Movies are a primary source of entertainment, but finding specific content can be challenging given the exponentially increasing number of movies produced each year. Recommendation systems are extremely useful for solving this problem. While various approaches exist, Collaborative Filtering (CF) is the most straightforward. CF leverages user input and historical preferences to determine user similarity and suggest movies. Matrix Factorization (MF) is one of the most popular Collaborative Filtering (CF) techniques. It maps users and items into a joint latent space, using a vector of latent features to represent each user or item. However, traditional MF techniques are static, while user cognition and product variety are constantly evolving. As a result, traditional MF approaches struggle to accommodate the dynamic nature of user-item interactions. To address this challenge, we propose a Dynamic Matrix Factorization CF model for movie recommendation systems (DMF-CF) that considers the dynamic changes in user interactions. To validate our approach, we conducted evaluations using the standard MovieLens dataset and compared it to state-of-the-art models. Our preliminary findings highlight the substantial benefits of DMF-CF, which outperforms recent models on the MovieLens-100K and MovieLens-1M datasets in terms of Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) metrics.