feel more useful and help students build problem-solving skills. I think it'll be a fun avenue to explore with students.

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Stillman's article (2015) is about finding and posing problems and how to use them through mathematical modelling.

Mathematical modelling involves using maths to understand and solve a real-life situation relating to real-world scenarios, whereas problem solving involves using maths to answer and develop solutions to a mathematical question.

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Insights about modelling in Primary School

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Insights about modelling in Primary School

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Maths modelling is turning real world problems into a maths problem using mathematical processes and problem solving strategies, where the solution is applied to the real world (Parish, 2023). In a primary school context we can use themes of natural disasters, sports, events, mentor texts and many more scenarios can shape mathematical modelling in a primary school (English, 2013). A principles of mathematical modelling is to make meaning of real world situations to connect life events and contexts to maths and make meaning of these situations through maths (English, 2013). We can use students' experiences and interests to foster mathematical modelling, while doing this it provides entry points for students at all different levels and engages students to problem solve.

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Post a summary statement about your insights into implementing Mathematical modelling with primary school students that were evident in the readings.

It was evident through both readings that collaboration is key to developing different skills and learning that they may not have thought of if they had just completed a task individually. It was also clear that students first attempting problems individually and without direct instruction allow them to identify what they know and can connect to the real world. They can then share ideas and opinions with peers to expand learning.

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A. Started with the messy situation that was given of a person wanting to bring a supply of toothpaste for a year to another country.

B. Created a mathematical situation and some assumptions of:

365 days brushing your teeth 2 times a day 730 brushes

Using the recommended amount of toothpaste 0.25g

1 tube of toothpaste is 175g

C. created a model of (730 * 0.25 = 182.5)

D. Solution - 2 tubes of toothpaste for a year.

E & F. When applied to the real world we felt it unrealistic to use only 2 tubes of toothpaste for an entire year. So we revised our definition of 'pea sized amount' to 0.5.

C. created a new model/table to show the relationship between toothpaste brush size (0.25 - 1g), amount that needs per year, and how many packets.

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Benefits and Challenges of Mathematical Modelling

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Benefits and Challenges of Mathematical Modelling

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benefits:

The connection and application to the real world context. Being able to explore issues, topics, interests through maths and doing it creatively is beneficial to the productive disposition of students.

Engagement to a range of problem solving and critical thinking

Students from all different achievements can access mathematical modelling

Challenges:

- Timing often teachers complain about timing and issues with timing.

Lots of planning and resources required to put in a mathematical modelling unit.

Confusion

lack of guidance students could get lost or take a wrong turn

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My final reflection on mathematical modelling is that I would really like to implement a unit in the future. In the beginning I wasn't aware of mathematical modelling and wondered how it was any different to problem solving. I realised Mathematical modelling isn't about finding a specific answer students can have all different answers for example in the toothpaste task my initial answer seemed crazy so I revisited and changed my answer. Giving students the ability to seek answers and problem pose will build critical thinking, problem solving skills and even resilience. Not only can you run a modelling unit but I feel that in between you can have those teachable moments where students are learning those things in the curriculum. I believe mathematical modelling builds on all things maths. It builds on procedural fluency, productive disposition and problem solving skills.

Mathematical modelling makes meaning out of our current context, we can apply it to our own life and situations around us. It encourages exploring our world and ideas that students have. It involves collaboration and team work.

Overall, my understanding of mathematical modelling has been profound and I find excitement in wanting to implement my own unit on mathematical modelling.

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Which stages of the mathematical modelling cycle were you aware of utilising today when working through your task?

Provide examples with your explanations, and remember to refer back to the numbers and letters in the chart below.

I was aware of all of the stages of mathematical modelling when working through the toothpaste task, repeating in my head where I was up to in the cycle when completing the question. The step that has stuck with me and become the most clear when working out, not just the toothpaste tasks but the other tasks throughout my portfolio, is step 2, where I begin to assume real examples to work them into the mathematical model.

For example, in the toothpaste task, I assumed that the individual was quite a hygienic person because they are worried about the health and safety laws of the country they will be living in for a year. So I assumed that they brush their teeth at least twice a day, meaning they will need enough toothpaste to brush their teeth twice a day for the year. I also assumed that they would want some leftovers in case, for any chance, they run out early. I assumed that the average amount of toothpaste used to brush your teeth is 0.5g.

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List 3 benefits of implementing mathematical modelling in primary
school mathematics

It benefits students by educating them on other important learning opportunities that promote their safety.

Students can learn in a range of learning areas within mathematical modelling.

Students are encouraged to use their own critical thinking skills rather than relying on being spoon fed by their classroom teachers.

List 3 challenges for teachers in implementing mathematical modelling
in primary school mathematics

The tasks can often be quite long and require more time to complete.

It can be hard for teachers to understand and learn the mathematical modelling cycle, let alone for students to learn and be confident in using it within their education.

The tasks can be very messy, which may stress and confuse students because there are so many ways to go about solving the questions given.

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One individual and final reflection that captures one or two of the big ideas you have developed as a result of the mathematical modelling unit.

The idea I have developed as a result of the mathematical modelling unit is that, through mathematical modelling, it is okay to have multiple answers as long as you have the evidence to back them up. Multiple ways and strategies can be used for a real-world messy mathematical modelling problem. It is a great way to introduce collaboration to the class. I've really enjoyed sharing my ideas with my friends and family within this unit because it is interesting to see their perspectives relating to the cycle and the questions posed. It has been so satisfying when I complete my answers, but also being able to have those 'aha' moments with the people I have collaborated with, joining two and two together in areas I have gotten stuck, or comparing our answers and working out to extend my own learning.

The consistent use and repetition of the mathematical modelling cycle has allowed me to grow in confidence. Using it within my working out, and now enjoy going back through the questions I have answered and identifying what stage of the cycle I am in.

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Problem Solving v Mathematical Modelling

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Problem Solving v Mathematical Modelling

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The difference between problem-solving and Mathematical Modelling is that Problem Solving is Finding a Solution to a mathematical problem, whereas mathematical modelling using maths to make predictions about the real world

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Mathematical Modelling in Primary School

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Mathematical Modelling in Primary School

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Within primary schools, mathematical modelling is important for students to recognise the multiple different approaches and perspectives, because it allows all the different learners to engage with the tasks. It is also evident that collaboration among the students is very important for the learners, as working together can allow the students to express themselves and develop on each other's ideas. Parish (2023), highlights modelling in mathematics as an educational that encourages learners to explore flexible strategies and real-world connections.

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I need to find out how much toothpaste I need to take to sustain myself for 1 year

1. Research information based on how much toothpaste the average human should use every day.

2. Research information based on how much the average human should be brushing their teeth

3. Create a mathematical model.

1. The average human uses around 0.25 grams. 0.25 grams = approx. 0.3 ml. 210 grams in my tube (the size I would bring) = 246 ml.

2. The average Human should brush their teeth twice a day.

3. Toothpaste Needed (x) = (Grams per Brush) x (Brushes per day) x (days per year)

x = 0.25 x 2 x 365

x = 182.5 g

Since my tube contains 210 grams, one tube of toothpaste should be enough to last me the whole year

applying to a real-world definition. I did not think it would be applicable to use only one tube of toothpaste for the entire year, so I revised my model, changing the grams used to 0.5 instead of 0.25.

Now I am ready to begin my final report

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Benefits:

Encourages problem-solving skills

Promotes critical and creative thinking

Supports Collaboration and Communication

Challenges:

Complex real-world situations

Balancing assumptions with accuracy

Time Consuming

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Throughout this unit, I have learned a lot more than I originally would have thought. I believe that I have not only gained a newfound passion for mathematical modelling, but I have also found new ways to enjoy maths. I have always said that maths is my favourite subject because it's simple and easy to grasp, 1 + 1 will always equal 2, no matter which way you slice it. Mathematical modelling, however, has taught me that math can also not be like that, as you sometimes will have to make assumptions based merely on what the real-life scenario will look like. Whilst I was initially disinterested in this, I have come to appreciate what it has taught me, and have come to understand it much better.